Marie-Eliette Dury
email: m-eliette.dury@uca.fr

Bing Xiao
email: bing.xiao@uca.fr

Forecasting the Volatility of the Chinese Gold Market by ARCH Family Models and extension to Stable Models

Keywords: Forecasting, Return, Volatility, Gold Market, ARCH, GARCH, GARCH-M, IGARCH, NGARCH, EGARCH, PARCH, NPARCH, TARCH, Student's t distribution, Symmetric Stable models, H-self-similar processes JEL Classification: C53, C58, G17

Forecasting the Volatility of the Chinese Gold Market by ARCH Family Models and extension to Stable Models

Marie-Eliette Dury, Bing Xiao

Introduction

Gold is a precious metal which forms an integral part of many investment portfolios; it has similar characteristics to money (see [START_REF] Solt | On the efficiency of the markets for gold and silver[END_REF]. [START_REF] Ciner | On the long run relationship between gold and silver: a note[END_REF] indicates that gold plays an important role as a precious metal with portfolio diversification properties: holding gold leads to a more balanced portfolio. Lawrence (2003) finds that gold returns are less correlated with returns on equities and bonds than other assets. Many researchers and professionals believe that gold plays the role of a hedge against inflation. [START_REF] Sjaastad | The price of gold and the exchange rate[END_REF] claim that gold is a refuge value against inflation. Central banks and international financial institutions hold a large proportion of gold for their diversification capacity, and gold is considered as an insurance against market crises. According to [START_REF] Smith | London Gold Prices and Stock Prices in Europe and Japan[END_REF], when the economic environment becomes more uncertain, gold plays a role as a safe haven. A number of authors have reported the fact that gold reflects the value of the US dollar, because a depreciation in the dollar may increase interest in gold, [START_REF] Tully | A power GARCH examination of the gold market[END_REF] report that a lower US dollar makes gold less expensive for other international investors to buy dollar-denominated gold.

The Chinese assets market is one of the emerging assets markets which offer an opportunity for international diversification. Since the 1990s, reforms in regulations as well as in the attitudes of regulators have rendered the stock market more efficient. However, it would seem that in the Chinese assets market, anomalies persist (see [START_REF] Mookerjee | An empirical analysis of the equity markets in China[END_REF][START_REF] Mitchell | Seasonalities in China's Stock Markets: Cultural or Structural? IMF Working Paper[END_REF]. This article studies the volatility of gold prices in China through gold prices at the Shanghai Gold Exchange (SGE). As mentioned in [START_REF] Hoang | Is Gold Good for Portfolio Diversification? A Stochastic Dominance Analysis of the Paris Stock Exchange[END_REF], it is important to use local gold prices when studying the Chinese gold market since it is still forbidden for Chinese investors to trade gold abroad without authorization.

It has become more important for financial institutes to consider the volatility of a financial asset. The movements are usually measured by the volatility and can be seen as the risk of the asset. One of the problems with modelling the volatility is that it is non-stationary: there are periods with low movements and then periods with high movements. The first model that assumed that volatility is not constant is ARCH (autoregressive Conditional Heteroscedasticity Model) by [START_REF] Engle | Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[END_REF] The ARCH model has been transformed and developed into more sophisticated models, such as GARCH, EGARCH, PARCH and TARCH. The questions to ask are: Do the new models capture the volatility better? If one model better captures the volatility, would it lead to a more efficient forecast accuracy? Currently, results of research into the model's performance are conflicting and confusing.

These observations lead the author to determine how well these different models perform in terms of forecasting volatility and will be assessed based on the forecasts they produce. This study focuses on the gold prices at the Shanghai Gold Exchange (SGE); it contributes to the existing finance literature by investigating the Chinese gold market during the recent period.

In addition, this work opens another suitable way to model heavy-tailed data, such as returns.

Heavy-tailed data can be modelled very well by α-Stable distributions because of the high variability of the data.

The structure of this article is as follows. Section 2 provides a brief overview of the existing literature. Data and methodology are described in Section 3 which firstly recalls the different ARCH Family models. Then, construction and properties of Symmetric α-Stable processes are presented; the aim is to show the adequacy of this model in this context. Next, Section 4 displays the results of this study with the numerical comparison between Student and Gaussian distribution. [START_REF] Engle | Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[END_REF] study was the first to distinguish between unconditional and conditional variance. According to the ARCH models, the variance of the current error term is a function of the previous time period's error terms. [START_REF] Bollerslev | Generalized autoregressive conditional heteroscedasticity[END_REF] points out that the ARCH model has a long lag in the conditional variance equation. To avoid problems of negative variance parameter estimates, his solution was to generalize the ARCH model. [START_REF] Nelson | Conditional heteroscedasticity in asset returns: A new approach[END_REF] proposed the EGARCH model to account for the presence of asymmetric effects. [START_REF] Poon | Forecasting volatility in financial markets: A review[END_REF] noted that models that allowed for asymmetric effects are able to provide better forecasts owing to the negative relationship between volatility and shocks.

Literature Review

Most research on volatility modeling has focused on equity markets and foreign exchange markets, but [START_REF] Sadorsky | Modeling and forecasting petroleum futures volatility[END_REF] pointed out that one type of market cannot be generalized across other markets. It seems that stocks with higher kurtosis were better predicted by using the GARCH model and stocks with lower kurtosis were forecasted better by using EGARCH. [START_REF] Ederington | Forecasting volatility[END_REF] showed that the financial market has a longer memory than explained by the GARCH(1,1) model. Awrtani and Corradi (2005) found that the asymmetric models perform better than the GARCH(1,1) model. After comparing the different volatility models, [START_REF] Köksal | A Comparison of Conditional Volatility Estimators for the ISE National 100 Index Returns[END_REF] found that the EGARCH(1,1) performed best. [START_REF] Bracker | Detecting and modeling volatility in the copper futures market[END_REF] studied the volatility of the copper futures market, and concluded that both the GARCH and EGARCH models best fit this market's volatility. [START_REF] Carvalho | A systematic modeling strategy for futures markets volatility[END_REF] found evidence of asymmetric effects when using the EGARCH model.

However, not all the empirical studies agree with these findings. [START_REF] Ramasamy | Predictive Accuracy of GARCH, GJR and EGARCH Models Select Exchange Rates Application[END_REF] found that the GARCH models are better to predict the volatility of exchange rates and the EGARCH model does not improve the quality of the forecasts. [START_REF] Marcucci | Forecasting Stock Market Volatility with Regime-Switching GARCH Models[END_REF] found that the GARCH model performs much better than other models in a long time period, but not in a short time period. Zahangir et al. (2013) investigated the ARCH models for forecasting the volatility of equity returns. Their study showed that based on in-sample statistical performance, both the ARCH and PARCH models are considered the best performing model whereas all models except the GARCH and TARCH models are regarded as the best model for the returns series.

Data and Methodology

The main motive of this paper is to investigate the use of the ARCH family models for forecasting the volatility of the Shanghai Gold Exchange (SGE) by using daily data. GARCH, EGARCH, PARCH, IGARCH, GARCHM and TARCH models are used for this study.

Data

The data used is the returns on the Shanghai Gold Exchange (SGE) returns series (Figure 1).

In order to calculate these returns, we use data on the daily price. Data on prices spans the period from October 30, 2002 to May 6, 2016, a total of 3,278 observations. The total data set is divided into in-sample samples and out-of-sample samples. The requisite data is obtained from the Factset database. The price taken as the daily price is the last trading price of the day.

Figure 1 shows the gold prices at the Shanghai Gold Exchange (SGE) from October 2002 to May 2016, the crash of 2007 is clearly visible as well as the major long-run rise in the index in 2002-2011. The index is non-stationary, since its mean level is not constant and rises over time. The daily return on the index appears to be stationary with a constant mean and variance. The outliers, namely very large or very small returns, imply that the returns are nonnormal with fat tails and the distribution may be asymmetric. A positive skewness of 0.11876799 and negative kurtosis of -1.04121692 are revealed in the gold price summary statistics at the Shanghai Gold Exchange (SGE) (Table A1 in the Appendix). At a confidence interval of 99%, the SGE Index is non-normal, in accordance with Jarque-Bera statistics. Therefore, it is necessary to remodel the gold price series into a return series. Plotting autocorrelation and partial autocorrelation of the SGE index designates the series to be non-stationary (Figures A1 and A2 in the Appendix). Applying the Dickey-Fuller test and the Phillips-Perron test to the series confirms this (Table A2, A3 in the Appendix), and suggests that it cannot be used to model volatility.

Movements of stock indices series are not suitable for study as they are usually non-stationary and it is therefore necessary to remodel the daily price into a return series. The SGE index series is converted into a returns series by using the following equation:

= -1 (1.1)
The logarithm of the gross return is given by:

-15,00%

-10,00%

-5,00%

Specification of the Models used in this study

In order to model the volatility of the returns, we need to determine their mean equation. The return for today will depend on returns in previous periods (autoregressive component) and the surprise terms in previous periods (moving order component). In this empirical study, plotting the autocorrelation and partial autocorrelation of the returns series can help determine the order of the mean equation. Like most financial time series, the returns series exhibits what is referred to as "volatility clustering" (Figures A5 and A6 in the Appendix). In order to model such patterns of behavior, the variance of the error term is allowed to depend on its history. The classic model of such behavior is the ARCH model introduced by [START_REF] Engle | Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[END_REF], which simultaneously models the mean and variance of a series.

ARCH(q) model

Autoregressive conditional heteroscedasticity (ARCH) models are used when the error terms will have a characteristic size or variance. The ARCH models assume the variance of the current error term to be a function of the actual sizes of the previous time period's error terms.

The ARCH model is a non-linear model which does not assume the variance is constant. The basic linear ARCH model may be presented as:

= + . ( 2
)
The error terms are split into a stochastic piece and a time dependent standard deviation:

= (3)
The random variable is a white noise process, the series is the volatility of the time series which changes over time, and (variances of the residual) is modelled by:

= + + ⋯ + " " = + ∑ $ " $% $ (4)
Where > 0 ( $ > 0.

GARCH(p, q) model

The GARCH model is a generalized ARCH model, developed by [START_REF] Bollerslev | Generalized autoregressive conditional heteroscedasticity[END_REF] and [START_REF] Taylor | Modeling financial time series[END_REF] independently. They introduced a moving average term into the ARCH estimation. A fixed lag structure is imposed. The GARCH(p, q) model, where p is the order of the GARCH terms and q is the order of the ARCH terms .

= * + + ⋯ + " " + + + ⋯ + + , , = * + ∑ $ " $% $ + ∑ + $ , $% $ (5)
The form of GARCH(1,1) is given below, the equation ( 5) is the conditional variance equation, is the one period forecast variance based on past information, is determined by , and .

Where the news about volatility from the previous period is , measured as the lag of the squared residual from the equation ( 2), and is used to be considered as the last period's (forecast) variance.

= + + + (6)
Engle and [START_REF] Bollerslev | Generalized autoregressive conditional heteroscedasticity[END_REF] indicated that the coefficient -+ + measures the volatility shock, when -+ + is closed to one, the volatility shocks are persistent, this means that the volatility may take long time to return to a quieter phase.

GARCH-M model

The M in GARCH-M stands for "in the mean". This model is an alternative ARCH model developed by [START_REF] Engle | Modelling the Persistence of Conditional Variance[END_REF]. GARCH-M is used when the expected financial time series return is related to the expected asset risk. The conditional variance is included in the conditional mean equation. The GARCH-M (1,1) is written as:

. = /0 1 2 + 3 + (7)

=

The equation shows that the returns (. has a positive relation to its own volatility. Engle and Bollerslev proposed to introduce the logarithm of conditional variance into the mean equation; the equation ( 7) can be expressed as:

= + 4 log + (8)

IGARCH

Consider the GARCH model in ARMA equation:

= = + ∑ $ $ " $% + ∑ + 7 7 , 7% (9)
Where the parameter α is the ARCH parameter and β is the GARCH parameter, α(L) and β(L) is defined polynomials, and > 0, $ ≥ 0, + $ ≥ 0 ( ∑ $ + + $ < 1

;<= ,," $% .

EGARCH model

The EGARCH model was developed by [START_REF] Nelson | Conditional heteroscedasticity in asset returns: A new approach[END_REF] as a solution to avoid problems with negative variance parameter estimates. If "bad news" has a more pronounced effect on volatility than "good news" of the same magnitude, then a symmetric specification such as ARCH or GARCH is not appropriate since in standard ARCH/GARCH models the conditional variance is unaffected by the sign of the past periods' errors (it depends only on squared errors). The logarithmic function ensures that the conditional variance is positive and, therefore, the parameters can be allowed to take negative values. The form of GARCH(1,1) is given below:

log = * + + log + > ? @A B + C |? | @A B -@ 2 F G H (10)
According to Engle and Ng. (1993), the EGARCH model allows positive return shocks and negative return shocks so that there are different effects on volatility; the coefficient > measures the asymmetry effect. Gokan (2000) indicated that when > = 0, the goods news (positives return shocks) has the same effect on volatility as bad news represents the negative return shocks.

In equation ( 10), positive return shocks, namely good news, has * + > impacts on return volatility while the negative return shocks, bad news, has a * -> impacts. If * and > are positive, the good news will have more effect on return than bad news. According to previous studies in this subject, the coefficient > is often negative; this suggests negative return shocks have more impact on return volatility than good news.

PARCH model

The PARCH model is a GARCH model with an additional term to account for the asymmetries effect. It employs an indicator function as follows (PARCH(1, 1)):

= + + + + > I (11)
The indicator function takes a value of 1 if the error > 0, and 0 otherwise. For the effect of the previous period's bad news to be greater than the effect of good news of the same magnitude, γ should be significant and have a negative sign.

TARCH model

The Threshold GARCH (TARCH) model by Zakoïan (1994) is one on conditional standard deviation instead of conditional variance. The effect of good and bad news is captured separately through the two coefficients, α and γ, respectively. The TARCH model adds a separate variable for negative shocks.

= * + ∑ $ $ " $% + ∑ + 7 7 , 7% + ∑ > J J I J K J% (12)
I J LLLLL equals one if is less than zero and zero if else. The form of TARCH(1,1) is given below:

= * + + + + > I LLLLL (13)
In equation ( 12) and ( 13), good news (positive return shocks) and bad news ( < 0) have different impacts on the conditional variance. Positive return shocks have an --effect on volatility, while bad news has an (-+ >)-effect on the conditional variance (volatility). If > equals zero, the TARCH model becomes a linear GARCH (symmetric) model. If > ≠ 0, then that suggests an asymmetric effect.

NGARCH model

Nonlinear GARCH (NGARCH) is known as nonlinear asymmetric GARCH(1,1).

= + -N + + (14)
, + ≥ 0; > 0

For the return series, parameter φ is positive, it means a leverage effect: negative returns increase future volatility by a larger amount than positive returns of the same magnitude.

Student's t distribution

One of the problems with forecasting volatility is the distribution: there are periods with low movements and periods with high movements. [START_REF] Köksal | A Comparison of Conditional Volatility Estimators for the ISE National 100 Index Returns[END_REF] indicates that the Student's t distribution characterizes better the heavy-tailed returns than the Gaussian distribution. It seems that stocks with higher kurtosis were better predicted by using GARCH with student's distribution and stocks with lower kurtosis were better forecasted by using EGARCH model (see Grek A., 2014).

In the ARCH models, the first part is = with P ~R 0,1 . In the GARCH model with student distribution, the first part is written as part = . with ~S ( and ( is the degrees of freedom.

Extension to Stable Models

The

For 1, . ∈ ℝ V 0 W,X 1; . = |1 -.| X V W -|.| X V W 3 W,X 1; . = Y1Z [1. . -1 |.| X\ V W
for some + > 0. Next we take + =the stability index, or + = - * such that

1 - + 1 - * = 1.
If -= - * = 2, we come back to the Gaussian framework. Then α-stable stochastic processes are defined as the integral, for a random measure^_, of the previous kernels:

1 = `0W,X 1; . ℝ a

^_ (. 15

and

P 1 = `3W,X 1; . ℝ a ^_ (. 16
where process is the Moving Average and process P is the harmonizable representation.

Measures of the Statistical Performance of the Model

After producing the forecasts, they are evaluated by comparing out-of-sample forecasts with historical volatility. To identify the best-performing model in both the in-sample data set and the out-of-sample data set of this study, statistical performance measures are applied.

Measures such as MAE (mean absolute error), MAPE (mean absolute percentage error) and RMSE (root mean squared error) are used. Their definition and way of computation is:

^de = f 1 G g ∑ h i $ -$ h j $% (17) ^d e = 1/ ∑ h i $ -$ / $ h j $% (18) ^le = 1 G @∑ i $ -$ j $% ² (19)
We detail the empirical findings in next Section. Then, from this study, we think that Stable non-Gaussian processes would fit better the heavy-tailed returns of such data than the Gaussian distribution. Actually, consider a non-Gaussian --Stable process n with distribution l _ , +, o , where 0 < -< 2 is the stability index, ≥ 0 is the scale parameter, -1 ≤ + ≤ 1 is the skewness parameter, o ∈ ℝ is the shift parameter.

The case -= 2 can be added, but it comes back to the Gaussian framework as when + = 0 then this Stable distribution corresponds to the Normal law l , 0, o ≔ Ɲ o,2 ).

A symmetric α-stable non-Gaussian process n_n with distribution l _ , 0,0 for -< 2 satisfies an important characteristic property

| | > 1 ~ " _ _ 1 _ when 1 → +∝ (20)
Namely, the tails of the distribution decay like a power function while it is an exponential decay for a Gaussian process. Consequently stable non-Gaussian processes exhibits more variability than Gaussian ones. Thus, the smaller α, the highest is the variability: as described in the books of Taqqu et al., a Stable process is likely to take values far away from the median, which is called the Noah Effect (defined by Mandelbrot for "very severe flood").

This high variability is given by the following property of the order-p moments e | | , = +∝, ∀Z ≥ -. 21

Property (21) will entail in particular an infinite variance. This high variability of Stable distributions is one of the reasons they play an important role in modeling. Stable non-Gaussian processes appear as good candidates to take into account heavy-tailed data.

Empirical Findings (Analysis and Results)

Our aim is to determine how well these different models perform in terms of forecasting volatility. The forecasting approach used is such that the last 100 observations of the sample are used to assess out-of-sample forecasts.

p-values are given in parentheses

There is second-order dependence in the squared residuals of the mean equation and, hence, the presence of conditional heteroscedasticity in the returns (Figures A7 andA8 in the Appendix). Further, the ARCH-Lagrange Multiplier (LM) test confirms the presence of ARCH effects and the need to model this conditional heteroscedasticity using the ARCH family models (Table A3 in the Appendix).

The ARCH and GARCH models are easy to identify and estimate. But if « bad news » has a more pronounced effect on volatility than « good news » of the same magnitude, the symmetric specification such as ARCH or GARCH is not appropriate, because their conditional variance is unaffected by the sign of the past period's errors. It depends only on squared errors. Before applying the asymmetric models, we can test the presence of asymmetric effects. Engle and Ng (1993) propose various tests to detect the asymmetric effects. After the GARCH regression, the squared residual is given by:

= + I + Y‰‰Š‰ (22)
I = 1 where < 0, and 0 otherwise. If the dummy coefficient is significant and positive, this suggests the presence of asymmetric effects. Then we can determine whether the size of the negative shock also affects the impact on conditional variance by equation ( 23).

For the existence of a size effect, the coefficient must be negative and significant.

= + ‹ I + Y‰‰Š‰ (23)

The positive sign bias test determines if the size of a positive shock impacts its conditional variance, the regression is given by equation ( 24). For the size effect to be present, the coefficient of I and I \ must be significant.

= + ‹ I \ + Y‰‰Š‰ (24)
Tables 3 and4 present the results of the models fitted to the data on returns with Gaussian distribution and Student's t distribution. The outputs on returns show that the constant is statistically significant in the mean equation. The ARMA(1,1) term is also statistically significant for all models except the ARCH(1). The variance equation illustrates that all the terms are statistically significant at 1% level of significance which implies that the volatility of risk is influenced by past square residual terms. It can be mentioned that the past volatility of returns is significantly, influencing the current volatility. The EGARCH variance equation also signifies that an asymmetric effect in volatility exists, which means that positive shocks are affecting volatility differently to negative shocks. significantly positive, the coefficient of the ARCH term is positive at 10%, this indicates the positive return shocks will have greater impacts on volatility. TARCH is created to capture the negative movements of the volatility that usually is bigger than the positive movements.

In our case, the coefficient γ is 0.0277673 but significant at 1%.

Table 4 presents the coefficients obtained with student's distribution. The likelihood parameter is greater than regression with Gaussian distribution, but the coefficients of mean equation are not significant. The result of GARCH regression confirms the persistent volatility shocks, α+β equals 0.9801919. The asymmetry parameter of the EGARCH model is 0.1760426 (significant at 1%), this result confirms the asymmetry return shocks. The coefficient γ of TARCH model is significant by negative (-0.1333102 at 1%). This is an unusual outcome; the result is contradictory in relation to our finding by using Gaussian distribution. The negative coefficient means good news has a greater impact than bad news. In a general way, the quality of the student's distribution is not satisfactory, because of poor significant coefficients of the mean equation. According to recent research, the financial return time series with high kurtosis was better predicted by using the student's distribution, we will study the forecasting quality of the GARCH type models in the next section. We test for the presence of asymmetric effects. The sign bias test yields the following results:

= 0.0001273 + 0.000305l + Y‰‰Š‰ p-value (0.000) (0.120) = 0.0001579 -0.000305l \ + Y‰‰Š‰ p-value (0.000) (0.120)

A positive but not significant coefficient indicates the presence of leverage effects, implying the positive and negative shocks may have a different effect on the conditional variance.

Estimating the negative and positive sign bias tests yields the following results:

= 0.0000751 -0.0170669l + Y‰‰Š‰ p-value (0.000) (0.000) = 0.0001372 + 0.0012538l \ + Y‰‰Š‰ p-value (0.000) (0.352)

Significant coefficients on the negative sign bias-test imply that there are sign effects and size effects. Positive and negative shocks do have a different effect on the conditional variance and the negative effect on the variance depends on the size of the shocks.

In-Sample Statistical Performance

The following tables present the comparison of the in-sample statistical performance results of the selected models. For the models with Gaussian distribution, they reveal that the

Out-Sample Statistical Performance

Having estimated the models, our next step is to assess their forecasts. We use the models to make dynamic forecasts of volatility for the next 100 observations. For the

Conclusion

This study has implications for investors who wish to price, hedge and speculate in the Chinese gold market. Gold is an underlying asset in which volatility is an important factor when pricing options. Secondly, the investor may use the Gold futures contracts to hedge their underlying Gold position. Forecasting volatility may be important for investors for adjusting their hedging strategies. In a general way, understanding how information (bad news and good news) impacts on return volatility improves the performance of portfolio management.

For example, this knowledge allows the investors to have a better portfolio selection in asset pricing and allows them a more efficient risk management. In addition, the Chinese gold market offers an opportunity for international diversification.

Our study has attempted to model gold prices at the Shanghai Gold Exchange (SGE) return and assess the forecasting ability of the ARCH family of models. We have used historical volatility for modeling purposes through the ARCH family of models and made dynamic forecasts of future volatility. The analysis covers from October 30, 2002 to December 7, 2015 and from December 8, 2015 to May 6, 2016 as in-sample and out-of-sample sets respectively.

For the Gaussian distribution, the results of the in-sample statistical performance show that the GARCH and EARCH models are selected as the best performing models for the returns.

According to the outcomes of MAE and MAPT, the EGARCH model is better than the GARCH model in explaining the return (modeling the volatility), furthermore, using t-student distribution, the EGARCH model gets the best MAPE estimation of all models. This finding confirms our asymmetric effect analysis. Outcomes of the out-of-sample statistical performance demonstrate that the GARCH is considered to be the best model. Based on Student's t distribution, the GARCH and the ARCHM models are the best models for in and out-of-samples. This result confirms the power of the GARCH model in prediction volatility by using t-student distribution. At the same time, the ARCHM model shows good predicting capacity, in our study, volatility shocks appear persistent for the Gold return series as the sum of the coefficients α and β is close to unity for all estimated models. According to [START_REF] Engle | Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[END_REF]Bollerslev (1986, 1987), including conditional variance in the conditional mean equation is more appropriate for financial time series when the expected return on an asset is related to the expected asset risk. At the same time, the ARCHM model shows good predicting capacity, this result corroborates the finding of Zou, Rose and Pinflod (2007), in which they conclude the EGARCH and ARCHM models outperform all other models in capturing the dynamic return volatility for Australian Three-Year T-Bond futures contracts. Two other facts have caught our attention: firstly, the specification of mean equation by using t-student distribution is not satisfactory; this study demonstrates that it is necessary to improve the quality of the mean equation estimates. Secondly, the quality of PARCH regression is not satisfactory, according to the PARCH model, the power term allows the capture volatility by changing the influence of the extreme value. But, according to new literature review, when the return is non-normally distributed, the use of a power transformation is not appropriate.

We think using stable process distribution would be a solution to this issue, the extension to Stable Models opens up new paths for this research, this approach allows us to represent high

Figure 1 :

 1 Figure 1: Chines gold market prices and returns (Daily, 2002 -2016)

  most famous stochastic model for self-similar phenomena is certainly the Fractional Brownian Motion (fBm) popularized by Benoit Mandelbrot in the 60's. The fractional Brownian motion is the only H-self-similar centered Gaussian process with stationary increments in dimension 1. There exist several generalizations of the fractional Brownian motion, such as the multifractional Brownian motion (mBm) defined independently by Peltier and Lévy-Véhel, and by Benassi et al. Such Gaussian models are well known and applied in different fields. Nevertheless, as soon as the observed phenomenon has large fluctuations or high variability, they are no longer appropriate. Such limitations lead us to propose stable non-Gaussian models as those data present large fluctuations and variability on the collected values.The stable non-gaussian framework is however much more complicated than the Gaussian one. It is richer as there exist at least two distinct models of H-self-similar symmetric α-stable (SαS) family of processes: the so-called Moving Average and the Harmonizable stable process. Actually, they are distinct since they form two disjoint classes of processes, as proved inCambanis et al. and in the reference book of Samorodnitsky and Taqqu. In the Gaussian case where -= 2, the two classes describe in fact the same, since they have the same law, up to a constant. Let us then consider stable non-gaussian stochastic processes; they are defined in the following way:

  FiguresFigure A1: AC of SGE indexFigureA2: PAC of SGE index

Figure

  Figure A7: AC of res. mean equation Figure A8: PAC of res. mean equation

Table 1 : Summary statistics for returns

 1

	15,00%
	10,00%
	5,00%
	0,00%

Figure 2: Leptokurtic distribution of SGE return series

	According to recent research, it seems that returns with higher kurtosis were better predicted
	by using GARCH with student's distribution and returns with lower kurtosis were forecasted
	better by using EGARCH. Skewness is -0.05748, this indicates that return volatiles are

negatively skewed (left skewness). Negative skewness indicates that the upper tail of distribution is thinner than the lower tail. That indicates that in the SGE market, prices fall more often than they rise. The ADF-test, as well as the PP-test, are used to get confirmation regarding whether the return series is stationary or not. The value of the ADF test statistic, -62.283, is less than its test critical value, -3.410, at 5%, level of significance, which implies that the gold price return series is stationary. The findings of the PP test also confirm that the return series is stationary, since the values of the PP test statistic is less than its test critical value. The plotted autocorrelation and partial autocorrelation of squared returns indicate dependence and hence imply a time-varying volatility

(Figures A3 and A4 in the Appendix)

.

Table 2 : Mean equation estimated

 2

		AR(1)	ARMA(1,1)	AR(2)	ARMA(2,2)	AR(3)	ARMA(3,3)	AR(4)	ARMA(4,4)	AR(5)	ARMA(5,5)
	Log likelihood	9873.992	9874.152	9862.642	9862.172	9862.607	9862.825	9862.54	9862.525	9864.74	9864.856
	Cons	0.000427 (0.031)	0.0004271 (0.033)	0.0004272 (0.044)	0.0004272 (0.046)	0.0004271 (0.040)	0.000427 (0.039)	0.0004272 (0.044)	0.0004272 (0.044)	0.0004275 (0.05)	0.000428 (0.055)
	AR	-0.0844319 (0.000)	-0.2212373 (0.070)	0.0152087 (0.178)	0.2311969 (0.758)	-0.0156923 (0.126)	0.2676657 (0.652)	0.0125475 (0.39)	-0.0764161 (0.931)	0.0388731 (0.000)	0.2769624 (0.323)
	MA		0.1380424 (0.260)		-0.2151455 (0.775)		-0.2855026 (0.628)		0.0890251 (0.920)		-0.2387045 (0.404)
		AR(6)	ARMA(6,6)	AR(7)	ARMA(7,7)	AR(8)	ARMA(8,8)	AR(9)	ARMA(9,9)	AR(10)	ARMA(10,10)
	Log likelihood	9862.868	9864.543	9862.59	9862.593	9862.27	9862.791	9863.369	9866.058	9862.366	9862.42
	Cons	0.0004269 (0.037)	0.0004212 (0.016)	0.000427 (0.039)	0.0004269 (0.039)	0.0004267 (0.041)	0.0004272 (0.042)	0.0004275 (0.046)	0.0004274 (0.043)	0.0004274 (0.044)	0.0004272 (0.046)
	AR	-0.0192116 (0.067)	0.9011165 (0.000)	-0.0141387 (0.221)	0.0228311 (0.985)	-0.0020933 (0.854)	-0.7500928 (0.043)	0.0259658 (0.089)	-0.8711368 (0.000)	0.0079391 (0.494)	-0.3105028 (0.812)
	MA		-0.917304 (0.000)		-0.0370078 (0.975)		0.761945 (0.037)		0.8948036 (0.000)		0.3198109 (0.806)

Table 3

 3 presents linear and non-linear GARCH parameter estimations for Chinese gold market returns with Gaussian distribution. The coefficients of ARCH and GARCH models are statistically significant, and GARCH (1,1) presents better likelihood at 10324. For the GARCH model, the coefficient α+β =0.9762251 (0.1211033+0.8551218), indicates the volatility shocks of SGE returns are persistent. The coefficients of IGARCH's mean equation are not significant. For the EGARCH model, the asymmetry parameter equals 0.2571219, it is

Table 3 : Estimated coefficients for the ARCH models

 3

		ARCH(1)	GARCH(1,1)	IGARCH(1,1)	EARCH(1,1)	PARCH(1,1)	TARCH(1,1)	ARCHM(1)	NARCH(1)
	Cons_	0.0004326	0.0003881	0.0003732	0.0004771	0.0003918	0.0004503	0.0022644	0.0003865
		(0.019)	(0.011)	(0.016)	(0.007)	(0.013)	(0.010)	(0.000)	(0.047)
	AR(L1)	-0.5587494	-0.7068501	0.7353978	-0.9887848	-0.7230892	-0.7066202	-0.6623146	-0.5795511
		(0.000)	(0.005)	(0.284)	(0.000)	(0.002)	(0.002)	(0.000)	(0.000)
	MA(1)	0.4949706	0.6787811	-0.7264394	0.9958122	0.6942069	0.6761211	0.5985465	0.5111406
		(0.000)	(0.009)	(0.297)	(0.000)	(0.004)	(0.005)	(0.000)	(0.000)
					Variance equation
	Cons_	0.0001086	4.26 e -06	3.04 e -06	-0.334647	8.12 e -07	3.98 e -06	0.0001015	0.000108
		(0.000)	(0.000)	(0.000)	(0.000)	(0.056)	(0.000)	(0.000)	(0.000)
	ARCH(L1)	0.2366763	0.1211033	0.1420618	0.0112612	0.113781	0.107985	0.3098583	0.2381519
		(0.000)	(0.000)	(0.000)	(0.087)	(0.000)	(0.000)	(0.000)	(0.000)
	GARCH(L1)		0.8551218	0.8579351	0.9610151	0.8464523	0.8576062
			(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	Alpha				0.2571219
					(0.000)
	Power					2.359485
						(0.000)
	TARCH(L1)						0.0277673
							(0.001)
	ARCHM(σ²)							-14.72094
								(0.000)
	NARCH (k)								0.0015396
									(0.000)
	likelihood	10011.67	10324.82	10317.69	10305.09	10326.75	10326.24	10026.58	10013.13
	p-values are given in parentheses.

Table 4 : Estimated coefficients for the ARCH models (Student distribution)

 4

		ARCH(1)	GARCH(1,1)	IGARCH(1,1)	EGARCH(1,1)	PARCH(1,1)	TARCH(1,1)	ARCHM(1)	NARCH(1,1)
	Cons_	0.000677	0.0006195	0.0006202	0.0006417	0.0006812	0.0006775	0.0006564	0.0006234
		(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.004)	(0.000)
	AR(L1)	-0.240092	-0.2711803	-0.2691433	-0.2181451	-0.2378837	-0.1672472	-0.2691172	-0.2240068
		(0.281)	(0.343)	(0.349)	(0.404)	(0.284)	(0.487)	(0.348)	(0.335)
	MA(1)	0.1850198	0.2158731	0.2131997	0.1571124	0.1824761	0.1151906	0.2138958	0.1712863
		(0.417)	(0.457)	(0.464)	(0.552)	(0.421)	(0.637)	(0.462)	(0.470)
					Variance equation
	Cons_	0.0001107	3.25 e -06	2.54 e -06	-0.1617319	0.0002089	0.0098154	3.24 e -06	0.0001083
		(0.000)	(0.000)	(0.000)	(0.000)	(0.622)	(0.000)	(0.000)	(0.000)
	ARCH(L1)	0.275836	0.0957356	0.1114599	0.0205378	0.2775119	0.3175995	0.0955799	0.274595
		(0.000)	(0.000)	(0.000)	(0.065)	(0.000)	(0.000)	(0.000)	(0.000)
	GARCH(L1)		0.8844563	0.8885376	0.9806184			0.8846665
			(0.000)	(0.000)	(0.000)			(0.000)
	Alpha				0.1760426
					(0.000)
	Power					1.858312
						(0.000)
	TARCH(L1)						-0.1333102
							(0.004)
	ARCHM(σ²)							-0.3989969
								(0.004)
	NARCH (k)								0.002783
									(0.015)
	likelihood	10410.54	10543.41	10540.86	10550.85	10410.58	10411.7	10543.43	10413.6
	df.	3.332802	4.416499	3.997225	4.271666	3.331899	3.328959	4.416377	3.34935
	p-values are given in parentheses.

  EGARCH has the lowest MAE and the lowest MAPE, the GARCH model and the IGARCH model have the lowest RMSE at 3.53e-07. Based on the Student's t distribution, the GARCH and ARCHM model have the lowest MAE and the lowest MAPE. The IGARH model has the

	lowest RMSE.
	So, it can be said that, based on the outputs of in-sample statistical performance the GARCH
	and EGARCH models are the best models for Gaussian distribution and the ARCHM model
	is the best model for Student distribution. The ARCH, PARCH and NARCH models have the
	worst MAE, MAPE and RMSE.

Table 5 : In-sample statistical performance results (Gaussian distribution)

 5

	Model	MAE	MAPE	RMSE
	ARCH(1)	0.000193	8173.961	3.60 e -07
	GARCH(1,1)	0.0001914	5421.735	3.53 e -07
	EGARCH(1,1)	0.0001905	5156.383	3.55 e -07
	PARCH(1,1)	0.0001964	5437.983	3.55 e -07
	TARCH(1,1)	0.0001944	5345.467	3.55 e -07
	ARCHM(1)	0.0001925	8077.519	3.64 e -07
	IGARCH(1,1)	0.0002	5589.213	3.53 e -07
	NARCH(1)	0.0001932	8195.746	3.61 e -07

p-values are given in parentheses.

Table 6 : In-sample statistical performance results (Student distribution)

 6

	Model	MAE	MAPE	RMSE
	ARCH(1)	0.0001945	8490.761	3.56 e -07
	GARCH(1,1)	0.0001944	5385.746	3.57 e -07
	EGARCH(1,1)	0.0001917	5197.358	3.57 e -07
	PARCH(1,1)	0.0001945	8486.639	3.57 e -07
	TARCH(1,1)	0.0001981	8691.579	3.74 e -07
	ARCHM(1)	0.0001944	5383.354	3.57 e -07
	IGARCH(1,1)	0.000201	5798.238	3.55 e -07
	NARCH(1)	0.0001972	8520.639	3.57 e -07

Table 7 : Out of sample statistical performance results (Gaussian distribution)

 7

	Model	MAE	MAPE	RMSE
	ARCH(1)	0.0001322	154.084	6.34 e -08
	GARCH(1,1)	0.000126	129.4682	6.69 e -08
	EGARCH(1,1)	0.0001314	142.6208	6.68 e -08
	PARCH(1,1)	0.0001266	131.3939	6.76 e -08
	TARCH(1,1)	0.0001276	133.4691	6.72 e -08
	ARCHM(1)	0.0001323	145.0933	6.37 e -08
	IGARCH(1,1)	0.0001279	137.4174	6.77 e -08
	NARCH(1)	0.0001329	153.1993	6.36 e -08
	p-values are given in parentheses.

Table 8 : Out of sample statistical performance results (Student distribution)

 8

	Model	MAE	MAPE	RMSE
	ARCH(1)	0.0001359	158.3068	6.37 e -08
	GARCH(1,1)	0.0001254	127.5605	6.67 e -08
	EGARCH(1,1)	0.0001284	133.2779	6.59 e -08
	PARCH(1,1)	0.0001358	157.9436	6.35 e -08
	TARCH(1,1)	0.0001345	154.4988	6.32 e -08
	ARCHM(1)	0.0001254	127.5211	6.07 e -08
	IGARCH(1,1)	0.0001348	135.4212	7.03 e -08
	NARCH(1)	0.0001351	156.5947	6.41 e -08

Zahangir Alam, Noman Siddikee and Masukujjaman, Forecasting Volatility of Stock Indices with ARCH Model, International Journal of Financial Research, (2013) Vol. 4, No. 2 Zakoïan J.-M., Threshold heteroscedastic models. Journal of Economic Dynamics and Control, (1994), 18, 931-955. Zou L., Rose L., Pinfold J., Asymmetric Information impacts: Evidence from the Australian Treasury-Bond Futures Markets, Pacific Economic Review, (2007) 12:5 Appendix: Tables Table A1:


Irina Nesterenko
email: irina_nesterenko@yahoo.com

Stephane Rauzy
email: stephane.rauzy@lpl-aix.fr

Roxane Bertrand
email: roxane.bertrand@lpl-aix.fr

Prosody in a corpus of French spontaneous speech: perception, annotation and prosody ~ syntax interaction

Keywords: prosody ~ syntax interface, prosodic phrasing, conversational speech, corpus annotation

Our study focuses on the issue of prosodic annotation and of the prosody ~ syntax interface in conversation and is based on a large corpus of conversational speech in French. The results of inter-transcriber agreement tests show that two expert transcribers are consistent in their labeling of prosodic phrasing and the consistency is well above the chance. A qualitative analysis reveals transcribers' individual strategies, namely in reference to Intermediate Phrases sometimes found for French in specific intonation patterns. The syntactic division of the corpus both in terms of syntactic chunks and in terms of pseudo-phrases is further analyzed in its interaction with the distribution of major prosodic breaks. In more than 60% of cases the boundaries of the pseudo-phrases co-occurs with the boundaries of major prosodic units (Intonational Phrases, IPs). At the same time, 50% of IP boundaries are aligned with smaller syntactic constituents. On the other hand, in our study beginnings of intonational phrases are more often misalign with syntactic constituent boundaries than their ends. We discuss as well the issue of conversational corpus annotation in terms of prosodic units, given specific constraints on planning and execution in spontaneous speech.

Introduction

Our study focuses on the issue of prosodic phrasing in conversational speech and of the relationship between prosody and syntax. Prosodic phrasing refers to the structuring of speech material in terms of boundaries and groupings. These boundaries vary as to their relative strength thus defining a number of levels in prosodic constituency. A body of psycholinguistic research has shown that this information is of importance for effective speech processing [START_REF] Clifton | Informative prosodic boundaries[END_REF] and ambiguity resolution [START_REF] Price | The use of prosody in syntactic disambiguation[END_REF][START_REF] Pynte | Prosodic breaks and attachment decisions in sentence parsing[END_REF]. In addition, to implement a reliable algorithm for prosodic boundary placement is important for speech technologies, both in speech synthesis and in speech recognition.

Prosodic phonology [START_REF] Nespor | Prosodic Phonology[END_REF] has proposed a universal hierarchy of prosodic constituents. Two approaches to prosodic phrasing may be distinguished: an edge alignment approach [START_REF] Selkirk | The prosodic structure of function words[END_REF] and an intonation-based approach [START_REF] Beckman | Intonational structure in Japanese and English[END_REF]. If the latter largely relies on the structure of melodic contour, the former approach acknowledges the sensitivity of prosodic structure to syntactic constituency; at the same time, it states that prosodic structure is not isomorphous to syntactic structure and cannot be predicted from syntactic information alone [START_REF] Gee | Performance structures: A psycholinguistic and linguistic appraisal[END_REF][START_REF] Bachenko | A computational grammar of discourse-neutral prosodic phrasing in English[END_REF].

In the models of prosodic phrasing proposed for different languages it is common to distinguish two levels of phrasing above the word: the level of phonological phrases1 (PhP) (to use the terminology of Selkirk [START_REF] Selkirk | Phonology and Syntax: The Relation Between Sound and Structure[END_REF]) and the higher level of intonational phrases (IPs). Our study deals with the larger prosodic units alone. Intonational phrases are primarily defined in terms of domains of distinctive pitch contours, though semantic-pragmatic information is also taken into account. At the same time, it is considered that several syntactic constructions form IPs of their own. This is the case for root clauses, vocatives and parentheticals; certain leftperipheral constituents (sentential adverbs) and certain rightperipheral elements are also separated by an obligatory IP boundary.

Though there seems to be a large body of research on the syntax ~ prosody interface, very few studies deal with the issue in connection to spontaneous speech. Our study aims to fill in this gap and provide evidence relating to the syntax ~ prosody interface in conversation. It should be noted that conversational speech is subject to specific constraints on planning and execution: interruption of speech flow, restarts, hesitations and pausing, for example, are typical for conversational speech and reflect planning and lexical search processes. Another characteristic property of conversational speech resides in the role of context and non-verbal information, which influence the syntactic and prosodic structure of utterances.

In the present study, we undertake the division of speech into pseudo-phrases (analogues of phrases in the written text) and further focus our attention on the relationship between predicted punctuation marks and perceived prosodic boundaries. In punctuation, we distinguish between strong punctuation marks, which separate sentences, and weak punctuation marks, which separate clauses, sentential adverbs and parentheticals. From the discussion above, it follows that both strong and weak punctuation marks are quite likely to coincide with IP boundaries. The rest of the paper is organised as follows: first, in section 2 we present the corpus our study is based on and we detail the undertaken prosodic and syntactic annotations. Section 3 presents the results of inter-transcribers agreement tests and the results of our analyses concerning the co-occurrence of prosodic and pseudoorthographic boundaries, the prosody ~ syntax interface and the influence of planning and execution constraints in conversation. Finally, we discuss the impact of the adopted approach as well as future work that remains.

Corpus and methodology

Our study is based on an excerpt from the Corpus of Interactional Data [START_REF] Bertrand | Le CID -Corpus of Interactional Data -Annotation et Exploitation Multimodale de Parole Conversationnelle[END_REF] (http://crdo.up.univaix.fr/corpus.php?langue=fr). We focused on one dialogue between two familiar female speakers who conversed on humorous situations in which they may have found themselves involved. The total size of the corpus was 12681 words.

The corpus was manually transcribed using an enriched orthography: in order to facilitate further processing of the corpus, our transcription conventions include special notations to signal a number of reduction phenomena (i.e. elisions, word truncations). Next, this transcription was automatically converted to a phonemic transcription of speech material and then automatically aligned to the speech signal. Subsequently, the corpus was enriched with various linguistic annotations (manual or (semi-)automatic) as a means to study interfaces between phonetics, phonology, prosody, morphology, syntax, pragmatics, discourse and gesture as they operate in conversational speech. In the following paragraphs we detail the syntactic and prosodic annotation underlying our study.

Prosodic annotation

The general prosodic annotation scheme for the corpus includes

• metrical structure in terms of perceived prominences;

• tonal structure: we distinguish the level of underlying tones and the level of surface tones (INTSINT); • prosodic constituency.

The corpus was manually annotated in terms of Intonational phrase boundaries by two of the authors. This annotation was guided by perception, based on a distinction between strong and weak prosodic breaks. Other acoustic and perceptual cues to an IP boundary are: i) an intonation unit is associated with a specific melodic contour; ii) there is a high (H) or a low (L) boundary; iii) there is pitch reset; and iv) there is pre-boundary lengthening.

As this work deals with spontaneous speech, we introduced one more category at the level of IPs: an uncompleted IP (ipa) corresponding to a stretch of speech larger than AP which wasn't completed due, among others to planning constraints. In reference to the typology of acoustic/phonological cues to IP boundaries, these units were not full IPs as there was no distinctive pitch contour associated with them; at the same time, there was a perceived pitch reset at the beginning of the following IP. Note that this category was introduced to satisfy the Exhaustivity constraint on prosodic phrasing as formulated in [START_REF] Selkirk | The prosodic structure of function words[END_REF]. Note that prosodic structuring of speech flow in conversation could by masked by performance phenomena: we sought not to melt in one category of major prosodic units both structural units (IPs) and performance units (marked by speech flow interruption or a filled pause).

Syntactic annotation

On the basis of enriched orthographic transcription and phonetic transcription larger units such as words were recovered and automatically aligned with speech signal; they form the basic input to the syntactic analyser. Non-syntactic objects such as laughter, and dysfluencies were removed from the input. After the first filtering stage, a modified version of the syntactic parser StP1 was applied on the data.

The syntactic parser StP1 [START_REF] Blache | Influence de la qualité de l'étiquetage sur le chunking : une corrélation dépendant de la taille des chunks[END_REF] is a stochastic parser for written French text developed at the Laboratoire Parole et Langage. In the first step, for each word token it provides an automatic annotation of its morphosyntactic category. In the second step, the tokens are grouped in larger units (chunks) following the EASY flat grammar [START_REF] Paroubek | Data Annotations and Measures in EASY, the Evaluation Campaign for Parsers in French[END_REF] described in the PEAS guidelines [START_REF] Gendner | PEAS, the first instantiation of a comparative framework for evaluating parsers of Frenc[END_REF]: in such an approach, chunks represent minimal syntactic phrases of the tree structure. The EASY grammar comprises six constituents: GN (Noun Phrase), GP (Prepositional Phrase), GR (Adverbial Phrase), GA (Adjective Phrase), NV (Verbal Nucleus), PV (Verbal group introduced by a preposition), organized in a sentence with a flat structure.

The StP1 chunker obtains relatively good results on written texts (see [START_REF] Blache | Influence de la qualité de l'étiquetage sur le chunking : une corrélation dépendant de la taille des chunks[END_REF] for more details), an F-measure score being of 0.94 for the tagging stage and of 0.92 for the chunking stage. These performances are reduced for conversation speech corpora, an Fmeasure score being of 0.79 for chunks formation, but still remain interesting for providing us with an automatic annotation of the syntactic information.

The StP1 chunker has been modified in order to account for the specificities of conversational speech. Two levels of hierarchy were introduced in the syntactic treatment, corresponding to the strong punctuation marks (final point, exclamation mark) and weak or soft punctuation marks (comma) that can be found in written text. The modified stochastic parser automatically inserts these two kinds of frontiers on the basis of the syntactic context.

This symbolic annotation underlines probabilistic modelling of speech division into phrase-like units (4 levels) undertaken in our study. We would like to emphasize that all syntactic analyses in this study are automatic and there was no manual correction applied.

Results

We present first the results on the distribution of IP boundaries and we evaluate the reliability of prosodic annotation. The data on the most probable division of our corpus in terms of pseudo-phrases are then analysed in their interaction with the distribution of perceived IP boundaries. Finally, we analyse the distribution of ipa boundaries in relation to syntactic structure.

Distribution of prosodic boundaries

In Table 1 we present the data on the distribution of prosodic boundaries independently for each annotator and each speaker. It follows that 24-30% of word boundaries in the corpus were annotated as boundaries of higher constituents in prosodic hierarchy: there was a prosodic boundary perceived every 3-4 words.

Another finding deals with the use of ipa labels: it was used in 8-13% of cases (mean 10,9%), the differences between transcribers being non-significant (for AB: χ² = 3.7877, df = 1, pvalue = 0.052; for CM χ² = 2.1008, df = 1, p-value = 0.15). At the same time, RB used significantly more ipa labels for CM compared to AB (8% versus 11,3%; χ² = 10.2708, df = 1, p-value = 0.001). A qualitative analysis reveals that many of disagreements between transcribers could be imputed to the existence of a third level of phrasing in French, namely the level of intermediate phrases: several authors provide evidence for the existence of Intermediate phrase units in French [START_REF] Jun | Realizations of accentual phrase in French intonation[END_REF][START_REF] Di Cristo | Vers une typologie des unités intonatives du français[END_REF], which occur in a restricted set of marked constructions. In our annotation study, transcribers use different strategies when there seems to be an Intermediate phrase boundary: while one of the annotators signalled the presence of an IP boundary (adding a special note for the unit to be an intermediate phrase, ip), the other transcriber restricted the use of IP labels for the full IPs, cf.

Bon je vois qu'tu es tellement à court d'idées (Well I see you really lack the ideas) 1 st transcriber [[ ] IP (=ip)

] IP 2 nd transcriber [ ] IP Note that relative clauses and sententional adverbs represented the most frequent disagreement contexts.

Inter-Transcribers' reliability test

Traditionally, one resorts to Cohen's kappa statistics when the question of measuring inter-annotator agreement arises. Both pairwise agreement and kappa coefficients allow accessing the consistency in annotators' performance, though only the latter proceeds by comparison of the observed agreement with the probability of the two transcribers agreeing by chance.

The data on inter-transcribers agreement and kappa statistics are presented in Table 2. The kappa values in Table 2 show that there is a good agreement between the annotators well above chance. At the same time, there is a significant difference in the % of inter-transcriber agreement between speakers (χ² = 33.1609, df = 1, p-value < 0.001): further acoustic, phonetic and phonological analyses will show whether there is a difference in salience of acoustic cues used by each of the speakers to signal prosodic structure as well as in the frequency of use of different boundary cues (melodic contour, pitch resetting, presence of high or low boundary tone, pre-boundary lengthening etc.)

The Prosody ~ Syntax interface

In this section we present the results on the relationship between prosodic annotation and syntactic structure. Left and right boundaries of IP were dealt with separately. Figure 1 plots the mean number of IP boundaries, which cooccur with strong and weak punctuation marks and with syntactic constituents. In table 3 we present evaluation statistics of the algorithm for pseudo-phrases only. It appears that left IP boundaries co-occur with a punctuation mark in 46% and right boundaries in 48% of cases. At the same time, if there is a punctuation mark inserted by the algorithm, there are around 65 % of chances that there would be a prosodic boundary aligned with it. F-measure statistics are 0.54 and 0.55 respectively. Note though that the underlying grammar was built from the corpus of written texts; consequently, we could expect better performance if the model is trained on an annotated corpus of spontaneous speech.

At the same time the data on the distribution of prosodic boundaries with respect to syntactic constituency show a significant asymmetry between the left and the right IP boundaries for both speakers (χ² = 37.7547, df = 3, p-value <<0.001 for AB; χ² = 22.5927, df = 3, p-value << 0.001 for CM).

Another important result is the proportion of IP boundaries which are located within syntactic chunks (24% of left IP boundaries and 17% of right IP boundaries; χ² = 24.1606, df = 1, p-value << 0.001). This means that beginnings of intonational phrases are more often misalign with syntactic constituent boundaries than their ends. At the same time, this result quantifies the non-isomorphism between prosodic and syntactic structure: for while most theories assume that prosodic phrase breaks do not always coincide with syntactic phrase boundaries, the magnitude of the effect was not evaluated.

Uncompleted IPs

Uncompleted IP (ipa) account for suspensions in speech delivery. They correspond to approximately 11 % of all annotated units: note though that this annotation doesn't take into account all the perceived dysfluencies and interruptions within intonational phrases. Our further analyses will reveal whether or not the boundaries of ipa coincide with AP boundaries.

The data on the co-occurrence of punctuation marks and syntactic constituents and ipa prosodic boundaries are presented on Figure 2. These data show that in 52 % of cases for the speaker AB and in 46% of cases for the speaker CM the inserted punctuation marks are aligned with left boundaries of uncompleted IPs (ipa), though this is the case for only for 25% and 27 % of right boundaries respectively. On the other hand, 50 % and 36 % of right ipa boundaries occur within syntactic constituents; for the left ipa boundaries we observed such a pattern in only 23% and 28 % of cases. In this respect the ipa units differ from full IPs, though their special status should be further investigated. We have mentioned previously that the main criterion used for annotating an uncompleted IP was a perceived pitch reset: we plan to address the issue of pitch reset across boundaries in our future work. At the same time, melodic contours associated with the ipa units need also to be investigated first, with the reference to the typology of distinctive pitch contours for French and secondly, in their interaction with discourse structure. A preliminary analysis of the morphosyntactic category of words occurring at ipa boundaries indicates that uncompleted prosodic units tend to end in syntactically unmotivated positions. At the same time, these interruptions tend to occur rather at the beginning of a syntactic constituent (after initial function words, such as determiner, preposition, auxiliary verb or conjunction, 49.62% of cases). This result suggests that speakers start their utterances before planning it completed. Alternatively, in an interactive setting, it may reflect a strategy whereby the speaker seeks to keep his turn in conversation and non to be interrupted.

Discussion and Conclusions

In this study we investigated the dependency relationships between syntactic and prosodic organisation in a large annotated corpus of French conversational speech. The results of intertranscriber agreement test show that two annotators are consistent in their labelling of prosodic phrasing at the level well above the chance. At the same time, a qualitative analysis reveals annotators' individual strategies, namely in respect with potential Intermediate Phrases in French: the issue of phonetics and phonology of Intermediate phrase boundaries needs thus further research based both on attested corpora and on specially designed stimuli. One of the central syntactic units in our study was the pseudophrase, as defined by strong and soft punctuation marks. In more than 60% of cases the boundaries of these pseudo-phrases are the boundaries of IPs. At the same time, 50% of IP boundaries are aligned with smaller syntactic constituents or fall within these constituents. It should be taken into account that statistical models underlying syntactic parsing were first developed for the analysis of written texts. On this basis we expect that syntactic parsers specially designed for and trained on conversational speech corpora would perform better.

We also found that 24% of left IP boundaries and 17% of right IP boundaries occur within syntactic constituents. These data provide a quantitative of the non-isomorphism between syntactic and prosodic structure. In future studies we plan to compare the misalignment effect in spontaneous and read speech as well as to investigate the impact of eurhythmic constraints in their interaction with syntactic structure in conversation.

In this study we have introduced a new unit, the uncompleted Intonational phrase (ipa). This unit appears to account for cases where a continuous delivery of speech is interrupted. We assume that such interruptions could not be treated as major prosodic breaks, or IP boundaries, since they do not serve any structural function in speech. They do however intervene in turn-taking organisation in conversation. In fact, ipa boundaries, more often than structural IP boundaries, are found within syntactic constituents. Specifically, right ipa boundaries are internal to syntactic constituents in 43% of cases, though this is the case for only 17% of full IP boundaries. We observed that the ipa units were associated with at least 3 different conversational events: word search, turn holding or turn yielding. We assume (and our preliminary informal observations seem to confirm it) that ipa units differ in their prosodic properties according to the category of conversational event.

Overall, our results provide a better understanding of the syntax ~ prosody interface as it is realised in conversational speech. It thereby provides an insight into the factors governing the structuring of speech. Our future work aims at developing acoustic and linguistic models of prosodic phrasing in conversation. Our present and future results are expected to be useful both for text-to-speech synthesis, for speech recognition applications and for the development of tools for corpus annotation.

Figure 1 .

 1 Figure 1. Mean percentage of co-occurrence of IP boundaries with punctuation mark or syntactic constituent

Figure 2 :

 2 Figure 2 : Co-occurrence of ipa boundaries and syntactic constituent boundaries

Table 1 :

 1 Distribution of perceived prosodic boundaries

	Transcriber	Speake	ipa	IP	# of	Mean
		r			words	interval
	IN	AB	162	1309	6162	4,19
	IN	CM	230	1546	6519	3,67
	RB	AB	132	1438	6162	3,92
	RB	CM	225	1757	6519	3,29

Table 2 .

 2 Inter-transcriber agreement and Cohen's

		Kappa scores
	Speaker	AB	CM
	% of agreement	92.84	89.95
	Cohen's kappa	0.81	0.76

Table 3 .

 3 Evaluation statistics.

		Left	Right
		boundary	Boundary
	Recall	0.46	0.48
	Precision	0.65	0.66
	F-measure	0.54	0.55

Related units are Intermediate phrases of[START_REF] Pierrehumbert | Japanese Tone Structure[END_REF] and for French -Accentual phrases described in[START_REF] Jun | Realizations of accentual phrase in French intonation[END_REF]

Acknowledgement

This research was supported by the ANR French agency under grant no ANR BLAN08-2_349062 (Tools for Multimodal Annotation / Outils de traitement de l'information multimodale project).


Jérôme Hugues

Jean-Marie Gauthier

Raphaël Faudou

Integrating AADL and FMI to Extend Virtual Integration Capability

Keywords: FMI, AADL, Cyber-Physical Systems, Co-Simulation, Virtual components

Virtual Integration Capability is paramount to perform early validation of Cyber Physical Systems. The objective is to guide the systems engineer so as to ensure that the system under design meets multiple criteria through high-fidelity simulation. In this paper, we present an integration scheme that leverages the FMI (Functional Mock-Up interface) standard and the AADL architecture description language. Their combination allows for validation of systems combining embedded platform captured by the AADL, and FMI components that represent physical elements, either mechanical parts, or the environment. We present one approach, and demonstrator case studies.

Introduction

Virtual integration capability is paramount to perform early validation of Cyber Physical Systems. The objective is to guide the systems engineer so as to ensure that the system under design meets multiple criteria through high-fidelity simulation. The general approach is to leverage models as primary artefacts to capture all facets of a system, and tool supports to analyze and simulate the system.

Early study [START_REF] Feiler | System Architecture Virtual Integration: An Industrial Case Study[END_REF] demonstrated the importance of Architecture Description Language to capture many facets of a system, for the embedded perspective, supporting multiple kind of analysis such as timing performance, or safety analysis. Other standards like FMI [START_REF]MODELISAR Consortium and Modelica Association Project "FMI" -Functional Mock-up Interface for Model-Exchange and Co-Simulation[END_REF] did the same for the mechanical and control sphere, supporting co-simulation of high-level mechanical models (e.g. built on Modelica) or control command models built around Simulink or SCADE. FMI has been defined with primary objective to support system-level simulations, with a strong emphasis on early validation of systems made of separated models.

A remaining challenge is to combine both spheres. As a matter of fact, architecture description languages capture the organizational structure of the system to be designed, and the exchange of information. The physics is abstracted through devices (sensors and captors) that interact with the environment and mechanical parts. These models capture their behavior as a set of model elements that ultimately lead to equations. FMI allows one to build reusable components from these models, but does not address the construction of simulation itself. This rupture in abstraction makes it difficult to build integrated simulation, and motivates our contribution.

Considering an architectural description model of an embedded system as a primary artifact, we want to streamline the construction of a virtual integration test bench that would integrate external models as environment stimulus, hence allowing through tests of the embedded (or cyber) part. Our contribution builds on the AADL [START_REF] Feiler | Model-Based Engineering with AADL: An Introduction to the SAE Architecture Analysis & Design Language[END_REF] architecture description language, and the FMI standard. Our main contribution in this paper concerns a model-based approach to integrate FMI blocks and AADL so as to leverage existing code generation strategy and build either model-in-the-loop or hardware-in-the-loop simulations.

The paper is organized as follows: in section 2, we review the main technological elements used: AADL and FMI. In section 3, we report on existing FMI-based integration workflows. In section 4 we propose an AADL-based workflow that leads to the generation of simulations. Section 5 is a case study that illustrates the approach. Section 6 proposes future work directions.

Standards in use a. AADL, Architecture Analysis and Design Language

The "Architecture Analysis and Design Language" (AADL) [START_REF] Feiler | Model-Based Engineering with AADL: An Introduction to the SAE Architecture Analysis & Design Language[END_REF] is both a textual and graphical language for model-based engineering of embedded real-time systems. AADL is used to design and analyze software and hardware architectures of embedded real-time systems.

The AADL purpose is to model hardware components (memory, bus, processor, device, virtual processor, virtual bus) and their associated embedded software (data, thread, thread group, subprogram, process). It focuses on the definition of clear block interfaces, and separates the implementations from these interfaces. From the separate description of these blocks, one can build an assembly of blocks that represent the full system. The AADL defines the notion of properties. They model non-functional properties that can be attached to model elements (components, connections, features, instances, etc.). Properties are typed attributes that specify constraints or characteristics that apply to the elements of the architecture such as clock frequency of a processor, execution time of a thread, bandwidth of a bus. As defined, AADL is an Architecture Description Language. Without loss of generality, similar notation such as EAST-ADL or UML/MARTE would provide the same power of expression.

AADL has a rich ecosystem to model, analyze and generate code from models, such as Ocarina [START_REF] Hugues | From the prototype to the final embedded system using the Ocarina AADL tool suite[END_REF]. The later aspect is interesting to ease the transition of AADL models' tasks, and communication semantics to an implementation on top of a regular Real-Time Operating Systems. We detail this part in the next section.

Let us note that in such models, the time interval is given by the CPU clock rate (or simulated by a scheduler): AADL models are discrete by nature and fit in the cyber part of cyber-physical systems.

b. FMI, the Functional Mock-Up Interface

FMI, the Functional Mock-Up Interface, is a standard for the simulation of systems, combining heterogeneous models. The initial revision of FMI mostly focused on models relevant for multi-physical aspects of automotive systems. Since then, it has been widely adopted in several settings, especially for the modelling and simulation of Cyber-Physical Systems, e.g. as part of the Ptolemy project at UC Berkeley [START_REF] Cremona | FIDE: An FMI Integrated Development Environment[END_REF]. FMI is already supported by an increasing number of tools used in several domains, e.g. Modelica1 tools, Simulink2 or SCADE Suite 3 . Through this standard, system designers may mix and co-simulate heterogeneous models built by experts to better understand how a system may be integrated. FMI, defines an interface to be implemented as a component called FMU (Functional Mock-up Unit). The FMI functions are used (called) by a simulation environment to create one or more instances of the FMU and to simulate them, typically together with other models. An FMU may either embeds its own solver (FMI for Co-Simulation) or requires the simulation environment to perform numerical integration (FMI for Model Exchange). For both approaches, each model is exported in a zip file, called FMU, which contains a binary file of the model and an XML file (named modeldescription.xml) which describes the model contents, properties, and interfaces (its associated model variables).

In this paper, we only focus on FMI 2.0 for Co-Simulation, as we are interested in combining self-contained executable blocks and their integration in a system level simulation.

c. FMI for Co-Simulation

The FMI Standard for Co-simulation is intended to provide an interface standard for coupling two or more simulation tools in a co-simulation environment. Co-simulation is a technique used for the simulation of coupled models.

A coupled model, is a model that describes a system as a network of (logically or physically) coupled (or connected) components [START_REF] Zeigler | Theory of Modelling and Simulation[END_REF][START_REF] Vangheluwe | The discrete event system specification (DEVS) Formalism[END_REF]. In the coupled model formalism, the connections between subsystems are represented with connectors, or mathematical equalities. Formally, a coupled model may be represented as a graph structure. For non-causal and continuous models, the graph is undirected. For causal models, the graph is directed. A coupled model is valid if connected ports are compatible regarding their type and causalities [START_REF] Vangheluwe | An introduction to multi-paradigm modelling and simulation[END_REF].

The Figure 1 depicts an FMU represented by a block, with internal state variables x(t), connected to other subsystems of the coupled problem by inputs u(t) and outputs y(t) [START_REF] Broman | Determinate Composition of FMUs for Co-simulation[END_REF].

Figure 1 : Data flow between the environment and an FMU for CS [2]

As depicted by the Figure 2 there are two possibilities for providing slave subsystems for co-simulation:

• subsystems with their specific solver, they can be simulated in stand-alone mode • subsystems with the simulation tools in which they have been developed

Figure 2: FMU (CS) integration in stand-alone, and with tool coupling [2]

The FMI 2.0 specification defines the life cycle (different noticeable states and guarded transitions) of an FMU as the Figure 4. A master algorithm serves several purposes: to instantiate, to initialize, to execute and to synchronize FMUs [START_REF] Bastian | Master for Co-Simulation Using FMI[END_REF]. An instantiated FMUs is called a slave. Master algorithms synchronize FMUs by controlling the data that are exchanged between FMUs at specific synchronization points called communication steps. The communication step sizes are defined as hci = tci+1 -tci, where tci are communication points. In the interval between two communication points, the subsystems are solved independently by their respective solvers. Master algorithms control exchanges of data between the subsystems and the synchronization between slaves.

For co-simulation two basic groups of functions should be realized:

1. functions for the data exchange between subsystems, 2. functions for algorithmic issues to synchronize the simulation of all subsystems and to proceed in communication steps tci → tci+1 from initial time tc0 = tstart to end time tcN = tstop.

d. Combining ADL and FMI -benefits and challenges

An Architecture Description Language (ADL) model captures the organizational structure of the system, along with executable blocks that represents its inner structure. It is fully configured so as to faithfully represent its behavior in terms of timing and communication. Several studies explored the capability to perform model checking or analysis of such model. Yet, a usual limit is the difficulty to capture a model of the environment that would act as a stimulus for the verification part. FMI has been designed to support system simulation. We claim it can also be used also for verification of real-time embedded systems, by combining a mock of the environment as an FMU and the system under test. In this paper, we illustrate our approach to address this part using AADL.

Combining AADL and FMI would equip system architects with a tool to prepare in advance integration phases through a virtual test bench. Indeed, this would make easier the early validation of AADL models: the stimulus provided by FMUs (that represent the physical environment) could be considered as test cases for AADL models. Using FMU would also give access to models with high-level of fidelity, with connections to other engineering models beyond a naïve model of a plant. However, this combination of discrete-time execution semantics for the cyber part (AADL) with systems dynamics (FMI, multi-physics simulation) is not an easy task. Such hybrid models raise issues regarding time management in co-simulation, typical issues concern the time step used to synchronize elements, or intermediate extrapolations performed by each model when no inputs are exchanged. In [START_REF] Hoepfer | Towards a comprehensive framework for co-simulation of dynamic models with an emphasis on time stepping[END_REF], the author provides a thorough review of these topics in the general case.

In the following, we review existing work prior to propose an integrated workflow in section 4.

Related Work

FMI was first designed to co-simulate physical and hybrid systems (continuous and discrete) specified using DAEs (Differential and Algebraic Equations) and discrete events. In this paper, we focus on the use of FMI in the context of critical embedded software design with AADL. We plan also on leveraging existing code generation from AADL that targets Real-Time Operating Systems (RTOS).

In the following, we present related work that a) integrate FMI with modelling language, b) that combine FMI with RTOS code, and c) that use FMI for hybrid systems co-simulation.

a. Integrating FMI with high-level modelling language

The integration of FMI with modelling language such as UML or SysML is an addressed challenge. In [START_REF] Guermazi | Integration of UML Models in FMIbased Co-simulation[END_REF], the authors proposed a co-simulation environment that combines the execution of UML models (with fUML 4 ) and FMI within the Moka Papyrus plugin. This work the co-simulation of hybrid systems, e.g. a controller modelled as an activity diagram (discrete), and its environment as physical and continuous FMUs. Feldman et al. [START_REF] Feldman | Simulating Rhapsody SysML Blocks in Hybrid Models with FMI[END_REF] proposed to export Rhapsody SysML blocks into FMUs, with a limitation on flow ports and attributes (the behavior of SysML block, e.g. state-machines or activities, is not supported for now).

Combining EAST-ADL and FMI has also been investigated during the MAENAD project [START_REF] Cavdar | Supporting Embedded Systems Development -Tool Support for EAST-ADL import of Modelica FMU[END_REF]. The work resulted in FMI 1.0 import capability within EAST-ADL model using model transformation technology. However, this work focused more on the semantic mapping between EAST-ADL and FMI, than on cosimulation issues and execution. Let us note current FMI technology lacks means to build simulation assemblies. The standard System Structure and Parameterization (SSP) [START_REF] Köhler | Modelica-Association-Project "System Structure and Parameterization"--Early Insights[END_REF] will complement FMI on this particular topic.

As our work concentrates at a lower level of CPS design, i.e. embedded software modelling and simulation using AADL, we propose to complete these related works at the lower left-side of the V-cycle with RTOS validation capabilities using FMI.

b. Combining FMI with RTOS code

In [START_REF] Nicolai | FMI for Co-Simulation of Embedded Control Software[END_REF], the authors propose to adapt embedded software to comply with FMI for co-simulation. More precisely, the authors propose to advance the clock of the RTOS, by overwriting the idle thread and waiting for a signal to start execution. Pohlmann et al. [START_REF] Pohlmann | Generating Functional Mockup Units from Software Specifications[END_REF], proposed to generate FMUs from UML software specification, where the clock is specified in a DSL named MechatronicUML. This clock is used to measure execution time and to specify Real-Time properties within timed state-machines.

On the contrary, we aim at validating a system from its ADL model. Hence, we propose to simulate the behavior of the embedded processor, which executes the target code. Hence, one can perform co-simulation of CPS, closest to the actual implementation without the need of specific hardware (between Software-In the Loop and Hardware in the Loop), or on the final target. This is left as a late-binding decision.

c. FMI for hybrid co-simulation

Co-simulating discrete (software) and continuous models (physical), raises several issues encountered during the study and experiments. Indeed, mixing continuous and discrete behavior in a co-simulation framework is not well handled by FMI. The representation of time and its management are the key issues of FMI based co-simulation approaches. In Cremona et al. [START_REF] Cremona | Hybrid Co-Simulation: It's About Time[END_REF], the authors identified extensions to FMI for supporting hybrid co-simulation: use integer time instead of floating point time representation, automatic choice of time resolution, use of "super-dense" time, and the use of absent signal. The proposed solution of [START_REF] Cremona | Hybrid Co-Simulation: It's About Time[END_REF] satisfies all the requirements for hybrid co-simulation stated in [START_REF] Broman | Requirements for Hybrid Cosimulation Standards[END_REF]. Unfortunately, it imposes strong constraints on the usability: these extensions are not backward-compatible with existing FMI 2.0 FMUs. Finally, using the dependency graph as an asset to get more precise hybrid co-simulation results is an issue investigated in several works, especially in [START_REF] Van Acker | Generation of an Optimised Master Algorithm for FMI Co-simulation[END_REF], whose authors propose to generate master algorithm based on the dependency graph (with and without loop) and on the step-size of each FMU (multi-clock management). We are also interested in the recent results of DACCOSIM [START_REF] Galtier | Experimenting with Matryoshka Co-Simulation: Building Parallel and Hierarchical FMUs[END_REF], which propose to generate master algorithms for parallel and distributed co-simulation using hierarchical FMUs.

Integrating FMUs as AADL blocks

In this Section, we present the integration workflow of FMU components within AADL models. We view the integration of FMU as an integration process. Starting from an AADL model, one aims at integrating FMU as an executable block, similar to the inclusion of other functional models in AADL, such as C, Ada, Scade, Simulink that are already supported by our AADL toolchain Ocarina. Each block is integrated as a subprogram block, that is triggered by its enclosing component such as a thread or a device.

Ocarina5 [START_REF] Broman | Requirements for Hybrid Cosimulation Standards[END_REF] is a model processor for the AADL. It supports code generation targeting a wide variety of RTOS (RTEMS, RT-POSIX, FreeRTOS, ARINC653). It maps AADL constructs onto the PolyORB-HI runtime that abstract RTOS constructs. It preserves the initial semantics of the AADL model.

a. Integration of FMU in AADL workflow

First, let us say that one receives an FMU that models and simulates the mechanical part (physical) of a larger system. This FMU should be integrated with a controller (cyber part), designed with AADL. The goal is to verify that the controller behaves as expected. The integration workflow is presented Figure 4. The first step consists in an automated translation of the FMU as AADL model using an algorithm, which 1) unzips the FMU file, 2) parses the modeldescription.xml file to create AADL elements respecting the mapping of Table 1, and 3) creates the FMI wrapper as set of AADL constructs: subprogram that capture the execution (entrypoint of the simulator) and corresponding C implementation, thread and device abstractions. Then, one could connect the FMU with the larger AADL model to build a coupled model. However, in the case of algebraic loop detection, the calculation of the dependency graph is aborted, and a generic Master Algorithm is provided. In parallel, the target RTOS code is generated from the AADL model, using Ocarina. Finally, the whole code is compiled and linked to be executed. 1, FMU blocks are mapped to AADL device, that is an abstraction of a device interacting with the physical world captured by the FMU model. Hence, FMU interactions are explicitly discretized by the activation of the device by other part of the model, e.g. reading from a sensor will trigger the corresponding FMU at the corresponding sampling time. Hence, one can integrate either continuous time or discrete time in the simulation.

In our approach, FMUs are embedded inside an AADL model that already have an execution semantics, and a scheduler. As a result, the Master Algorithm is implicitly defined by the combination of the scheduling parameters of all blocks: signals are captured in AADL event port communications; data propagation as AADL data port communications; scheduling is controlled by the scheduler of the system, e.g. prioritydriven scheduler. Thus, the cyber part of the system interacts with the environment through polling (periodic read), interrupts (reception of events from the environment) or actuation. These are captured by corresponding port directions in the AADL model.

As a consequence, the co-simulation time is linked to scheduler time. We used signals to start the scheduler until the communication time step is reached. The implementation of the master algorithm is automatically generated using the Ocarina AADL code generator by translating AADL tasks and communication ports to the corresponding C artefacts. Thanks to the versatility of the code generation process, we can either really on true (wall clock) time, or simulated time using a simulator of a RTOS. Hence, this approach allows seamless integration of FMU as functional models.

Case Study and Experiment Results

In this section, we list two case studies built on the previous integration workflow 6 .

a. Moonlander

A Moon Lander model [START_REF] Fritzson | Introduction to modeling and simulation of technical and physical systems with Modelica[END_REF] was used to investigate co-simulation's time and scheduler's time issues. We built a Modelica model of the physical model and exported it into an FMU 2.0 for Co-Simulation. The controller implements a basic strategy to control the descent of the vehicle, and triggers the thrusters. A first version has been implemented in Modelica to check the correctness of the controller, and simulated in the OpenModelica framework.

Then, the FMU of the physical model was imported as an AADL component following the semantics mapping of the Table 1, and connected to a reimplementation of the controller in C. This controller and the plant, seen as an AADL device that samples the environment, have been connected in an AADL model (see Figure 6). This model indicates the data types exchanges and the scheduling parameters of the controller.

From the system designer perspective, the AADL model captures the configuration of the controller, and a device that interacts with the environment as a regular device driver. Here, FMI plays its role of "mockup", instead of connecting this model to the implementation of a driver, we connect it to the model that simulated the environment it interacts with.

To simulate the overall system, we generated the C code of the AADL controller with Ocarina, along with code archetype for the various tasks and communication channels. We linked it to the FMU as an external library. We rely on the FMUSDK2 from Modelon (adapted by University of California -Berkeley7 ) to build a generic entry point to load FMUs and to compute simulation steps triggered by the host process. For this experiment, we relied on the GNU/Linux OS, combined with RT-POSIX API call to implement a real-time behavior for the controller.

Through analysis of the execution logs, we could assess the simulation has the same behavior for both the FMI-coupled model and the Modelica model.

ROSACE case study

The ROSACE case study [START_REF] Pagetti | The ROSACE Case Study: From Simulink Specification to Multi/Many-Core Execution[END_REF] was used to investigate co-simulation graph issues, but also scalability. ROSACE has multiple implementations in C/POSIX, C/ARINC653, Simulink Giotto or Ptolemy. It is a reference benchmark for CPS simulation.

The environment of the controller is composed of three FMUs: an engine, an elevator, and the aircraft dynamics. These FMUs are connected to exchange physical quantities, and to the controller that is modeled in AADL. This controller is made of 11 periodic tasks interconnected. This model has a higher level of complexity compared to the MoonLander case study, with more FMUs and tasks.

To build these FMUs, we modelled the environment using the Modelica language and we generated the FMUs with JModelica. The controller has been implemented in Simulink, and later translated in C. Then, based on [START_REF] Van Acker | Generation of an Optimised Master Algorithm for FMI Co-simulation[END_REF][START_REF] Galtier | Experimenting with Matryoshka Co-Simulation: Building Parallel and Hierarchical FMUs[END_REF] we have investigated the construction of the overall dependency graph to generate automatically the Master Algorithm. This algorithm has been translated as a set of AADL scheduling configuration parameters. The models are simple enough to be full discretized, thus a causal graph can be deduced to capture the whole simulation behavior.

We could leverage the ROSACE validation script to ensure that our simulation was also consistent with other simulations done either in Simulink, Ptolemy/HLA or Giotto.

c. Lessons learnt

Through these two case studies, we could generate virtual integration test bench for cyber physical systems. We demonstrated the capability to connect ADL model with models simulating the environment using the FMI framework. This is a first step towards full generation of simulation environment.

The architectural description of the system has been demonstrated to be enough to interact with the FMU-based environment blocks. This is a consequence of using causal systems: one can simulate the environment up to the instant required by the cyber part.

Conclusion and Further Work

In this paper, we addressed the early validation of embedded systems. We proposed a general approach to bind architectural description, amenable to code generation, to FMU blocks. This enables the construction of virtual integration test bench. First, we presented the various elements of contexts and related work. Then, we illustrated how FMI blocks can be bound to AADL models so to serve as a mock of the environment seen through a device. Hence, one can test an AADL model considering a representative model of the environment. Leveraging high-fidelity model turned into FMU, one can test more precise interaction scenario. Future work activities will increase the number of case studies, to stress timeliness issues, e.g. multi-clock scenarios. Another aspect will consider integrating multiple simulators like Instruction Set Simulators for precise simulation of hardware blocks, and interoperability with domain-specific simulators to simulate the occurrence of faults and defects.

Figure 3 :

 3 Figure 3: State-machine of FMI Co-Simulation[START_REF]MODELISAR Consortium and Modelica Association Project "FMI" -Functional Mock-up Interface for Model-Exchange and Co-Simulation[END_REF]

Figure 4 :

 4 Figure 4: Integrating an FMU as an AADL component -Workflow b. Integration of FMU execution semantics FMU-based simulations rely on the concept of a Master Algorithm that orchestrates the overall simulation at each time step. Then, the FMUs perform a calculation step, and the resulting values are propagated to the scheduler, which launches tasks depending on the overall simulation time. The Master Algorithm can be built based on the dependency graph of the coupled model.

Figure 5

 5 Figure 5 AADL model of the lunar lander b. ROSACE case study

Table 1 :

 1 Mapping Between FMI and AADL

	Concepts	FMI	AADL
	Component	FMU	Subprogram/Device
	Input/Output port	Causality In/Out	In port / Out port
	Discrete port / Continuous port	Variability Discrete/Continuous	Event port / Data port
	Types	Real, Integer, Boolean	Base_Types::Float,
			Base_Types::Integer,
			Base_Types::Boolean
	As stated by Table

https://www.modelica.org/ [last visited 30/05/2017]

https://fr.mathworks.com/products/simulink.html [last visited

31/05/2017] 3 http://www.esterel-technologies.com/products/scade-suite/ [last visited 31/05/2017]

http://www.omg.org/spec/FUML/1.2.1/ [last visited 02/06/2017]

http://openaadl.org

Other case studies are available through http://www.openaadl.org

https://github.com/cxbrooks/fmusdk2 [last visited 03/06/2017]