Imène Mootamri
email: imene.mootamri@etumel.univmed.fr

Long Memory Process in Asset Returns with Multivariate GARCH Innovations

Keywords: Forecasting, Long memory, Multivariate GARCH, Stock Returns. JEL classi…cation: C22, C51, C53, G12

The main purpose of this paper is to consider the multivariate GARCH (MGARCH) framework to model the volatility of a multivariate process exhibiting long term dependence in stock returns. More precisely, the long term dependence is examined in the …rst conditional moment of US stock returns through multivariate ARFIMA process and the time-varying feature of volatility is explained by MGARCH models. An empirical application to the returns series is carried out to illustrate the usefulness of our approach. The main results con…rm the presence of long memory property in the conditional mean of all stock returns.

Introduction

Long memory seems to be in recent years a very widespread phenomenon in the modelling of economic and …nancial time series. It can be de…ned in terms of the persistence of the autocorrelations which decays at a very slow hyperbolic rate. A large numbers of papers demonstrate the existence of long memory in …nancial economics. [START_REF] Peters | Chaos and order in the capital markets. A new view of cycles, prices, and market volatility[END_REF] and [START_REF] Greene | Long-term dependence in common stock returns[END_REF] found evidence of long-term positive dependence in stock returns by applying the rescaled range (R=S) statistic 1 proposed by [START_REF] Hurst | The long-term storage capacity of reservoirs[END_REF] and modi…ed by [START_REF] Lo | Long-term memory in stock market prices[END_REF]. Similar evidence on the German stock return is given by [START_REF] Lux | Long-term stochastic dependence in …nancial prices: Evidence from the German stock market[END_REF]. However, [START_REF] Jegadeesh | Evidence of predictable behavior of security returns[END_REF] challenged the notion of mean reversion for stock returns. He reported negative …rst order serial correlation and signi…cant positive serial correlation for longer lags using monthly returns for individual stocks. [START_REF] Kim | Mean reversion in stock prices? a reappraisal of the empirical evidence[END_REF] also challenged the …ndings of mean reversion. Their …ndings for post war data showed persistence in returns. [START_REF] Volos | Long range dependence in stock market returns[END_REF] examined the presence of longrange dependence in a sample of 34 stock index returns using the procedure of Geweke and Porter-Hudak (1983) and [START_REF] Robinson | Gaussian semi-parametric estimation of long range dependence[END_REF]. Their results provided signi…cant and robust evidence of fractional dynamics in most major and small stock markets over the sample periods. [START_REF] Goetzmann | Patterns in three centuries of stock market prices[END_REF] applied R/S tests which provided some evidence that the London stock exchange and New York Stock Exchange stock market prices may exhibit long-term memory. Some authors found signi…cant and robust evidence of positive long-term persistence in the Greek stock market [START_REF] Barkoulas | Long memory in the Greek stock market[END_REF]), in the Brazil stock market [START_REF] Cajueiro | Possible causes of long-range dependence in the Brazilian stock market[END_REF] and Cavalcante et al. ( 2004)), and in the Finnish stock market return data (Tolvi (2003)). [START_REF] Sadique | Long-term memory in stock market returns: international evidence[END_REF] examined the presence of long memory in weekly stock returns of seven countries. They found evidence of long-term dependence in four countries. Moreover, [START_REF] Cajueiro | Evidence of long range dependence in Asian equity markets: The role of liquidity and market restrictions[END_REF] found that the markets of Hong Kong, Singapore and China exhibited long-range dependence, while [START_REF] Mills | Is there long-term memory in UK stock returns?[END_REF] and [START_REF] Zhuang | The great rebound, the great crash, and persistence in British stock prices[END_REF] investigated British stock returns and found little evidence of long-range dependence. However, [START_REF] Limam | Is long memory a property of thin stock markets? International evidence using Arab countries[END_REF] analyzed stock index returns in 14 markets and concluded that long memory tends to be associated with thin markets and Huang and Yang (1999) applied the modi…ed R=S technique to intraday data and provide evidence of long memory phenomenon in both the New York Stock Exchange and Nasdaq indices.

In fact, all these empirical works are based on univariate models. How-ever, for many important questions in empirical literature, multivariate settings are preferable. For example, suppose one is considering a portfolio of many assets. The return of the portfolio can be directly computed if one knows the asset shares and the return of each asset [START_REF] Brooks | Multivariate GARCH models: software choice and estimation issues[END_REF]). [START_REF] Granger | An introduction to long memory time series models and fractional di¤erencing[END_REF] proposed the univariate fractionally integrated autoregressive moving average (ARFIMA) model to explain the long memory property that exists in the conditional mean. Therefore, we consider in this study the multivariate ARFIMA model 2 , where the fractional integration parameters determine the long memory properties of the data. Apart from the presence of long term dependence in the conditional mean, we will take into account the volatility's properties of the series 3 . More precisely, the time-varying feature of volatility is explained by multivariate generalized autoregressive conditionally heteroscedastic models (MGARCH). Despite the fact that univariate descriptions are useful and important, various …nancial operations require a multivariate framework, since high volatilities are often observed in the same time periods across di¤erent assets. The development of MGARCH models from the original univariate speci…cations represents a major step forward in the modelling of time series: these models permit time-varying conditional covariances as well as variances. To this end, the main contribution of this paper is then to incorporate the MGARCH framework to model the volatility of a multivariate process exhibiting a long term dependence and slow decay in the stock returns. More precisely, we have examined the long memory property in the …rst conditional moment of daily stock returns; the robustness of the results is also investigated by considering that its innovations are generated by a MGARCH process. We found that the long memory property existed in the conditional mean of the Nasdaq 100, New York Stock Exchange (NYSE) composite and Russell 3000 stock returns.

The rest of this paper is organized as follows. We brie ‡y review the multivariate models in the next Section. Section 3 outlines the Quasi-maximum likelihood estimation and testing procedures for the models which are applied to US stock returns. Section 4 describes multi-step forecasting with some MGARCH model and Section 5 presents the data used and provides empirical results. The paper ends with a short concluding section.

Econometric framework

The following is a brief description of the time series models used in this study. The vector ARFIMA models are discussed in detail in [START_REF] Sowell | Maximum likelihood estimation of fractionally integrated time series models[END_REF] and Lucee no (1996). [START_REF] Tsay | Maximum Likelihood Estimation of Stationary Multivariate ARFIMA Process[END_REF] provided a more detailed description for estimation of the vector ARFIMA models. He suggested a conditional likelihood Durbin-Levinson algorithm to e¢ ciently evaluate the conditional likelihood function of the vector ARFIMA processes. [START_REF] Hosoya | The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence[END_REF] and [START_REF] Nielsen | E¢ cient inference in multivariate fractionally integrated time series models[END_REF] proposed a class of maximum likelihood estimators and tests. [START_REF] Lobato | A semiparametric two-step estimator in a multivariate long memory model[END_REF] analyzed a two-step estimator of the long memory parameters of a vector process by using a semiparametric version of the multivariate Gaussian likelihood function in the frequency domain.

Consider a vector ARFIMA processes:

(L) (L) (y t ) = (L) " t (1)
where y t = (y 1t ; ::::; y nt ) 0 ; t = 1; :::; T; is an n dimensional vector of observations, = ( 1 ; ::::; n ) 0 is the conditional mean vector of the process, (L) = I n 1 L :::: p L p and (L) = I n + 1 L + :::: + q L q are (n n) matrix polynomials in the lag operator L, and satisfy the usual stationary and invertible conditions respectively, i.e., the roots of det ( (L)) 4 and det ( (L)) are outside the unit circle. I n is the identity matrix of order n and (L) = diag h

(1 L) d 1 ; ::::::;

(1 L) dn i :
The fractional di¤erencing operator is de…ned by the binomial expansion,

(1 L) d i = 1 X j=0 ( d i + j) ( d i ) (1 + j)
L j ; for i = 1; :::; n where (:) is the Gamma function 5 . Hence, the long-range dependence between observations is eventually determined only by the fractional di¤erencing parameter. These characteristics can be seen in the shapes of the spectral density and the autocorrelation function. Indeed, if jd i j < 0:5 for i = 1; :::; n; the multivariate process is stationary and invertible. If 0 < d i < 0:5; the process is characterized by strong positive dependency between observations. This is noted in the frequency domain by the spectral density increasing to an in…nite value at the zero frequency. In the time domain, the persistence is indicated by the slow decline of the autocorrelation functions which are not absolutely summable. In this case, y t is said to have a long memory 6 . If 0:5 < d i < 0; the process exhibits negative dependency between observations. In the frequency domain, this is indicated by the decline of the spectral density to zero, as the frequency approaches zero. The time domain indicates the antipersistence by the rapid decline of the autocorrelation functions.

So, in this paper, we consider a vector ARFIMA model, which generates the long memory property in the …rst conditional moment and which allows its innovations to be generated by a multivariate MGARCH process. As an illustration, the proposed model is applied to the daily stock returns of Nasdaq, New York Stock Exchange and Russell indices.

The most commonly employed distribution in the literature is the multivariate normal. Thus, we assume that the stochastic vector process " t = (" 1t ; ::::; " nt ) 0 is conditionally multivariate normal with zero expected value and covariance matrix H t :

" t = H 1=2 t z t ; " t j t 1 N (0; H t ) (2)
with E t 1 (" t ) = 0: We denoted by t 1 the information set generated by the observed series until time t 1.

H t = (h ijt ) is an (n n) conditional covariance matrix of " t : H t = E t 1 (" t " 0 t
) and z t is an independent identically distributed random vector error process such that E (z t ) = 0 and E (z t z 0 t ) = I n .

As noted by Silvennoinen and Teräsvirta (2008) 7 , the speci…cation of an MGARCH should be ‡exible enough to be able to represent the dynamics of the conditional variances and covariances, and, as the number of parameters in an MGARCH model often increases rapidly with the dimension of the model, the speci…cation should be parsimonious enough to allow for easy estimation of the model. Another feature that needs to be taken into account in the speci…cation is that the conditional covariance matrices should be positive de…nite.

Generalizations of the univariate GARCH model: VEC and BEKK Models

The V EC (p; q) model of [START_REF] Bollerslev | A capital asset pricing model with time varying covariances[END_REF]

h t = C + q X j=1 A j e t j + p X j=1 B j h t j (3)
where h t = vech (H t ) 8 , H t is the (n n) conditional covariance matrix, e t = vech (" t " 0 t ) ; C is a n(n+1) 2 parameter vector and, A j and B j are

n(n+1) 2 n(n+1) 2
parameter matrices. The main disadvantage of this model is the number of parameters which is equal to n(n+1)

2 h (p + q) n(n+1) 2 + 1
i and which becomes larger and larger as the number of variables increases. Thus, the estimation of the parameters is di¢ cult. Furthermore, the positivity of H t is not guarantee. To overcome this problem, [START_REF] Bollerslev | A capital asset pricing model with time varying covariances[END_REF] suggest the diagonal VEC 9 model in which A j and B j are assumed to be diagonal, each element h ijt depending only on its own lag and on the previous value of " it " jt . This restriction reduces the number of parameters to n(n+5)

2

. But even under this diagonality assumption, large scale systems are still highly parameterized and di¢ cult to work with in practice.

One of the most general forms, proposed in Engle and Kroner (1995), is the BEKK (Baba-Engle-Kraft-Kroner) representation. This formulation developed a general quadratic form for the conditional covariance equation which eliminated the problem of assuring the positive de…niteness of the conditional covariance matrix. The BEKK (p; q; K) representation for the (n n) conditional covariance matrix H t takes the form:

H t = C 0 C + q X j=1 K X k=1 A 0 kj " t j " 0 t j A kj + p X j=1 K X k=1 B 0 kj H t j B kj (4)
where the summation limit K determines the generality of the process, C is upper triangular (n n) matrix, and A kj and B kj are both (n n) parameter matrices. This representation guarantees that H t is positive de…nite. Although the form of the above model is quite general especially when K is reasonably large, it su¤ers from the problems due to overparametrization 10 . 8 vech is an operator that replaces the columns of the lower triangular part of H t in a n(n+1) 2

1 vector column. 9 See also [START_REF] Bauwens | Multivariate GARCH models: A survey[END_REF] and Silvennoinen and Teräsvirta (2008). 10 See [START_REF] Engle | Multivariate simultaneous GARCH[END_REF] for more discussion on the identi…cation problem of this model.

The parameters of the BEKK model do not represent directly the impact of the di¤erent lagged terms on the elements of H t , like in the VEC model.

The number of parameters in the BEKK model is equal to

(p + q) Kn 2 + n(n+1) 2
and is still quite large. Thus, as we already mentioned, a problem with these models is that the number of parameters can increase very rapidly as the dimension of the process increases, what creates di¢ culties in the estimation of the models due to several matrix inversions. So it is typically assumed that p = q = K = 1 in applications of this model. A further simpli…ed version of (4) in which A kj and B kj are diagonal matrices has sometimes appeared in applications. This is a diagonal BEKK model 11 where the number of parameters is equal to (p + q) Kn + n(n+1)

2

. This model is also a DVEC model but it is less general, although it is guaranteed to be positive de…nite while the DVEC is not.

Nonlinear combinations of univariate GARCH models: CCC and DCC Models

Bollerslev (1990) proposed a class of MGARCH models in which the conditional correlation matrix is time-invariant and thus the conditional covariances are proportional to the product of the corresponding conditional standard deviations. This model is so-called Constant Conditional Correlation (CCC). This restriction greatly reduces the number of unknown parameters and thus simpli…es the estimation. So, the conditional covariance H t , may always be decomposed as:

H t = D t RD t where h ijt = ij p h iit h jjt ; 8 i 6 = j D t = diag p h 11t ; p h 22t ; :::; p h nnt (5)
where h iit can be de…ned as any univariate GARCH model, and R is a (n n) symmetric positive de…nite matrix of conditional correlations with typical element:

ijt = cov t 1 (" it ; " jt ) var t 1 (" it ) 1=2 var t 1 (" jt ) 1=2
with ii = 1; 8 i = 1; :::; n: D t denotes the (n n) diagonal matrix with typical element var t 1 (" it ) : The CCC-GARCH model assumes that the conditional correlations are constant ijt = ij , so that the temporal variation in H t is determined solely by the time-varying conditional variances for each of the elements in " t . As long as each conditional variances are positive 12 , the CCC model guarantees that the resulting conditional covariance matrices are positive de…nite.

Despite the simplicity of this model, the assumption that the conditional correlations are constant may seem too restrictive and unrealistic. [START_REF] Engle | Dynamic conditional correlation: A simple class of multivariate GARCH models[END_REF] proposed a new class of estimator that both preserves the ease of estimation of Bollerslev's constant correlation model yet allows for non-constant correlations. Dynamic Conditional Correlation (DCC)-GARCH 13 preserves the parsimony of univariate GARCH models of individual assets' volatility with a simple GARCH process. Further, the number of parameters estimated using maximum likelihood is considerable improvement over both the VEC and the BEKK models. [START_REF] Tse | A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations[END_REF] have also proposed a dynamic correlation MGARCH model, however no attempt has been made to allow for separate estimation of the univariate GARCH processes and the dynamic correlation estimator.

The DCC model of [START_REF] Engle | Dynamic conditional correlation: A simple class of multivariate GARCH models[END_REF] computes the time changing conditional correlation matrix from the standardized residuals series:

8 < :

H t = D t R t D t D t = diag p h 11t ; p h 22t ; :::; p h nnt R t = Q 1 t Q t Q 1 t (6)
where Q t = (diagQ t ) 1=2 ; Q t is the (n n) symetric positive de…nite matrix given by:

Q t = (1 1 2 ) Q + 1 u t 1 u 0 t 1 + 2 Q t 1 (7)
1 and 2 are non-negative scalar parameters satisfying 1 + 2 < 1: Q is the (n n) unconditional covariance matrix composed from the standardized residuals resulting from the …rst step estimation, where u t = (u 1t ; u 2t ; :::; u nt ) 0 is the standardized residuals vector 14 , and

Q 1 t = diag 1 p q 11 ; 1 p q 22 ; :::; 1 p q nn
The typical element of R t will be of the form: ijt = q ijt p q ii q jj 12 See Nelson and Cao (1992) for discussion of positivity conditions for h it in univariate GARCH (p; q) models. 13 Various generalizations of the DCC-GARCH model are proposed in the literature (Pelletier (2006), Billio and Caporin (2006), [START_REF] Cappiello | Asymmetric dynamics in the correlations of global equity and bond returns[END_REF], [START_REF] Silvennoinen | Modelling multivariate autoregressive heteroskedasticity with the double smooth transition conditional correlation GARCH model[END_REF]...). 14 u it = "it p hiit ; for i = 1; :::; n:

A slightly di¤erent formulation was suggested by [START_REF] Tse | A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations[END_REF]:

R t = (1 1 2 ) R + 1 t 1 + 2 R t 1 ( 8
)
1 and 2 are non-negative scalar parameters such that 1 + 2 < 1: Here R = ij is a time-invariant (n n) symmetric positive de…nite parameter matrix of conditional correlations with ones on the diagonal and t 1 is a (n n) correlation matrix of the past m standardized residuals u t = (u 1t ; u 2t ; :::; u mt ) : The positive de…niteness of R t is ensured by construction if R and t 1 are positive de…nite such that m n . The typical element of t 1 will be of the form:

ij;t 1 = P m l=1 u i;t l u j;t l q P m l=1 u 2 i;t l P m l=1 u 2 j;t l (9)
where u it = " it p h iit ; for i = 1; :::; n: The number of parameters in both the DCC models is equal to (n+1)(n+4) 2 if the conditional variances are speci…ed as GARCH [START_REF] Aydogan | Are there long cycles in common stock returns?[END_REF][START_REF] Aydogan | Are there long cycles in common stock returns?[END_REF]. However, to check if the assumption of the conditional correlations is empirically relevant, one can test 1 = 2 = 0: A drawback of the DCC models is that 1 and 2 are scalars, so that all the conditional correlations obey the same dynamics. This is necessary to ensure that R t is positive de…nite through su¢ cient conditions on the parameters.

3 Estimation of MGARCH model [START_REF] Bollerslev | Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model[END_REF] introduced the CCC-GARCH speci…cation, where univariate GARCH models are estimated for each asset and then the correlation matrix is estimated using the standard closed form MLE correlation estimator by transforming the residuals using their estimated conditional standard deviations. The assumption of constant correlation makes estimating a large model feasible and ensures that the estimator is positive de…nite, simply requiring each univariate conditional variance to be non-zero and the correlation matrix to be of full rank. However, the constant correlation estimator, as proposed, does not provide a method to construct consistent standard errors using the multi-stage estimation process. [START_REF] Bollerslev | Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model[END_REF] noticed that the notion of constant correlation is plausible but [START_REF] Tse | A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations[END_REF] and [START_REF] Tse | A test for constant correlations in a multivariate GARCH model[END_REF] found that it can be rejected for some assets.

For the maximum likelihood estimation (MLE) of parameters we assume the conditional normality of the errors. The log-likelihood function of the model:

(L) (y t ) = " t ; " t = H 1=2 t z t H t = D t R t D t ( 10
)
has the following form:

L T ( ) = 1 2 T X t=1 n log (2 ) + ln jH t j + " 0 t H 1 t " t (11)
where is the vector of all the parameters in the model.

Estimating the parameters simultaneously with the conditional variance parameters would increase the e¢ ciency at least in large samples, but this is computationally more di¢ cult. For this reason, we estimate the fractionally integrated model for the conditional mean and we consider (L) y t as the data for …tting the MGARCH model, where

(L) = diag (1 L) b d i ; for i = 1; :::; n:
Engle and Sheppard (2001) 15 showed that the loglikelihood can be written as the sum of a mean and volatility part, depending on a set of unknown parameters and a correlation part that is:

L T ( ) = 1 2 T X t=1 n log (2 ) + ln jH t j + " 0 t H 1 t " t (12) = 1 2 T X t=1 n log (2 ) + ln jD t R t D t j + " 0 t D 1 t R 1 t D 1 t " t = 1 2 T X t=1 n log (2 ) + 2 ln jD t j + ln jR t j + u 0 t R 1 t u t
The conditional variance matrix of a DCC model can be expressed as

H t = D t R t D t .
The DCC model was designed to allow for two stage estimation, where in the …rst stage univariate GARCH models are estimated for each residual series, and in the second stage, the residuals, transformed by their standard deviations estimated during the …rst stage, are used to estimate the parameters of the dynamic correlation. The likelihood used in the …rst stage involves replacing R t by the identity matrix in [START_REF] Doukhan | Theory and applications of long-range dependence[END_REF]. Let = ( 1 ; ::::; n ; ) = ( ; ) ; where the elements of i correspond to the parameters of the univariate GARCH model for the i th asset reurns, i = (c i ; i ; i ) ;for i = 1; :::; n:

The resulting …rst stage quasi-likelihood function is:

Q1L T ( ) = 1 2 T X t=1 n log (2 ) + 2 ln jD t j + ln jI n j + " 0 t D 1 t I n D 1 t " t (13) = 1 2 T X t=1 n log (2 ) + 2 ln jD t j + " 0 t D 2 t " t = 1 2 T X t=1 n log (2 ) + n X i=1 ln (h iit ) + " 2 iit h iit ! = 1 2 T X t=1 n X i=1 log (2 ) + ln (h iit ) + " 2 iit h iit
which is simply the sum of the log-likelihoods of the individual GARCH models for each of the asset returns. Once the …rst stage has been estimated, the second stage is estimated using the correctly speci…ed likelihood, conditioned on the parameters estimated in the …rst step:

Q2L T j b = 1 2 T X t=1 n log (2 ) + 2 ln jD t j + ln jR t j + " 0 t D 1 t R 1 t D 1 t " t (14) = 1 2 T X t=1
n log (2 ) + 2 ln jD t j + ln jR t j + u 0 t R 1 t u t where u t = D 1 t " t are the univariate GARCH standardized residuals. Since we are conditioning on b , the only portion of the log-likelihood that will in ‡uence the parameter selection is ln jR t j + u 0 t R 1 t u t , and in estimation of the DCC parameters, it is often easier to exclude the constant terms and simply maximize:

Q2L T j b = 1 2 T X t=1 ln jR t j + u 0 t R 1 t u t (15)

Test of constant conditional correlations

The …rst step of modelling time-varying conditional correlations is to test the hypothesis of constant correlations. Testing data for constant correlation has proven to be a di¢ cult problem, as testing for dynamic correlation with data that have time-varying volatilities can result in misleading conclusions and can lead to rejecting constant correlation when it is true due to mis-speci…ed volatility models. [START_REF] Bera | Testing constancy of correlation and other speci…cations of the BGARCH model with an application to international equity returns[END_REF] have provided tests of a null of constant correlation against an alternative of a dynamic correlation structure. It is an information matrix-type test that besides constant correlations examines at the same time various features of the speci…ed model. An alternative test has been proposed by [START_REF] Longin | Is the Correlation in International Equity Returns Constant: 1960-1990?[END_REF]. We are interested in testing the null of constant correlation against an alternative of dynamic conditional correlation via the Lagrange Multiplier (LM) approach suggested by [START_REF] Tse | A test for constant correlations in a multivariate GARCH model[END_REF] which tested a null of constant conditional correlation against an ARCH in correlation alternative. A rejection of the null hypothesis supports the hypothesis of time-varying correlations. Rewrite the DCC model:

8 < :

H t = D t R t D t D t = diag p h 11t ; p h 22t ; :::; p h nnt R t = Q 1 t Q t Q 1 t Then, we test H 0 : h ijt = ij p h iit h jjt
against the alternative

H A : h ijt = ijt p h iit h jjt
where the conditional variances are GARCH (1,1). Under H 0 ; the LM statistic is asymptotically 2 (n (n 1) =2). Under the normality assumption the conditional log-likelihood of the observation at time t is given by:

l t = 1 2 ln jD t R t D t j 1 2 y 0 t D 1 t R 1 t D 1 t y t
and the log-likelihood function L is given by L = P n t=1 l t : Engle and Sheppard (2001) proposed another test of the constant correlation hypothesis in the DCC models. The null hypothesis: R t = R 8 t is tested against the alternative: vech (R t ) = vech R + 1 vech (R t 1 ) + :::: + p vech (R t p ) : The test is easy to implement since H 0 implies that coe¢ cients in the regression X t = 0 + 1 X t 1 +::::+ p X t p +r t are equal to zero, where

X t = vech u (b z t b z 0 t I n ) ; vech u is

Portmanteau Statistics

It is crucial to check the adequacy of the MGARCH speci…cation. Bollerslev (1990) suggested some diagnostics for the constant correlation MGARCH model. He computed the Ljung-Box portmanteau statistic on the cross products of the standardised residuals across di¤erent equations. Critical values were based on the 2 distribution. As mentioned by [START_REF] Tse | A test for constant correlations in a multivariate GARCH model[END_REF], diagnostics for conditional heteroscedasticity models applied in the literature can be divided into three categories: portmanteau test of the Ljung-Box type, residual-based diagnostic and Lagrange multiplier test. So, to check the overall signi…cance of the residual autocorrelation, we consider the Ljung-Box portmanteau statistic. This test was introduced by Box and Pierce (1970) for goodness-of-…t checking of univariate strong ARMA models. Ljung and Box (1978) proposed a slightly di¤erent portmanteau test which is nowadays one of the most popular diagnostic checking tools in ARMA modelling of time series. Following [START_REF] Hosking | The multivariate portmanteau statistic[END_REF]Hosking ( -1981b)), a multivariate version of the Ljung-Box portmanteau 16 statistic is given by:

Q m (k) = T 2 k X j=1 (n j) 1 tr C 1 Yt (0) C Yt (j) C 1 Yt (0) C 0 Yt (j)
where tr denotes the trace of a matrix. Y t = vech (y t y 0 t ) and C Yt (j) is the sample autocovariance matrix of order j. Under the null hypothesis, Q m (k) is distributed asymptotically as 2 (p 2 k) : Duchesne and Lalancette (2003) generalized this statistic using a spectral approach and obtained higher asymptotic power by using a di¤erent kernel than the truncated uniform kernel used in Q m (k). This test is also used to detect misspeci…cation in the conditional variance matrix H t , by replacing y t by b z t = b H 1=2 t b " t : Ling and Li (1997) proposed an alternative portmanteau statistic for multivariate conditional heteroscedasticity. They de…ned the sample lag-h (transformed) residual autocorrelation as:

G (h) = P T t=h+1 b " 0 t b H 1 t b " t n b " 0 t h b H 1 t h b " t h n P T t=h+1 b " 0 t b H 1 t b " t n 2
Their test statistic is given by LL (k) = T P k h=1 G 2 (h) and is asymptotically distributed as 2 (k) under the null hypothesis. In the derivation of the asymptotic results, normality of the innovation process is not assumed.

The statistic is thus robust with regard to the distribution choice. [START_REF] Tse | A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations[END_REF] showed that there is a loss of information in the transformation b " 0 t b H 1 t b " t of the residuals and the test may su¤er from a power reduction.

Multivariate GARCH Prediction

Forecasting is one of the main objectives of multivariate time series analysis.

Predictions from multivariate GARCH models can be generated in a similar fashion to predictions from univariate GARCH models 17 . Indeed, for the univariate GARCH models, such as CCC model and principal component model, the predictions are generated from the underlying univariate GARCH models and then converted to the scale of the original multivariate time series by using the appropriate transformation. This section focuses on predicting from diagonal BEKK and DCC model.

To illustrate the prediction of conditional covariance matrix for multivariate GARCH models, consider the conditional variance equation for the diagonal BEKK(1,1,1) model:

H t = C 0 C + A 0 " t 1 " 0 t 1 A + B 0 H t 1 B (16)
where C, A and B are (3 3) matrices, C is upper triangular and A and B are diagonal matrices. The model ( 16) is estimated over the time period t = 1; :::; T: Given the information at time T , the one-step-ahead prediction (k = 1) of conditional covariance matrix at time T + 1 is given by:

E T (H T +1 ) = C 0 C + A 0 E T (" T " 0 T ) A + B 0 E T (H T ) B = C 0 C + A 0 " T " 0 T A + B 0 H T B; when k = 2, it can be shown that E T (H T +2 ) = C 0 C + A 0 E T " T +1 " 0 T +1 A + B 0 E T (H T +1 ) B = C 0 C + A 0 E T (H T +1 ) A + B 0 E T (H T +1 ) B
where E T (H T +1 ) is obtained in the previous step. This procedure can be iterated to obtain E T (H T +k ) for k > 2:

Let us consider the DCC (1; 1)-GARCH (1; 1) model given by [START_REF] Ding | A long memory property of stock market returns and a new model[END_REF], which can be written as: 8 > > < > > : 17 For more details see [START_REF] Moon | Hedging performance of commodity futures: out-of-sample evaluation of multivariate GARCH models[END_REF] and [START_REF] Hlouskova | Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management[END_REF].

H t = D t R t D t , D t = diag p h iit for i = 1; :::; n h t = c + " 2 t 1 + h t 1 R t = Q 1 t Q t Q 1 t Q t = (1 1 2 ) Q + 1 u t 1 u 0 t 1 + 2 Q t 1

14

where

Q 1 t = diag q 1=2 ii
; Q t is the (n n) symetric positive de…nite matrix, 1 and 2 are non-negative scalar parameters satisfying 1 + 2 < 1 and Q is the (n n) unconditional covariance matrix composed from the standardized residuals resulting from the …rst step estimation. However, the k-step ahead forecast of a standard GARCH(1,1) and the DCC evolution process are given by: 8 <

:

h t+k = P k 2 i=0 c ( + ) i + ( + ) k 1 h t+1 = P k 2 i=0 c ( + ) i + ( + ) k h t Q t+k = (1 1 2 ) Q + 1 u t+k 1 u 0 t+k 1 + 2 Q t+k 1 ( 17
)
where

E t u t+k 1 u 0 t+k 1 = E t (R t+k 1 ) and R t+k = Q 1 t+k Q t+k Q 1 t+k :
Thus, the k-step ahead forecast of the correlation cannot be directly solved forward to provide a convenient method for forecasting. In examining methods to overcome this di¢ culty, two forecasts seem to be the most natural, each requiring a di¤erent set of approximations. The …rst technique proposed would be to generate the k-step ahead forecast of Q t by making the approximation that

E t u t+1 u 0 t+1 Q t+1 . Using this approximation, we then have the k-step ahead forecast of Q t is E t (Q t+k ) = k 2 X i=0 (1 1 2 ) Q ( 1 + 2 ) i + ( 1 + 2 ) k 1 Q t+1 ( 18
)
for i 2 (1; ::::; k) and

R t+k = Q 1 t+k Q t+k Q 1 t+k :
An alternative approximation would be that Q R and that E t (Q t+1 ) E t (R t+1 ) : Using this approximation, we can forecast R t+k directly using the relationship

E t (R t+k ) = k 2 X i=0 (1 1 2 ) R ( 1 + 2 ) i + ( 1 + 2 ) k 1 R t+1 (19)
In order to test which of these approximations performs better, Engle and shepard (2001) have conducted a Monte Carlo experiment. They have concluded that the forecast produced by solving forward for Q t+k was more biased than the method for solving R t+k forward which had better bias properties for almost all correlations and horizons. Also of interest is that both forecasts appear to be unbiased when the unconditional correlation is zero, and that they make essentially the same forecast when the unconditional correlation is zero. While none of these two techniques signi…cantly outperformed the other, it would seem that a logical choice for forecasting would be the method that directly solves forward R t+k which appear easier to implement. Therefore, we will choose this second technique for further work.

Empirical application

The data

The data employed in this study are taken from Datastream and are the 4530 daily observations on the Nasdaq 100 (NAS), New York Stock Exchange composite (NYA) and Russell 3000 (RUA) stock returns over the period January 4, 1988 to December 21, 2005. The returns series denoted by r t are calculated as r t = 100 log (y t =y t 1 ) ; where y t is the price index: Models used are Full-BEKK(1,1), Diagonal BEKK(1,1), CCC(1,1)-GARCH and DCC(1,1)-GARCH where each of the univariate GARCH models estimated is a GARCH(1,1) and we focus our attention to the covariance matrix modelling.

Figures 1 and2 give the plots of the daily price indices and daily stock returns. We can see that the market volatility is changing over time which suggests a suitable model for the data should have a time varying volatility structure as suggested by the GARCH model.

Estimation results

For the above mentioned indices, the sample mean of returns, standard deviation of returns, skewness and kurtosis coe¢ cients as well as the Jarque-Bera and the Ljung-Box (univariate and multivariate version) tests are all reported in Table 1. Skewness is used to describe asymmetry from the normal distribution in a set of statistical data, taking two forms: positive or negative, it depends on whether data points are skewed to the left (negative coe¢ cient) or to the right (positive coe¢ cient) of the data average. Negative skewness means that there is a substantial probability of a big negative return, whereas positive one means that there is a greater than normal probability of a big positive return wich indicates that the tail on the right side is longer than the left one and the bulk of the values lie to the left of the mean. The kurtosis measures the peakedness and fatness of the tails of a probability distribution. A fat tailed distribution has higher than normal chances of a big positive or negative realization. For all series, the returns distributions display positive skewness. Moreover, the data indicates high degree of excess kurtosis (leptokurtic), since the kurtosis coe¢ cients are signi…cantly larger than those of a normal distribution which is three. The returns series appear extremely non normal based on the Jarque-Bera test. The Ljung-Box test applied to the series and squared series, provides clear evidence against the hypothesis of serial independence of observations and indicates the existence of ARCH e¤ect. The unit root tests of Phillips and Perron (1988), Kwiatkowski et al. (1992) and Dickey-Fuller Augmented (1979) reject the stationarity hypothesis at both 5% and 1% signi…cance levels for all series 18 .

The estimation of fractional integration parameter d based on the GPH procedure as well as the CCC and DCC -GARCH are given in Tables 2 and3 respectively. The results reveal a clear evidence of long-range dependence for all stock returns, since d estimates are signi…cantly positive implying covariance-stationarity of the process. These results are statistically signi…cant and contrast with most of the studies of long memory in asset returns which have generally found weak or no evidence for long memory. However, Henry (2002) investigated long range dependence in nine international stock index returns and found evidence of long memory in four of them, the German, Japanese, South Korean and Taiwanese markets, but not for the markets of the UK, USA, Hong Kong, Singapore and Australia 19 . Furthermore, [START_REF] Serletis | Mean reversion in the US stock market[END_REF] analyzed daily data on four US stock market indices and concluded that US stock market returns display antipersistence. This implies that the behaviour of stock returns is inconsistent with the e¢ cient market hypothesis, which asserts that returns of a stock market are unpredictable from previous price changes ( [START_REF] Narayan | Do shocks to G7 stock prices have a permanent e¤ect? Evidence from panel unit root tests with structural change[END_REF] and [START_REF] Narayan | Mean reversion versus random walk in G7 stock prices evidence from multiple trend break unit root tests[END_REF]).

Moreover, we observe that the correlations across the three stock returns give strong evidence of time-varying correlations between them. The last column of Table 3 present the results of the estimation of the DCC parameters. we note that the estimate of 2 is statistically signi…cant at 1% signi…cance level meaning that the correlation is signi…cantly time varying. The DCC parameters estimates imply a highly persistent correlation with b 1 and b 2 , however, they satisfy the 0 < b 1 + b 2 < 1 condition of stationarity. Thus, the model is mean reverting and the conditional correlation matrix is positive semi-de…nite. Apart the tables, we compute the Lagrange Multiplier statistic proposed by [START_REF] Tse | A test for constant correlations in a multivariate GARCH model[END_REF] for constant conditional correlation test for the trivariate model which is signi…cant at the 5% level: its p-value is 0:0001. Thus, there is evidence against time-invariant correlations among the selected stock returns. In Figure 3 20 , we observe a slow decay of the autocorrelation functions which indicate the presence of long memory behaviour. The plots of conditional variance of BEKK-GARCH models and CCC-GARCH are shown respectively in Figures 4 and5. To check the goodness of …t of our model, we consider several diagnostic tests on the standardized residuals, the Ljung-Box test for the 12-th order serial autocorrelation and heteroskedasticity, when it is applied on the standardized residuals. We use the Jarque-Bera test, the skewness and the kurtosis coe¢ cients to test the normality of standardized residuals. From Table 3, the multivariate portmanteau test reveal that the hypothesis of no residual autocorrelation is rejected in the residuals only for both Full and Diagonal-BEKK(1,1,1) models at 5% level of signi…cance. From Table 4, we can see that, for most series, the hypothesis of uncorrelated standardized and squared standardized residuals is well supported, indicating that there is no statistically signi…cant evidence of misspeci…cation. The skewness and kurtosis coe¢ cients indicate that the standardized residuals are still not normally distributed, which is con…rmed by the Jarque-Bera test. Finally, the hypothesis of no conditional heteroscedasticity are not rejected in the residuals for all the series at 5% level of signi…cance.

Forecasting performance of estimated models

The DCC model seems better with respect to the other models in terms of information criteria. So, in order to assess the out-of-sample forecasting performance for diagonal BEKK, CCC and DCC models, we still use root mean square error (RMSE) and mean absolute error (MAE) as two criteria for comparison. we have selected an out-of-sample forecast data set using the last 1000 observations of the original data. We have re-estimated the models adding a new observation and obtaining the k-day-step ahead forecasts for k = 1; 3 and 5. The results are shown in Table 5. They appear to show a trend that the forecasting errors are proportionate to the forecasted periods. Moreover, we draw clear inference to the e¤ect that they all appeared to be more accurate in DCC than in the other models, regardless of what criterion is adopted. This seems to be consistent not only in RMSE but also in MAE (the DCC model has the lowest RMSE and MAE). In addition, predicting results of CCC perform even worse than diagonal BEKK . The results successfully provide evidence in favour of the predictive superiority of the DCC model against the diagonal BEKK and CCC. We can thus conclude that the forecasts of the DCC modelling are signi…cantly better than those of the other model.

Conclusion

The aim of the present paper is to study the dynamic modelling of the US stock returns. We considered multivariate GARCH framework to model the time-varying covariance matrices of a process exhibiting a long term dependence and be used to produce out-of-sample forecasts. In particular, we examined the persistence phenomenon in the …rst conditional moment of daily stock returns; the robustness of the results was also investigated by considering that its innovations was generated by a multivariate GARCH process. As illustration, we applied our models to the trivariate systems.

The estimated parameters show that the returns series are characterized by long memory behaviour and time-varying correlations. These results are statistically signi…cant and contrast with most of the studies of long memory in the returns series showing weak or no evidence for long term dependence. Using daily returns of Nasdaq 100, New York Stock Exchange composite and Russell 3000, the results successfully provide evidence that DCC model outperforms the other ones in estimating and forecasting covariance matrices for out-of-sample analysis.

Figure 1 .Figure 2 .

 12 Figure 1. Daily price indices

Full BEKK( 1 , 1 , 1 )

 111 Diagonal BEKK(1,1,1) CCC-GARCH(1,1) DCC-GARCH[START_REF] Aydogan | Are there long cycles in common stock returns?[END_REF][START_REF] Aydogan | Are there long cycles in common stock returns?[END_REF]

Figure 3 .

 3 Figure 3. Autocorrelation of returns series

Figure 4 . 1 )Figure 5 .

 415 Figure 4. Conditional variance of returns series in BEKK(1,1,1)

  like the vech operator but it only selects the

	elements under the main diagonal, b z t = b R standardized residuals (under H 0 ), and D t = diag 1=2 b D 1 t b " t is the (n 1) vector of p h 11t ; p h 22t ; :::; p h nnt :

Table 1 .

 1 Basic properties of the distribution of returns series : denotes the sample mean, is standard deviation, k is the Kurtosis (exc), sk is the Skewness cor¢ cient, JB is the Jarque-Bera normality test, Q (12) and Q 2[START_REF] Cappiello | Asymmetric dynamics in the correlations of global equity and bond returns[END_REF] are respectively the 12-th order Ljung-Box tests for serial correlation in the residuals and squared residuals. Q m[START_REF] Cappiello | Asymmetric dynamics in the correlations of global equity and bond returns[END_REF] and Q 2 m (12) are multivariate Ljung-Box version. The number in parenthese are the p-values.

		NAS	NYA	RUA
		0:586	0:502	0:521
		0:545	0:508	0:516
	sk	2:065	2:882	2:705
	K	9:651	21:082	18:431
	JB	5:305e + 003 (0:000)	3:117e + 004 (0:000)	2:314e + 004 (0:000)
	Q (12)	313:787 (0:000)	166:785 (0:000)	141:769 (0:000)
	Q 2 (12)	220:788 (0:000)	52:357 (0:000)	57:845 (0:000)
	Q m (12)	931:965 (0:000)	-	-
	Q 2 m (12)	526:008 (0:000)	-	-

Notes

Table 2 .

 2 Estimation of the long memory parameter

		b d N AS	b d N Y A	b d RU A
	GPH	0:301 (0:049)	0:206 (0:050)	0:245 (0:052)
	Notes: GPH are the Geweke and Porter-Hudak (1983) procedure. The number in
	parenthese are standard errors.

Table 3 .

 3 Estimation of the MGARCH model

Table 3 .

 3 Continued

	Full BEKK(1,1,1)	Diagonal BEKK(1,1,1) CCC-GARCH(1,1) DCC-GARCH(1,1)
		0:849
	22	(0:072)
		0:021
	23	(0:082)
	31	0:011 (0:010)	-	-	-
		0:072
	32	(0:068)
		0:870
	33	(0:083)
	AIC	756:715	743:369	758:793	760:490
	BIC	621:363	511:044	699:117	698:454
	HQ	707:114	768:169	781:993	787:756
	Q m (12)	646:262 [0:000]	487:183 [0:000]	141:769 [0:481]	151:019 [0:399]
	Q 2 m (12)	423:541 [0:000]	361:060 [0:000]	85:242 [0:948]	99:283 [0:797]

Notes: The number in parenthese are standard error, ij is the correlation coe¢ cient, AIC; BIC and HQ are respectively the Akaike, Bayesian and Hannan-Quinn information criterion. Q m

[START_REF] Cappiello | Asymmetric dynamics in the correlations of global equity and bond returns[END_REF]

and Q 2 m (12) are respectively the 12-th order multivariate Portmanteau tests for serial correlation in the standardized and squared standardized residuals (null Hypothesis: no serial correlation). The numbers in brackets are the p-values.

Table 4 .

 4 Diagnostic testsNotes: k is the Kurtosis (exc), sk is the Skewness coe¢ cient, JB is the Jarque-Bera normality test, Q (12) and Q 2 (12) are respectively the 12-th order Ljung-Box tests for serial correlation in the standardized and squared standardized residuals (Null Hypothesis: no autocorrelation). LM is the test for ARCH E¤ects (Null Hypothesis: no ARCH e¤ects).

		Full BEKK(1,1,1)		Diagonal BEKK(1,1,1)
		N AS	N Y A	RU A	N AS	N Y A	RU A
	Q (12)	166:771 (0.000)	270:155 (0.000)	6:996 (0.857)	43:283 (0.00202)	9:720 (0.640)	12:224 (0.427)
	Q 2 (12)	5:301 (0.947)	1:393 (0.999)	11:843 (0.458)	20:662 (0.055)	16:073 (0.187)	37:287 (0.021)
	LM	6:204 (0.905)	2:776 (0.996)	11:760 (0.465)	7:236 (0.654)	2:939 (0.965)	3:197 (0.805)
	sk	1:889	2:926	2:722	0:753	1:006	0:410
	k	6:969	19:891	16:882	4:456	21:923	17:2967
	JB	5449:493 3724:512 2725:128	380:193	31340	17700
		CCC-GARCH(1,1)		DCC-GARCH(1,1)
		N AS	N Y A	RU A	N AS	N Y A	RU A
	Q (12)	45:318 (0.0009)	0:838 (0.999)	1:066 (0.999)	8:735 (0.725)	5:711 (0.901)	5:390 (0.949)
	Q 2 (12)	8:758 (0.723)	0:012 (1.000)	0:013 (1.000)	4:491 (0.972)	1:593 (0.997)	1:690 (0.995)
	LM	0:9395 (0.998)	0:0027 (1.000)	0:0035 (1.000)	0:229 (1.000)	1:176 (0.999)	1:197 (0.998)
	sk	1:877	2:896	2:717	1:904	3:141	2:936
	k	5:994	18:415	15:870	6:817	24:626	21:209
	JB	4333:862 32283:720 24376:48	5283:913 55953:071 41956:369

Table 5 .

 5 Out-of-sample forecast

		Diag BEKK	CCC	DCC
	1	0:506	0:783	0:429
	RM SE 3	0:545	0:785	0:445
	5	0:611	0:790	0:478
	1	0:359	0:452	0:318
	M AE 3	0:368	0:457	0:329
	5	0:389	0:460	0:361

The R=S statistic is the range of partial sums of deviations of a time series from its mean, rescaled by its standard deviation.

For more details, see[START_REF] Sowell | Maximum likelihood estimation of fractionally integrated time series models[END_REF] and[START_REF] Gil-Alana | A fractional multivariate long memory model for the US and the Canadian real output[END_REF]-2007).

See Ding et al.(1993) and Doukhan et al.(2003).

See also[START_REF] Silvennoinen | Numerical aspects of the estimation of multivariate GARCH models[END_REF].

[START_REF] Bauwens | Multivariate GARCH models: A survey[END_REF] propose a scalar BEKK model, where A kj and B kj are equal to a scalar times a matrix of ones to reduce also the number of parameters.

See also[START_REF] Sheppard | Multi-step estimation of Multivariate GARCH models[END_REF].

For more details see[START_REF] Francq | Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors[END_REF].

The results are not reported here to conserve space but are available from the authors upon request.

See also[START_REF] Aydogan | Are there long cycles in common stock returns?[END_REF].

R11, R12 and R13 is respectively the returns series of NAS, NYA and RUA.

Acknowledgement

I would like to thank Anne Peguin and Mohamed Boutahar for their useful comments on an earlier version of this paper. I'm especially grateful to the anonymous reviewer and the editor (P.K. Narayan) for their detailed comments and numerous suggestions that helped to improve the paper. Any errors and or omissions are, however, are my own.


Hervé Aubert
email: aubert@enseeiht.fr

RFID Technology for Human Implant Devices Technologie RFID pour implants dans le corps humain

This paper presents an overview on Radio Frequency Identification (RFID) technology for human implants and investigates the technological feasibility of such implants for locating and tracking persons or for remotely controlling human biological functions. Published results on the miniaturization of implantable passive RFID devices are reported as well as a discussion on the choice of the transmission frequency in wireless communication between passive RFID device implanted inside human body and an off-body interrogator. The two techniques (i.e., inductive coupling and electromagnetic coupling) currently used for wirelessly supplying power to and read data from passive implantable RFID device are described and some documented biomedical and therapeutic applications of human RFID-implant devices are finally reported. Résumé -Cet article dresse un état de l'art sur la technologie des puces RFID implantées dans le corps humain. Il explore la faisabilité d'implants permettant de localiser en temps réel des personnes ou encore de contrôler à distance les fonctions biologiques du corps humain. Des résultats sur la miniaturisation des puces RFID passives et implantables dans le corps sont présentés. Des considérations sur le choix de la fréquence de la communication sans fil entre l'implant RFID et son lecteur sont formulées. Deux techniques usuelles (à savoir le couplage inductif et le couplage électromagnétique) pour alimenter sans fil et à distance l'implant RFID passif et pour lire les données de l'implant sont décrites. Des applications biomédicales et thérapeutiques des implants RFID sont finalement données.

I. Introduction

Implantable Radio Frequency Identification (RFID) devices are known as a technology for the remote identification (tagging) of animal or persons. A classical example of human identification based on RFID-implant is given by the VeriChip tag (11 mm long and about 1mm in diameter) which contains numerical code (identifiers) readable at 10 centimeters or less using a handheld reader [START_REF] Foster | IEEE Spectrum: RFID inside[END_REF]]. When illuminating by the low-frequency magnetic field (134 KHz) generated by the reader, the RFID tag powers itself up and transmits a 16-digit code that is unique to the tag. Recent developments in RFID technology have opened up new potential applications, where RFID devices are implanted in the human body for locating and tracking persons or for remotely controlling human biological functions. Such applications may raise ethical and juridical problems, but these are outside the scope of the present survey. In this paper only the advances and challenges in RFID technology for human implant devices are reported.

Sub-micron sized "spychip" implant connected to the Global Positioning System (GPS) is not achievable using the nowadays technology. A GPS device that would be required for the real-time tracking on earth presents dimensions that are too large for implanting inside human body. Miniaturization of such device for building a "rice-grain-sized GPS" implant is a very challenging technological issue that has to be solved before addressing the feasibility of "Human implant Personal GPS Tracker" [START_REF] Masters | Humancentric Applications of RFID Implants: The Usability Contexts of Control, Convenience and Care[END_REF]].

RFID technology for human implants is generally based on battery-less (passive) devices and allows achieving very short read range, typically 10cm or much less (see, e.g., [START_REF] Freudenthal | [END_REF]). Consequently RFID implants cannot communicate with GPS satellites (or other equivalent satellite-based positioning system) that would be required for the real-time tracking of a person. RFID technology is then not suitable for the realtime tracking of a person anywhere on the planet through RFID-chip deeply implanted in his body.

The remote control of human biological functions by using RFID technology seems to be more realistic. Following the estimations of Burke et al. [Burke 2009], a single chip (including antenna) radio system with on-board sensors of size 100 × 100 × 1 μm 3 seems to be feasible with available technology. Consequently, the wireless communication with small RFID implants in humans for reading information about chemical or physical quantity in biological systems or for providing the remote activation/deactivation of biochemical activity inside a single living cell seems to be "not completely out of reach" [Burke 2009]. Moreover, using nanotechnology, Jensen et al. [START_REF] Jensen | [END_REF]] have reported the fabrication of a FM-radio using a single nanotube of 1μm length and 10nm width. The nanotube radio could be inserted inside the living human cell to give a subcellular remote and real-time controlled interface [Kumar 2008]. This recent result in miniaturization of radio-chip could also find application in fabrication of smartdusts [START_REF] Cook | [END_REF]], i.e., tiny objects with sensing and communication abilities that may be massively distributed over some area for the remote tracking of human presence/displacement [START_REF] Warneke | [END_REF]] (recent review presented in [START_REF] Michael | Smart dust: nanostructured devices in a grain of sand[END_REF] discusses various techniques to take smartdust in sensor network beyond millimeter dimensions to the micrometer level). Another application could be on the fabrication of the very small physiological sensors implanted in human and communicating with a single central unit in Wireless Body Area Networks (WBAN) [Chen 2010].

Using current technology, a RFID device implanted inside the human body and wirelessly communicating with an off-body (or body-worn) reader can be very small and passive (see Section II): the smallest reported passive RFID device operating at 2.45GHz occupies an area of 400 x 400 m 2 [Usami 2004] (see Section III) while, at 13.56MHz a RFID device with an area of 2.5 x 2.5 mm 2 is available [Maxell 2010]. However the wireless communication with passive RFID device implanted inside the human body is generally performed at very short range. Based on inductive coupling (in free space) this range was measured to be 1cm at 13.56MHz [Lu 2007] [Sasaki 2007] and shorter than 1mm at 2.45GHz [Guo 2006] [ Chen 2008] (see Section IV.1). Based on electromagnetic coupling (in free space) this range is between 1m to 15.7m at 900MHz and may reach 7.5cm at 5.8GHz [Radiom 2010] (see section IV.2). For small passive transponders (2mm x 10 mm) deeply implanted in the human body (at 10cm to 30cm in depth) and power supplied by inductive coupling at 13.56MHz, the read range was found to be shorter than 10 cm from the body [START_REF] Freudenthal | [END_REF]].

This paper presents an overview on RFID technology for human implant devices. Section II reports the technical requirements that human implants having sensing and communication abilities have to satisfy. Justifications for the use of passive RFID devices implanted inside human body for achieving the remote electronic control at bio-molecular scale level conclude Section II. Section III is devoted to documented results on the miniaturization of RFID devices, while Sections IV.1 and IV.2 report wireless techniques for powering such devices. A discussion on the choice of the transmission frequency in wireless communication between RFID device implanted inside human body and an offbody interrogator is given in Section IV.3. Nowadays RFID devices implanted in the human body are expected (1) to transmit measurements of chemical or biological data inside the body and (2) to monitor biological activity or physiological functions of the human. Some published biomedical and therapeutic applications of human RFID-implant In-vivo implants have to be as small as possible. Moreover, it may be impractical to use a battery for supplying power to an electronic device injected into the body: the large size of batteries compromises their utilization and a passive (also called battery-less or fully autonomous) device may be preferred in practice. Another requirement concerns the selectivity of the remote control of human biological functions. For example, the remote control of a specific bio-molecular event inside a living cell has to be spatially localized for unaffecting other biological activities in the cell. Additionally bio-compatible material has to be used for fabricating the implant device and its packaging in order to avoid tissue reactions. Eventually, undesirable migration of the device inside the body has to be controlled or avoided.

Moreover secure and reliable wireless transmission of the personal/confidential data recorded by the device inside the body has to be established. Guaranteed confidentiality and high reliability are certainly among the main criteria that must be given priority to implement such wireless technology. Finally, for safety issues related to antennas implanted in human tissue, electromagnetic energy radiated (or backscattered/reradiated) by an implant device for wirelessly communicating with the outside world must respect the IEEE human tissue exposure standard [IEEE 1999][IEEE 2002]. To satisfy safety recommendations, an implantable antenna operating at 868 MHz when placed inside tissue layers has been designed in [Sani 2010] to ensure a Specific Absorption Rate (SAR) lower than 2 W/kg. In [Kim 2006] implantable antennas have been designed

for operating at the Medical Implant Communications Service frequency band (402-405

MHz), which is regulated by the Federal Communications Commission and the European Radiocommunications Committee for ultra-low-power active medical implants. To satisfy the recommendations of these institutions, antennas allowing a peak SAR lower than 1.6mW/g have been designed (estimation of the SAR in practical applications may be found in [Kim 2006]).

II.2 Remote control of molecular scale biochemistry

The first attempt to demonstrate the feasibility of the remote electronic control at biomolecular scale level has been reported in 2002 by Hamad-Schifferli et al. [Hamad-Schifferli 2002]. The control of the hybridization behavior of DNA molecules has been performed by monitoring the heating of gold nanoparticles interfaced (linked) to DNA.

Such local controlled heating performed by electromagnetic coupling at 1GHz induces the reversible hybridization/dehybridization of the DNA while leaving surrounding molecules relatively unaffected. Although the physics of heating nanometer particles has been little

explored [START_REF] Hanson | [END_REF]] and will certainly be the subject of future investigations, this experiment demonstrates for the first time the direct radio-frequency (RF) control over biomolecular machinery in a specific and fully reversible manner. Remote control at such very small scale level seems to not alter bio-molecular events occurring in the surrounding medium.

A discussion of the technological feasibility of tiny devices implanted inside a living cell for the remote control of a wide range of biological functions or the detection of presence or concentration of a protein or antibody can be found in [Burke 2009]. Based on known technological achievements and patents in nanoelectronics a "nanorobot" consisting in embedded smart sensors implanted in human body for tele-operated surgical procedures or early disease diagnosis has been designed in [Cavalcanti 2007]. Up to now, such nano-devices have not been fabricated.

II.3 RFID Technology for human implant devices

Basically, RFID is a technology that uses communication via electromagnetic waves to exchange data between an interrogator (also known as the reader) and an object called the transponder for identification and tracking purposes. The transponder is generally composed of an integrated circuit for storing and processing the data signal and an antenna for receiving and transmitting the signal [Finkenzeller 2003]. Such technology may fulfill the technical requirements listed Section II.1. Fabrication of very small RFID device with communicating ability is achievable (see Section III) and, following the recent estimations of Burke [Burke 2009], it appears technically possible to fabricate RFID device at the bio-molecular scale that interrogates its local chemical environment (sensing) or/and controls the biological machinery inside a single living cell. The remote monitoring at such a very small scale level is assumed to provide the selectivity requirement, that is, the local control of bio-molecular machinery without damaging cells or even affecting the biological events in the surrounding medium. New manufacturing techniques at nano-scale level may help to miniaturize RFID devices.

It may allow, for example, exploring the feasibility of very small antenna by using a carbon nanotube (overview of the high-frequency properties nanotube and nanowire technology for microwave applications can be found in [START_REF] Burke | [END_REF]). It reaches its maximum value at resonance frequency. In Eq. ( 1), I denotes the magnitude of the time-harmonic current in the interrogator coil, 2f is the radian frequency of the transmission. The coupling coefficient

I R r C L 1 C r R L L L k V 2 T 2 2 2 2 2 T 2 2 1                          (1) M I L 1 , r 1 L 2 , r 2 C R T V R I V I
2 1 L L M k 
between the two coils depends on the distance d between the transponder coil and the interrogator coil. In practice this coefficient is close to 10 -3 (e.g., k = 4 10 -3 at a distance d = 5 mm and k= 1.5 10 -3 at d=1 cm in [Lu 2007]). The voltage V given by Eq (1), once rectified and smoothed with a regulator, is used for supplying power to the IC. It must be large enough to operate this circuit. For a given distance d between the two coils, this condition allows to derive the minimum magnetic field that must be generated by the interrogator coil.. This field decreases rapidly with distance inside the near field region (as 1/d 3 where d designates the distance from the center of the interrogator coil to the transponder coil [Finkelzeller 2003]) and consequently, when the two coils are separated, it may rapidly become too weak for providing the transponder with the energy it needs to operate. From [Lu 2007], at a frequency f=13.56 MHz, voltages V ≈ 1 Volt (required for operating the RFID IC) may be induced in a small implantable transponder coil L 2 ≈ 100nH from an interrogator coil L 1 ≈ 1 H located at a distance d smaller than 1 cm.

Lu et al. [Lu 2007] have recently reported wireless communication with implantable RFID device (occupying approximately 25 mm 3 in volume) in the frequency range of 13.56-27 MHz at a distance of 1 cm. A successful wireless communication at 13.56MHz has also been established by [START_REF] Sasaki | Batteryless-Wireless MEMS Sensor System with a 3D Loop Antenna[END_REF]] at the same distance. Guo et al. [Guo 2006] have reported a successful communication with a small 2.45GHz RFID device (with a chip-area of 1 mm X 0,5 mm) at a distance of 1 mm. The design of a 2.45-GHz RFID device with its on-chip antenna smaller than 0.5 mm 2 with a thickness of 0.1 mm is reported in [Chen 2008]: with the reader generating an output power of 500mW, the RFID system was able to perform with RF read/write functions at a distance smaller than 0.5 mm.

IV.2. Electromagnetic coupling

The technique based on electromagnetic (or far field) coupling involves the use of electromagnetic waves that propagate from the antenna in the far field region to power the passive RFID chip. To transmit data, the IC changes the impedance of the transponder antenna which backscatters some of the incident RF energy to the interrogator. Figure 2(a) shows the constitutive elements of the RFID system based on such a coupling. In free-space, the electromagnetic power P rect received by the transponder antenna (gain G T ) is given by [Balanis 2005]:

I T 2 I rect P G d 4 G P          (2)
where P I designates the power transmitted by the interrogator antenna (gain G I ),  is the free-space wavelength and d denotes the distance between the interrogator and transponder antennas (polarization mismatch between antennas is assumed negligible . This can be obtained by choosing appropriate antenna orientation). The attenuation

factor 2 d 4       
 is called the free-space path loss. The power P R back-scatters by the transponder is given by [Balanis 2005]:

    I 4 3 2 I 0 R P d 4 G P     ( 3 )
where  designates the radar cross-section of the transponder, that is, the efficiency with which the transponder reflects incoming electromagnetic waves. As it can be observed from Eq.( 3), power is strongly attenuated by a factor 1/d 4 (in free-space) when it returns back to the interrogator. The range of the wireless reading of the transponder data can be derived from the interrogator sensitivity P Rmin , Systems based on electromagnetic coupling operate usually at UHF frequencies of 868MHz (Europe) and 915MHz (USA) and at microwave frequencies of 2.5GHz and 5.8GHz [Finkelzeller 2003]. Jia et al. [Jia 2008] have reported a RFID humidity sensor capable of passive wireless sensing at 868 MHz. The reader antenna was positioned at a fixed distance of 1.5m in front of the RFID chip. Very recently, a great improvement with respect to performances of existing passive UHF/microwave RFID chip has been reported in [Radiom 2010]: a fully integrated and implantable 900MHz RFID chips has been fabricated and the measured range is found to be 15.7m, assuming an off-chip G T =0dB antenna gain, while the device with its on-chip antenna operating at 5.8GHz can be read and powered-up up to 7.5cm distance.

A passive RFID device incorporating sensor based on electromagnetic transduction has been recently proposed in [START_REF] Jatlaoui | [END_REF] However the read range associated with LF (135 KHz) RFID implant is generally shorter than 1m due to rapid attenuation of the magnetic field with distance (see Section IV.1) and the necessarily small cross-sectional area of implanted transponder coil antenna.

Moreover the bandwidth of LF RFID chip is very small. This technical characteristic implies: (1) very slow data rates (low data transfer), (2) inability of the interrogator to read simultaneously multiple RFID implant devices, (3) vulnerability to transmission collapse in presence of strong environmental electrical noise (lack of robustness and reliability of the wireless link) and ( 4) difficulty to incorporate any cryptography in the transmitted signal (lack of security/confidentiality of the data transfer, although the very short range associated with such close coupling systems could be interesting for achieving secure transmission).

In [START_REF] Freudenthal | [END_REF]] the authors investigate the effectiveness of High Frequency (HF)

waves for communicating with implanted devices. Considerations that may justify the use of HF RFID for implanted medical applications can also be found in and thus are suitable for communication with RFID devices implanted inside the human body [Villancourt 1997]. Experiments performed at 4MHz emulating the human tissue electrical properties by introducing water bearing colloids between coils of the inductive coupling RFID system have revealed a small decrease in the amount of power transmitted by the interrogator to the transponder [Sauer 2005]. This attenuation was not large enough to cause data or power flow disruption or to lower the power supply voltage below the IC operating range. The read range of such HF inductive coupling system was then found to be quite the same than one observed in free space environment (that is 1 cm at 13.56MHz and shorter than 1mm at 2.45GHz). Moreover successful wireless communication with ten HF RFID devices (each one occupying an area of 2 x 10 mm 2 ) implanted at three locations within a human body (at 10cm to 30cm in depth) has been established in [START_REF] Freudenthal | [END_REF]]. It has been observed that deeply implanted transponders may be read at distance of 10 cm from the body, i.e., at distances-to-transponders similar to those observed for non implanted transponders.

From the review of state of the art it can be observed that inductive coupling operating in HF (13.56 MHz and below) frequency range is now one of the most common methods to wirelessly send power and data from off-body interrogator to RFID device implanted inside human body. In 1988, the design of millimeter-and sub-millimeter-sized power sources operating at 2MHz and 20 MHz for neural implant based on inductive coupling has been proven feasible [Heetderks 1988]. Power harvesting of implanted devices through inductive coupling has been successfully performed for various applications, e.g, for recording the neural signals from axons by using implanted telemetry system occupying an area of 4 x 6 mm 2 and operating at 2 MHz [START_REF] Atkin | [END_REF]], for wireless implantable neural micro-stimulation system [Ghovanloo 2004b], or for replacing defective photoreceptors in patients by implanting a retinal chip that achieves the transmission link between the extra-ocular and intraocular coil antennas at a frequency ranging from 1 to 10 MHz [Liu 2000].

Ultra-High Frequency (UHF) RFID device offers significantly higher bandwidth than LF or HF RFID. This allows, e.g., high data rates and the incorporation of privacy/integrity preserving cryptographic protocols for wireless transmission in order to protect information [Juels 2006]. Moreover, using UHF electromagnetic waves, high level of miniaturization of RFID chip (including its antenna) can be achieved (see Section III).

However UHF waves may be problematic for human RFID implants, due to the following reasons: (1) UHF and microwave fields are strongly attenuated by water (which is the primary constituent of human tissue) and consequently a passive RFID solution allows a very limited communication range (typically shorter than 1 m); (2) the UHF field (3) HF frequencies (in particular 2.45 GHz) may be unsafe for human for long-term exposure and/or when high electromagnetic densities are involved.

In the UHF band the human body, essentially composed of water, bones and tissues, can be viewed as a highly scattering and dissipative electromagnetic propagation channel in which multiple reflections (multi-paths) and strong attenuation occur. Specifically input impedance and radiation pattern of the transponder antenna may depend on the location of the antenna implanted inside the body [Kim 2006]. In order to perform an analysis of the UHF wireless communication efficiency and to analysis electromagnetic characteristics of antennas implanted inside the human body, a realistic electromagnetic model of the human body (with its various tissues and geometries) has to be elaborated. It will allow designing a reliable wireless communication system between a RFID device implanted inside human body and an off-body interrogator. The propagation analysis of UHF electromagnetic field in muscle tissue has been presented in [Arumugam 2008] while in [Kim 2006] [Sani 2010] the authors analyze the antenna performances (efficiency, radiation pattern, and input impedance) when implanted in human body or in an equivalent simplified tissue model. In [Kim 2006] it is observed that the return-loss characteristics of 400MHz antennas change with the location of the antennas inside the tissue-simulating fluid. The resulting range of the wireless communication with an UHF RFID-implant may then be greatly dependent on the implant location in human body.

At an operating frequency between 915MHz and 1GHz wireless communication between a transponder antenna and an interrogator antenna separated by 15mm of bovine muscle tissue has been established by [O'Driscol 2009]. In [Warty 2008] communication between antennas positioned below the scalp covering the frontal region of the skull was presented and the effect of the antenna packaging on the impedance matching of an implanted antenna was also analyzed. Using an inductively powered and implantable wireless neural recording device working at 3.2GHz, the in-vivo continuous recording continuous of Electro-Encephalogram from the hippocampus of an un-tethered rat is 2006]. An array of 16 activated iridium microelectrodes (5-6 mm in length within a cluster approximately 1.8 mm in diameter) suitable for long-term implantation into the brain, records signal from single neurons, and delivers as well localized microstimulation.

These microelectrodes may also be used therapeutically [START_REF] Freudenthal | [END_REF]]. However such therapeutic applications of RFID implants are still at the proof of concept stage. The benefits of such technology in terms of, e.g., improvement of quality of living or of patient care, have to be demonstrated.

VI. Conclusion

RFID technology has opened up new expectations in the fabrication of tiny devices implanted in the human body for locating and tracking persons or for remotely controlling human biological functions. A RFID-chip implanted inside the human body can transmit its data to an off-body interrogator at very short distance (typically 10cm or less). It cannot communicate, e.g., with GPS satellites (or other equivalent satellite-based positioning system) that would be required for the real-time tracking of a person. RFIDtechnology is then not suitable for the real-time tracking of a person anywhere on the planet through RFID-chip deeply implanted in its body. However, a RFID-based remote and reversible control of human bio-molecular machinery seems to be not completely out of reach using existing technology [Burke 2009]. The recent advances in fabrication of radio-chip at nano-scale level [START_REF] Jensen | [END_REF][START_REF] Rutherglen | Carbon nanotube radio[END_REF] may help the advent of nano-scale RFID chip. Due to their small size, such device could be inserted inside the human living cell to provide a sub-cellular remote controlled interface.

Comptes rendus à l'Académie des Sciences Special issue on nanosciences/nanotechnologies March 1st, 2011 Hervé AUBERT Many technological problems have to be solved for demonstrating the feasibility of the reliable remote control of human bio-molecular machinery using RFID implants: heat removal and elaboration of bio-compatible miniaturized packaging are two of them [O 2005]. Other questions have to be addressed: Could new power harvesting technique based on the properties of surrounding human tissue be exploited for supplying power to RFID devices implanted inside the body? Would electromagnetic fields transmitted by nano-radio implant damage surrounding tissue? Despite very promising recent technological advances, many challenges must be addressed for clearly validating the expected benefits of RFID-implant technology.

Figure 1 :

 1 Figure 1 : RFID system based on inductive coupling: (a) Constitutive elements and (b) equivalent circuit

Figure 2 :

 2 Figure 2 : Constitutive elements of a RFID system based on electromagnetic coupling

  ][Jatlaoui 2008][Jatlaoui 2009]. By using this device wireless data transmission and measurement of the physical quantity (e.g., pressure, temperature, gas concentration) can share the same electromagnetic wave. No electronics, no rectifier and no IC are needed and consequently, the overall RFID device losses are minimized. This allows transmission ranges of some tens of meters. Based on this technique, passive RFID devices incorporating pressure sensor [Jatlaoui 2008b][Jatlaoui 2009b][Jatlaoui 2009c][Jatlaoui 2009d][Jatlaoui 2010][Jatlaoui 2010b], temperature sensor [Thai 2010][Thai 2010b] or gas concentration sensor [Hamida 2010][Hamida 2010b][Hamida 2009][Hamida 2009b][Hamida 2009c] have been successfully tested. IV.3 Frequency and read range in wireless communication between RFID device implanted inside human body and an off-body interrogator Low frequency (LF) electromagnetic waves are not strongly attenuated by human tissues.

  Moreover RFID technology allows real-time remote monitoring of fully autonomous implants in human body (see Sections IV.1 and IV.2). In the power harvesting technique based on inductive or electromagnetic couplings, the RFID implant receives power from the interrogator and emits back to it a signal that contains data. For such passive solution RF power deposition inside tissue can be easily made compliant with safety regulations mentioned in Section II.1. In addition some technical requirements, relative to the fabrication of bio-compatible implant devices and to the establishment of secure and reliable wireless transmission of data recorded by implants, have already been addressed in the framework of RFID technology and preliminary solutions have been found (see e.g.,[Ricardi 2003] and[Sauer 2005]). The read range of communication for RFID implanted in human body is found to be shorter than 10 cm (see Section IV). Such short read range could be advantageous when RFID implants are subject to security/confidentiality requirement.

	Comptes rendus à l'Académie des Sciences Special issue on nanosciences/nanotechnologies March 1st, 2011 Hervé AUBERT Chip (operating at 13,56MHz) including coil antenna (1.5 mm 2 ), RF communication and digital processing within a surface of 16 mm 2 (including pads) while Maxell Corp. [Maxell 2010] has reported an OCA designed on a chip area of 2.5mm x 2.5mm. At the same operating frequency, a mini-RFID transponder occupying an area of 8 x 3 mm 2 (and a volume of 25 mm 3 ) has been recently published in [Lu 2007]. At 2.45GHz, a RFID chip-area of 1 x 0,5 mm 2 has been reported [Guo 2006], while using 0.18m CMOS technology, Usami et al. have presented in 2004 a smaller RFID chip occupying an area Special issue on nanosciences/nanotechnologies March 1st, 2011 of 400 x 400 m Comptes rendus à l'Académie des Sciences Hervé AUBERT
	6 7

III. Technological results on the miniaturization of RFID devices

From the review of the state of the art it can be observed that size of single chip RFID transponders with available technology is dominated by the antenna size and not by one of the integrated circuit (IC) used by the RFID transponder for storing and processing the data signal. The smallest size of the IC is 50×50×5μm 3 without antenna, i.e., for an offchip antenna

[START_REF] Usami | [END_REF]][Hitachi 2007[START_REF] Usami | [END_REF]

]. However, using either electromagnetic waves or inductive coupling for powering passive RFID device (see Sections IV.1 and IV.2) an off-chip antenna is typically cm in size. Smaller RF antennas (typically few mm by a few mm in size) can be fabricated when incorporating antenna on the same chip as the signal processing components (on-chip antenna or OCA). Using 0.25m CMOS technology Abrial et al.

[Abrial 2001

] have reported in 2001 a System-On-2 only

[Usami 2004] [Usami 2004b][Usami 2006

]. Using existing CMOS technology, Burke et al. estimate that the fabrication of a RFID-chip volume of 100 × 100 × 5 μm 3 "is not completely out of reach"

[Burke 2009

].

  For biomedical applications RFID-implant devices are expected to transmit various chemical or biological parameters measured inside the body. Such devices can be used by diabetes sufferers [M-Biotech]: a wireless alarm unit implanted in the abdominal region of the patient, continually reads the data of a sensor chip sensitive to glucose concentration of surrounding fluids. Recently, Sauer et al. [Sauer 2005] have used RFIDimplant technology for in vivo data collecting and wirelessly transmission of electroencephalograms taken during animal recording. For therapeutic applications RFID-implant devices are expected to monitor biological activity or physiological functions of human body and to modify them. Example is provided by the monitoring of brain function via implanted probes implanted that communicate via a transponder embedded within the skull [McCreery 2006b][McCreery

	Comptes rendus à l'Académie des Sciences
	Special issue on nanosciences/nanotechnologies
	March 1st, 2011
	Hervé AUBERT
	V. Biomedical/therapeutic applications of human RFID-implant devices
	possible [Irazoqui-Pastor 2003].
	14


Françoise Bodénan

Christine Bourgel

Perrine Chaurand

Gilles Franceschini

Marc Gamet

Mathieu Gautier

Francois Hanrot

Nour-Eddine Menad

Isabelle Moulin

Jacques Poirier

Recycling physically sorted steelworks slag for the metallurgical and cement industries: conclusions of the ORLA research project

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The "ORLA" research project is attempting to evaluate the pathways and limitations of recycling steelworks slag through sequential physical sorting. The objective was to concentrate two distinct fractions; one comprising the iron-bearing slag for intra-steelworks recycling, and the other the calcium-and calc-silicate-bearing slag for cement-plant recycling. The main minerals associated with the slag -Fe, substituted wustite and calcium ferrite, free lime and magnesia, calcium silicates-were studied in particular with respect to:

-crystallite size in terms of the liberation mesh for sorting and the possibility of a size increase through cooling; -the presence of free lime (even MgO) associated with the carbonation and hydration phenomena, as this penalises the tests themselves and potentially generates swelling in the relatively long term where the cement industry is concerned; -evaluating the phosphorus content and speciation, mainly in calcium silicates, which primarily penalises the cement industry. Batches of slag were prepared that were representative of a steelworks' annual production. The applied techniques showed the scrap to have a good grindability but a limited magnetic separation -the most effective method -due to the highly interlinked mineral phases and a ferric carrier liberation mesh often well below 100 µm. The dry and wet processes were assessed for their advantages and drawbacks in terms of recycling paths. Thermodynamic calculations and both laboratory and full-scale cooling tests have made it possible to determine the crystallisation sequences and the size limitations available for cooling. Cementitious formulas were developed for evaluating the cement-slag substitution capacities associated with current regulatory tests; the tests are encouraging. Ion incorporation [PO 4 3-] in the C3S-then C2S-type calcium silicate networks, which is dependent on the slag temperature, in fact pertains to distinct concentrations (application of standard tools -XRD, SEM-EDS, EMP: element mapping and WDS). More detailed studies, using XR µ-Fluorescence and P µ-Xanes on the slag and NMR of P and Si on synthetic samples, have indicated the presence of calcium phosphate microdomains. All the results have made it possible to validate realistic assumptions for recommending a life-cycle analysis of the two channels, thus confirming the interest of the approach in a scheme of CO 2 -emission reduction and the use of secondary raw materials. hal-00599322, version 1 -9 Jun 2011

  Recycling physically sorted steelworks slag for the metallurgical and cement industries: conclusions of the ORLA research project BRGM : F. Bodénan, N. Menad, M. Save, M. Gamet P. Piantone ArcelorMittal : G. Franceschini, F. Hanrot, CEMHTI : M. Gautier, C. Bourgel, J. Poirier, CEREGE : P. Chaurand, J. Rose, LERM : I. Moulin, N. Rafaï,