Refk Selmi

Jamal Bouoiyour
email: jamal.bouoiyour@univ-pau.fr

Amal Miftah
email: miftah_amal@yahoo.fr

China's "New Normal" : Will China's growth slowdown derail the BRICS stock markets ?

Keywords: China's growth slowdown, BRICS stock markets, scale-on-scale analysis. JEL codes : F36, G11, G15

After four decades of impressive performance, China's economic expansion has begun to slow. Considering the growing China's integration in global financial, we examine the effect of heightened uncertainty surrounding the China's transition to the new growth model on the remaining BRICS (in particular, Brazil, Russia, India and South Africa) stock markets. This analysis is novel in its methodological approach, which is conducted to pinpoint the dynamic spillover effects as alternative to the time and frequency. The impact of China's growth slowdown is found to be heterogeneous across the BRICS stock markets, suggesting that this crisis does not affect return dynamics in these markets in a uniform way. More specifically, South Africa hasn't been rattled as badly as Brazil, Russia and India. The intensity of bilateral trade and investment relationships, the position of market in terms of regulation and securities exchanges, the financial system efficiency and the ability of countercyclical policies to cope with the severe downturn have been put forward to explain the heterogeneous responses of BRICS equities.

Introduction

China's real GDP growth is slowing sharply from an average of about 10 percent between 1980 and 2013 to 7 percent between 2014 and 2016.In the past, China largely benefited from an increasing workforce, which stimulated GDP especially because younger workers tend to be more productive than older ones. However, since 2012 the working-age population started to shrink, the inevitable outcome of the "one child" policy, which was approved in 1979. The noticeable drop in growth rates is partly due to this demographic winnowing. Increasing wages pose another potential challenge. Chinese wages now exceed those of most other emerging market economies, making China a less attractive destination for foreign investors. And this growth slowdown is widening and that is likely to continue, amid recent trade tensions with the United States.

A decline in domestic demand in China can harmfully affect the world economy and slow down global economic growth. The United States is one of the countries that is likely to be adversely influenced by the Chinese economy's downturn. China is the U.S. biggest import partner whose imports were approximately $505.5 billion as of 2017 or nearly22% of the total imports of the United States. In light of these considerations, the future performance of the Chinese economy can bring about huge spillovers to other systemic economies as well as its potential trading partners. Given the emergence of China as a key driver of the global economy and its power in the world, it is highly expected that a faltering pace of China's economic growth may be a source of structural break in the international stock market integration; hence a fundamental purpose of this study is to address whether the deepening Chinese slowdown exacerbate risk spillovers among other BRICS (i.e., Brazil, Russia, India, and South Africa 2 ) stock markets. The existing investigations are likely to be qualitative and/or descriptive, for example, reports by International Monetary Fund (2015) and IMF Asia and Pacific Department Regional Economic Outlooks (2014). This idea is recognized by the fact that most of empirical research supports evidence that stock returns are positively related to economic activity and has a good power in predicting output growth (inter alia: Fama 1990, Galliger 1994[START_REF] Mauro | Stock returns and output growth in emerging and advanced economies[END_REF], [START_REF] Kim | The stock return-inflation puzzle and asymmetric causality in stock returns, inflation and real activity[END_REF][START_REF] Chen | Nonlinear Casual Nexus between Stock Prices and Real Activity: Evidence from the Developed Countries[END_REF][START_REF] Croux | Do stock prices contain predictive power for the future economic activity? A Granger causality analysis in the frequency domain[END_REF], Bouoiyour and Selmi 2018).Notably, most of the studies has investigated the stock returns-real activity relationship for developed countries (for example, Canova and Nicolo 1995, [START_REF] Croux | Do stock prices contain predictive power for the future economic activity? A Granger causality analysis in the frequency domain[END_REF]Reusens 2013, Chen and[START_REF] Chen | Nonlinear Casual Nexus between Stock Prices and Real Activity: Evidence from the Developed Countries[END_REF]. Because of the increasing speed of globalization, liberalization of capital movements, securitization of stock markets and the emergence of new equities, particularly in the Asian region, traders, investors and regulators become more interested by the responses of output growth to stock returns in emerging countries (see, for instance, [START_REF] Christoffersen | Do asset prices in transition countries contain information about future economic activity?[END_REF], Maysami et al. 2004[START_REF] Chen | Have China's enterprise reform led to improved efficiency and profitability[END_REF][START_REF] Deb | Does Stock Market Development Cause Economic Growth? A Time Series Analysis for Indian Economy[END_REF][START_REF] Tsouma | Stock returns and economic activity in mature and emerging markets[END_REF], Bouoiyour et al. 2015, among others). It must be stressed that the stock market capitalization of the BRICS has totalled 7.6 USD billion in 2013 compared to 1.1 USD billion in 2000.

Moreover, assessing both co-movement and causality among international stock markets has long been a popular research topic in finance [START_REF] Lin | Do bulls and bears move across borders? International transmission of stock returns and volatility[END_REF][START_REF] Karolyi | Why do markets move together? Investigations of U.S.-Japan stock return comovements[END_REF][START_REF] Forbes | No contagion, only interdependence: measuring stock market comovements[END_REF], Brooks and Del Negro 2004, etc.) as it has relevant implications for asset allocation and investment management. Since the seminal work of [START_REF] Grubel | Internationally diversified portfolios: welfare gains and capital flows[END_REF] on the benefits of international portfolio diversification, this issue has received a particular attention. While a growing number of studies have been devoted to the interdependence between stock markets, the empirical literature has shown mixed findings with respect the linkage between these variables, mainly due to different sample data and analysis methods. It must be pointed out that the majority of works on financial markets spillovers have used the covariance of excess returns [START_REF] Phylaktis | Capital market integration in the Pacific Basin region: An impulse response analysis[END_REF], OLS, standard Granger causality test or multivariate GARCH models [START_REF] Levy | International diversification of investment portfolios[END_REF][START_REF] Solnik | Why not diversify internationally rather than domestically?[END_REF][START_REF] Masih | Long and short term dynamic causal transmission amongst international stock markets[END_REF][START_REF] Sharkasi | Interdependence between emerging and major markets[END_REF]and Phuan et al. 2009, etc.). Other studies on this issue have conducted bivariate and multivariate cointegration models [START_REF] Taylor | The internationalization of stock markets and the abolition of UK exchange control[END_REF]Tonks 1989, Kasa 1992) to distinguish between long-run and short-run dynamics. Even though these kinds of works offered prominent contributions, the insights regarding the precise horizons for stock markets characteristics are rather limited. Overall, the information derived from these techniques turn out to be insufficient for risk managers and investors who have a specific time horizon in mind when managing their portfolios. The examination of the interconnectedness of stock markets is of paramount prominence for the understanding of a crisis and its propagation mechanism. Although spillover effects in equity markets have been extensively evaluated in the extant literature (for example, Diebold and Yilmaz 2009, Engle et al. 2013), a limited research has tried to differentiate the short-term and long-term correlations between stock markets using more sophisticated techniques (for instance, Fernandez 2005, Rua and Nones 2009, [START_REF] Raghavan | Impact of capital control measures on the Malaysian stock market: A multi-resolution analysis[END_REF][START_REF] Shah | Correlation and Coherence between India and Global Equity Market in Time Frequency Localization through Wavelet Transformation[END_REF], Wang et al. 2017, Yang et al. 2018). Wang et al. (2017) use wavelet approach to explore the relationship between stocks in the U.S. market over distinct time horizons from a network perspective. Besides, Yang et al. (2017) carry out a wavelet-based quntile regression to assess the interdependence between six Chinese stock markets and the international financial market including possible safe haven assets and global economic factors under several market states and investment horizons. Their findings provide fresh and very useful insights for participants in financial markets, especially for investors or hedgers who have various investment or hedging horizons.

Certainly, the wavelet approach is able to address investment, hedging and diversification opportunities through a proper decomposition of the stock market features for different time spans at a specific point in time. However, when applying a wavelet approach it is sometimes very difficult to identify local frequency changes, as the spectrum is generated by stepping through various predetermined frequency components yielding generally to blurred findings. The wavelet method presents problems of shift variance. More accurately, when the start point varies by, for example, dropping the initial point, the wavelet transform can reveal distinct outcomes. Hence the paramount importance to account for scales that are free from rigid mathematical constraints and that are driven to reflect inherent movements embedded in data without a priori knowledge. In this way, the Empirical Mode Decomposition (EMD) has proven effective when applied to a broad range of applications for extracting signals from data generated through noisy nonlinear and non-stationary processes [START_REF] Huang | The Empirical Mode Decomposition and Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis[END_REF][START_REF] Kim | The stock return-inflation puzzle and asymmetric causality in stock returns, inflation and real activity[END_REF][START_REF] Huang | Hilbert-Huang Transform in Engineering[END_REF]. Recently, a special attention has been given to EMD, given its ability to decompose signals into scale components, to manage non-stationary data and to provide an alternative representation of the relationship between time series on a scale-by-scale basis. Since actors across various stock markets operate heterogeneously, it seems required to carry out elaborate econometric techniques that control for the time varying dynamics in time series. In this way, the EMD is appealing as the behavior of stock markets usually seem to go through different phases.

Our results provide robust evidence of a significant causality running from Chinese stock market to Brazilian, Russian, Indian and South African equity markets. These spillovers do not appear uniform, but seem more pronounced with the increased uncertainty over China economic downturn. In particular, Brazil, Russia and India (in this order) suffered more than South Africa from the China's growth slowdown.

The outline of the paper is as follows. Section 2 presents a literature review on. In Section 3, we discuss the conducted methodology, and describe the data. Section 4 reports the empirical results. Section 5 concludes and provides some relevant portfolio implications.

Literature review

Over the last decades there has been a large strand of literature focused on the relationship among asset markets in developed and emerging markets. The theory suggests that large benefits can be derived through international portfolio diversification if the returns of distinct financial markets are not perfectly correlated. According to [START_REF] Choudhry | Common Stochastic Trends among Far East Stock Prices: Effects of the Asian Financial Crisis[END_REF], a statistically significant correlation among stock markets means that there is a common force that brings these markets together, implying then that the benefit of diversification is limited.

As a result, investors started to invest in distinct stock markets wherever they can earn more benefits. Nonetheless, the evidence from crisis events such as the global financial crisis underscores that market co-movements yield to contagion and then to strong correlations lessening the diversification opportunities. In this ground, a rigorous estimation of correlations between markets is of paramount importance to efficaciously capture changes in risk [START_REF] Engle | Anticipating correlations: a new paradigm for risk management[END_REF]. Since the dynamic correlations depict the historical linkages among different assets, investors and risk managers usually focus on correlation to frame expectations for how an investment portfolio may perform [START_REF] Longin | Extreme Correlation of International Equity Markets[END_REF]Solnik 2002).

Several researches have been carried out to examine the interdependence between distinct equity markets. In general, equities are said to be integrated when significant correlation exists between markets. Nevertheless, the studies on this issue provided mixed outcomes [START_REF] Hilliard | Relationship between Equity Indices on World Exchanges[END_REF][START_REF] Aggarwal | Dynamics of Equity Market Integration in Europe[END_REF][START_REF] Chi | Financial Integration in East Asian Equity Markets[END_REF]Abbas and Chancharat 2008, among others). The earliest empirical research on stock markets relationships consider the interdependence among markets as effects of the conditional means of the return of one country onto the conditional means of chronologically succeeding returns of another country.

They have concentrated on the analysis of short-term benefits of international portfolio diversification (for example, [START_REF] Levy | International diversification of investment portfolios[END_REF][START_REF] Solnik | Why not diversify internationally rather than domestically?[END_REF]. Other works have analyzed the interdependence between stock markets via the covariance of excess returns (for instance, [START_REF] Phylaktis | Capital market integration in the Pacific Basin region: An impulse response analysis[END_REF]. Another strand of literature has assessed the linkages across stock markets using bivariate [START_REF] Taylor | The internationalization of stock markets and the abolition of UK exchange control[END_REF] or multivariate cointegration methodology [START_REF] Kasa | Common stochastic trends in international stock markets[END_REF].

Apart from examining the dynamic relations between stock markets, many investigations have focused on the effect of major events such as global financial collapse on the stock market interdependencies (for example, [START_REF] Lim | Convergence and catching up in ASEAN: a comparative analysis[END_REF], Aggarwal et. al. 2008[START_REF] Ansari | Impact of globalisation on stock market synchronisation: Some empirical evidence[END_REF][START_REF] Joe | Co-Movements of and Linkages between Asian Stock Markets[END_REF][START_REF] Wang | Who moves East Asian stock markets? The Role of the 2007-2009 global financial crisis[END_REF]. [START_REF] Ansari | Impact of globalisation on stock market synchronisation: Some empirical evidence[END_REF] argued that the synchronization across the stock markets has changed sharply after the globalization. [START_REF] Joe | Co-Movements of and Linkages between Asian Stock Markets[END_REF] examined the contemporaneous co-movements and lead/lag relationships among different Asian stock markets over the period 2001-2011 and showed that the synchronization among the markets decreases during this period. Nevertheless, [START_REF] Wang | Who moves East Asian stock markets? The Role of the 2007-2009 global financial crisis[END_REF] evaluated the linkages between the U.S. stock market and six Asian stock markets and deduced that the global financial collapse has reinforced the linkages among these markets.

By conducting a network analysis for fourteen Asian stock markets, [START_REF] Aswani | Impact of global financial crisis on network of Asian stock markets[END_REF] documented that the interdependence between these stock markets rises markedly during the crisis period rather than the pre-crisis or the post-crisis period.

More recently, [START_REF] Bouoiyour | The Development in Financial Integration of the Chinese Market with the US Market in Normal, Bull, and Bear States[END_REF] tried to address whether or not the stock market of China is integrated with that of the US prior to and post 2016 U.S. presidential elections.

They used a Copula-quantile-on-quantile regression to examine the dependence structure between the quantile of US stock return on the quantile of China stock return. This technique is useful for risk managers working on portfolio optimization, asset pricing and the assessment of systemic risk. The results reveal a gradual transitioning feature in the correlation going from the centrally located quantiles (normal state) to the tail quantiles (bull and bear states). Specifically, a negative correlation is found when the China's market is improving and the US market is heading into decline, and also when the two markets are functioning around the normal circumstances.

The present research complements the existing literature by analyzing the role that may play the uncertainty over China's growth slowdown in exacerbating the risk spillovers among the China stock market and the remaining BRICS stock returns. We investigate the dynamic spillover effects prior to and after the China economic downturn. In times of heightened uncertainty, an effective defense is to be well informed about the correlation between different stock markets at distinct points of time. From a risk management perspective, accounting for nonlinearity (i.e., a multi-scale causality) is very beneficial for market participants (in particular, traders, investors and risk managers) as they would allow them to effectively protect against unforesseen shocks and rising uncertainties. Such a fine analysis could help investors in adjusting the portfolio composition to better match the desired portfolio risk profile

Methodology and data

To effectively control the risks that they face, portfolio managers generally need to consider the dependence between different equities in times of market distress or rising uncertainty. Because the co-movement or the causality between stock markets during high risk episodes may mask the irregularities we would like to identify, it is important to use techniques for decomposing a time series into a number of components. This would allow pinpointing the dynamic interconnectedness among different markets. For investors wishing to use the stock market hedging and diversification features to deal with uncertain exposure, it is relevant to have information about whether the linkages between the stock markets under study are consistent over time, or concentrated in specific times. Accordingly, this study uses a relatively new technique, called Empirical Mode Decomposition (EMD), based on the sequential extraction of energy associated with distinct frequencies ranging from highly fluctuating components (short-run) to less fluctuating modes (long-run).

Causality testing-based Empirical Mode Decomposition

Data from natural phenomena are often non-stationary due to their transient behaviors.

According to [START_REF] Huang | The Empirical Mode Decomposition and Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis[END_REF], the conventional signal approaches (such as Fourier transform and Wavelets) might lead to distorted or inaccurate information about nonstationary variables, like for instance ground motion recording. To reach clearer and complete information from signals that might be hidden when using standard econometric techniques, the Empirical mode decomposition (EMD) method may be very useful. It is a part of more general procedure known as Hilbert-Huang transformation (HHT) and by its nature resembles both Fourier decomposition and wavelet transformation. EMD is suited to extract monocomponent and symmetric components, known as Intrinsic mode function (IMF), from wide bands of signals [START_REF] Huang | The Empirical Mode Decomposition and Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis[END_REF][START_REF] Altaf | Rotation invariant complex empirical mode decomposition[END_REF][START_REF] Rilling | Bivariate empirical mode decomposition[END_REF][START_REF] Tanaka | Complex empirical mode decomposition[END_REF][START_REF] Zhang | Oil shock and economic growth in Japan: a nonlinear approach[END_REF][START_REF] Yu | Dynamic volatility spillover effect analysis between carbon market and crude oil market: a DCC-ICSS approach[END_REF]. The IMF denotes an oscillatory mode of a simple function Determining the dependence between BRICS stock markets in times of heightened uncertainty surrounding China growth's slowdown using EMD consists of (1) decomposing original time series into different intrinsic mode functions (IMFs) and one residue among different time scales, from high to low frequencies, and (2) utilizing nonlinear causality test to test whether a significant causality occurs across China-BRICS stock returns among matched modes and thus over different time-horizons. Figure 1 depicts the proposed analysis approach.

Specifically, two main steps are involved:

Step 1: Signal decomposition

The EMD technique is used to decompose the original time series data into matched modes on various time-scales, corresponding to possible hidden features. In practice, the intrinsic mode functions are derived by determining the maxima and minima of time series

) (t x ,
) ( ) ( ) ( t x t m t d - = (2)
where ) (t d is presented as the i th IMF , by replacing ) (t x with the residual

) ( ) ( ) ( t d t x t r - = .
Then, we connect the local maxima with the upper envelope and the minima with the lower one. This step allows us to determine the first component through the difference between the data and the local mean of the two envelopes. When residue successfully meets the conditions that the number of zero-crossings and extrema do not differ by more than one as mentioned above and the sifting process can be fully achieved if the total number of IMFs is limited to log2N (N denotes the length of a data series) or when the residue (r) becomes a monotonic function and data cannot be extracted into further intrinsic mode functions [START_REF] Huang | A confidence limit for the empirical mode decomposition and the Hilbert spectral analysis[END_REF], the original time series can be expressed as the sum of some IMFs and a residue:

) ( ) ( ) ( 1 t r t c t X N j j ∑ = + = (3)
In the sifting process, the first component contains the shortest period component of the time series. The residue after extracting the quickly fluctuating component corresponds to the longer period fluctuations in the data. Thus, the mode functions are extracted from high frequency to low frequency bands. The EMD is carried out here as a filter to separate high frequency (fluctuating process) and low frequency (slowing varying component) modes.

Basically, this procedure corresponds to high-pass filtering by adding fastest oscillations (i.e.,

IMFs with smaller index) to slowest oscillations (i.e., IMFs with larger index), consisting of:

(1) Computing the mean of the sum of ci for each component (except for the residue);

(2) Employing t-test to obtain for which j the mean departs from zero; (3) Once j is determined as a relevant change point, partial reconstruction with IMFs from this to the end is considered as the slow-varying component and the partial reconstruction with other IMFs is identified as the high frequency component.

Step 2: Scale-on-scale causality testing

After disentangling data variables into a set of different components by employing EMD, such that each component corresponds to a range of frequencies, a second step consists on testing the nonlinear causality on a scale-on-scale basis (i.e., depending to IMFs variations). In particular, a general causality test-based on a Taylor expansion (PéguinFeissolle and Teräsvirta 1999) has been performed.

t n t t q t t t x x y y f y ε θ + = - - - - ) , , , , , , ( * 1 1 * K K (4)
where * θ is a parameter vector and

ε θ + = - -K (5)
To test ( 5) against ( 4), we linearize * f in (4) by expanding the function into a k-order Taylor series around an arbitrary fixed point in the sample space. We obtain: 3

∑ ∑ ∑ ∑ ∑ ∑ = = = = = = - - - - - - + + + + = q j n j q j q j j q j n j j t j t j j j t j t j j j t j j t j t x y y y x y y 1 1 1 1 1 0 1 1 2 1 2 2 1 2 1 2 1 2 1 δ β γ β β ∑ ∑ ∑ ∑ ∑ = = = - = - - = - - + + + n j q j q j j q j j j t j t j j n j j j t j t j j k k k k y y x x 1 1 1 1 1 1 2 1 1 1 2 2 1 2 1 K K K K β γ ∑ ∑ ∑ = = - = - - + + + n j n j j n j j t j t j t j j k k k k x x 1 1 * 1 1 2 1 1 ε γ K K K K (6)
The stock return (STR) is calculated by considering the ratio stock price (in log) at time t and the lagged stock price (in log).

4The period of the study is motivated by the availability of the Brazilian and South African data and the fact that we required a common sample period for all the BRICS countries. The use of daily data enables to take into account the exact moment of each policy announcement and to assess the immediate market response to that particular news. With high frequency data, we can set a sufficiently narrow time window around each policy announcement and each untoward shock to assess if the markets respond to specific news.

Measuring the surprise in a limited time horizon ignores the noise owing to other events.

However, if we use weekly, monthly or quarterly data, the measurement of the immediate impacts of unforeseen shocks or events will be more complicated [START_REF] Selmi | Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold[END_REF]. Indeed, the occurrence of events is followed by investors who form or revise their expectations based on the results of these events. The informational efficiency hypothesis states that markets absorb news into asset prices in anticipation of an event' outcomes. By using daily data, we are able to account for the exact moment of each policy announcement and to assess the immediate market response to that particular news. In short, the use of daily data appears more appropriate for our purpose of characterizing the dynamic spillovers across stock markets especially in period of rising uncertainty.

We incorporate in the following gold prices and the Chicago Board Options Exchange Volatility Index (largely known by VIX) to check whether the results are still robust after the inclusion of global economic and financial factors. VIX measures the stock market expectations of the volatility implied by S&P 500 Gold has been largely served as a hedging tool against sudden stocks and as a safe haven during extreme stock market movements [START_REF] Baur | Is Gold a Safe Haven? International Evidence[END_REF]. We chose the gold price as potential exogenous variable since BRICS countries include the world's major consumers of gold (China and India), and also one of the biggest producers (South Africa). In addition to gold, the finance literature has been frequently relied on proxies of uncertainty such as VIX index that plays an important role in asset allocation and portfolio strategies (Hood and Malik 2013, Balcilar et The results of standard Granger causality test (Table 3, Panels A and B) go in the same direction. We will return later on the arguments explaining these results. But we must clarify that the results obtained through these "standard" methods, may be erroneous since they provide averages which do not satisfactorily account for the problems of asymmetry and nonlinearity. The question here is beyond whether there exist or not significant relationships between the Chinese market and the stock returns of Brazil, Russia, India and South Africa since we know yet that these markets are inter-linked. Rather, our focus in this study is to identify how these BRICS spillovers vary from one time-scale to another. Hence, a multiscale analysis is conducted in the following to uncover how exactly moves the relationship China-BRICS equities over different components, which can hardly be visible from VECM and Granger causality test [START_REF] Bouoiyour | How can stock return predict industrial production in BRICS? A comparative analysis through frequency causality[END_REF].

EMD findings

This paper attempts the dynamic spillovers across China and the remaining BRICS markets over different time-scales. Our main objective is to show how dividing variables into intrinsic mode functions can be useful in assessing the financial spillovers in periods of China's rapid growth and China economic downturn. By performing EMD, the dependent and independent variables were divided into several IMFs and one residue (the time-scale decomposition results are available for interested readers upon request). Asthe number of IMFs is limited and restricted to log2N where N is the length of data 7 , sifting processes produced eight IMFs for each variable over period of rapid China's growth (Panel A, Table 4), and only six IMFs for the period of China growth's slowdown. All of the derived IMFs are listed from high to the low frequency components and the last one is the residue. Throughout the rest of our study, we discuss three frequency components for the first period (Panel A):

short-run (IMF1, IMF2 and IMF3), medium-run (IMF4 and IMF5) and long-run (IMF6, IMF7 and IMF8) 8 . Fig. 2 presents our time scale interpretation of EMD. We adopt another grouping for the second period (Panel B): short-term (IMF1 and IMF2), medium-term (IMF3), and long-term (IMF 5 and IMF6). But this does not fundamentally change our results. 7 The EMD technique generates modes depending on the data used. For more information on the data extraction method used, please refer to [START_REF] Huang | A confidence limit for the empirical mode decomposition and the Hilbert spectral analysis[END_REF].

8

We adopt another grouping for the second period (Panel B): short-term (IMF1 and IMF2), medium-term (IMF3), and long-term (IMF 5 and IMF5). This does not fundamentally change our results. 5 reports some measures which are given to assess IMFs features: mean period of each IMF, correlation between each IMF and the original data series and the variance percentage of each IMF. The mean period corresponds to the value derived by dividing the total number of points by the number of peaks for each IMF. Two correlation coefficients, Pearson correlation and Kendall rank correlation coefficients are employed here to measure the relationships between IMFs and the original data. Because IMFs are intrinsically independent, it is possible to sum up the variances and use the percentage of variance to determine the contribution of each IMF to the total volatility of the original data. Together, these measures reveal interesting insights. In particular, for the period of rapid growth (Panel A, Table 5), we can distinguish two groups of countries: (1) China, Brazil and Russia which are driven by long term factors (IMFs6 _ 8; above 365 days) that may be a reflect of the great dependence of these spillovers to market fundamentals; (2) India and South Africa which appear to be sensitive to rapid oscillations (IMFs1 _ 3; less than 60 days). This result can be attributed to the fact that emotions determine the stock market price evolution. Accurately, a great optimism may drive prices up and a heavier pessimism may drive prices down. Besides, stock markets can be buoyed by sudden market-changing events, making the stock market behavior very hard to be effectively predicted. Moreover, the residues display a strong correlation with the central original series. The continuing rising trend can be explained by the growing attention to BRICS stock markets due to their rapid growth and substantial trade and investment integration with the most developed economies in, and their position as a promising era for international portfolio diversification. The results change marginally by moving from the first period (Panel A, Table 5) to the second period (Panel B, Table 5). While Chinese, Brazilian, and Russian equities remain determined by the same driving forces, Indian stock market appears highly driven by high frequency components. We note that South Africa joined the group of China, Brazil and Russia and hence becomes predominantly determined by low frequency components. Table 6 gives more accurate information about the three mono-components yet identified and confirmed the previous findings regarding the potential contributors of each of the BRICS stock markets over the period of China rapid growth and the period of China's slowdown (Panels A and B, respectively). After providing the decomposition findings of stock returns of China, Brazil, Russia, India and South Africa and the basic analysis of the different IMFs, the hierarchical clustering analysis was carried out. To do so, we have employed the "pdist" function9 to compute the Euclidean distance between pairs of IMFs, or the IMFs and the residue in order to create a hierarchical cluster tree using the smallest distance principle and to generate a dendrogram plot of the hierarchical cluster tree. Figure 2 reports the clustering outcomes for the two concerned periods. For the period of Chinese rapid growth, the eight IMFs may be grouped into three categories (as indicated in Table 4). Regarding the mean periods, the partial reconstruction with IMF1, IMF2 and IMF3 can be recognized as the shortest scales, IMF4 and IMF5 as the medium term scaling components, whereas the partial reconstruction with IMF6,

Causality testing-based EMD findings

A nonlinear Granger causality test is conducted to analyze causal linkages between the Chinese market and the remaining BRICS stock market returns at different modes by rigorous means of EMD. We show sharp variations in findings which are not congruent with earlier studies. Table 7 reports the corresponding results in which the p-values are listed.

As previously, the investigated countries can be categorized as follows: The first group includes Brazil and Russia where a strong causality is supported in the long-term (scale above 365 days; IMF6, IMF7 and IMF8). The second group includes India and South Africa where causality is validated at short-run horizons (less than 60 days, IMF1, IMF2 and IMF3).

Also, the residues of Chinese stock returns significantly cause the BRICS stock returns in the long-term (Table 7.1). By accounting for gold price and the VIX index (Panels A and B, Table 7.2), we note some differences among countries with respect to their responses to the current slowdown of China. This signals the sensitivity of the spillovers among BRICS to the global and financial factors. In the wake of China economic downturn (Panel B, Table 7.2), the scale length becomes longer for all the cases. In particular, we note a stronger influence on Brazilian and Russian equities (IMFs 6-8: above 365 days). Indian and South African markets appear less influenced (short and medium term effect at the range IMFs 1-5: less than one year).

Robustness checks

We now investigate how various econometric specifications and data may change our estimates. We first use an alternative time-frequency approach, namely wavelet decomposition (WD). A number of time-frequency transformations able to effectively Nonetheless, the empirical mode decomposition makes no assumptions a priori about the composition of the signal.10 Instead, it employs spline interpolation between maxima and minima to repeatedly traces out the IMFs. Each IMF will be a single periodic oscillator, and the number of IMFs cannot be anticipated prior to the decomposition; please see Appendix A

for more details about the wavelet transform. Comparing the scale on scale causality based WD findings (see Table 8) with those of the causality based EMD (Table 7), we robustly find the faltering pace of China's growth has intensified the risk spillovers across China and the remaining BRICS markets. In addition, we consistently show that the Chinese slowdown affects heterogeneously BRICS stock markets. While India and South Africa appear moderately affected by the great anxiety over slowing growth in the world's second-largest economy (i.e. the causality is driven by short-term hidden factors), Brazil and Russia seem the biggest losers (i.e. a causality supported in the long-term: above 240 days). This holds true for both the unconditional and conditional analyses (Tables 8.1 and 8.2, respectively). Also and as a robustness analysis, we re-run the exercise using weekly data to test whether a change in the frequency data may lead to some changes in our findings. The conducted unconditional and conditional investigations (Tables 9.1 and 9.2, respectively) confirm the previous results. Overall, even though it seems a challenging task to carry out signal processing techniques for non-stationary and noisy signals [START_REF] Lin | Signal feature extraction based on an improved EMD method[END_REF], this study highlights the efficacy of the EMD for capturing hidden factors that may drive the dynamic spillovers across stock markets especially in times of ongoing volatility. Combined with some other methods, this signal approach allowed finding fresh and precise insights into complex issues. This makes causality testing-based EMD a promising new addition to the existing toolboxes for non-stationary and nonlinear signals. Likewise, the wavelet decomposition has also proved its usefulness and relevance in this exercise. Nevertheless, for South Africa, the level of China's investment is relatively weak. We keep the same hierarchy when considering the BRICS FDI into China. This consistency in terms of countries' position deeply underscore that our findings are neither unusual nor striking.

Conclusions and some portfolio implications

In addition, compared to Brazil, Russia and India, Chinese and South African companies are still in the early stages of learning how to operate in each other's economies [START_REF] Gupta | China and India: Greater Economic Integration[END_REF]. Second, the position of South Africa in terms of regulation of securities exchanges and financial system development may play a powerful role in mitigating the adverse effects of China's slowdown on the performance of its stock market [START_REF] Ferhani | South Africa: Financial System Stability Assessment, Including Report on the Observance of Standards and Codes on the following topic: Securities Regulation[END_REF]Sayeh 2008, Bouoiyour et al. 2015). South Africa is recently ranked by the World Economic Forum's Global Competitiveness Survey (2015) as the first position out of 144 emerging countries in terms of regulation of securities exchanges and financial market sophistication.

The survey classified South Africa third in terms of its ability to raise finance via the local equity market, third in the effectiveness of corporate boards and fourth in protecting the rights of minority shareholder. Further, considering gold as a highly liquid asset that can be accessed any time, South Africa -the fifth largest gold producer in the world-can suffer less since investors turn to gold under turbulent times and over periods of financial stress. We must recall that gold possesses no credit risk and cannot turn worthless even though economic crisis (Baur and[START_REF] Baur | Is Gold a Hedge or Safe Haven? An Analysis of Stocks Bonds and Gold[END_REF][START_REF] Baur | Is Gold a Safe Haven? International Evidence[END_REF]. Indeed, over uncertain period, when investors attempt to get rid of their risky investments, they relocate their finances into the less risky assets such as gold. In brief, this yellow metal can provide great protection against losses when South African stock market experienced drops due to China's current upheaval.

Moreover, by looking at the obtained findings and the statistics summarizing in Table C.2 (Appendix), we can deduce that the stock prices of the companies belonging more to cyclical industries are more sensitive to China growth's slowdown. Unlike Brazil and Russia, the stock market price indices of India and South Africa which appear less influenced by the Chinese downturn are more based on defensive industries 11 .

We shouldn't neglect the problem of sincerity of the Chinese data on economic growth. In this context, some recent researches have doubts about these statistics (for example, Arthus and Virad 2016), but we leave this debate aside. To this we must add the findings of [START_REF] Bouoiyour | How can stock return predict industrial production in BRICS? A comparative analysis through frequency causality[END_REF] which argued that the effect of stock returns on real economic activity wasn't uniform across BRICS countries. More specifically, the authors suggested that South African and Indian stocks are better positioned regarding the predictability power for output growth. For China and Russia, the stock returns seem unable to satisfactorily predict the real activity. This last finding may be generally due to the lack of transparency in market transactions and the practices of corporate governance in these countries. Given these elements, we need to be careful in interpreting our results. Importantly, profitable investment strategies can be built on the basis of our results. The evidence that the reactions of BRICS equities to Chinese economic downturn change sharply from quickly to slowly fluctuating components may have profound consequences for portfolios that trade with 11

The defensive or non-cyclical industries are those that do well in turbulent times, since the demand continue to grow regardless of whether there is certain or uncertain situation. Accordingly, Damodaron (2014) argued that, in times of turmoil, cyclical companies see generally their earnings go up and down, providing excessive volatility. Thereafter, the wavelet decomposition can be written as following:

∑ ∑ + = k k J k J k k J k J d t s t f , , , , ) ( ) ( ψ φ ) ( ....... ) ( ) ( , 1 , 1 , 1 , 1 t d t d t k k k k k J k J ∑ ∑ + + + - - ψ ψ (a.5)
where J is the number of multi-resolution levels.

  with varying amplitude and frequency. It satisfies at least two requirements. The first one relies on the fact that functions should have the same numbers of extrema and zero-crossings or differ at the most by one. The second one consists in the need of symmetrical functions with respect to local zero mean. By exploring data intrinsic modes, the EMD helps display possible hidden features in the data, and aims indeed at transforming the studied time series to hierarchical structure by means of the scaling transformations It provides effective frequency information evolving over time and quantifies the changeability captured via the oscillation under different scales and locations. In brief, the IMFs have well defined instantaneous frequencies, which give an idea about the instantaneous energy and frequency content of signals.

Figure 1 .

 1 Figure 1. Framework of scale-on-scale causality testing

  IMF7 and IMF8 can be treated as the longest time-scales (Figure2, Panel A). The short scales correspond to the Euclidean distance smaller than two months (60 days); the medium scaling components represent the Euclidean distance within two months (60 days) and less than eight months (240 days); the longest scales correspond to the distance more than 12 months or one 9The hierarchical clustering investigation was also implemented in the Matlab R2015a software package. year (365 days). The clustering findings, over the period prior to China's economic slowmoving (Panel B, Figure2), confirm the previous results by often distinguishing the same two groups (i.e., whose determined by longer scale factors (China, Brazil and Russia), and whose driven by short-run factors (India and South Africa). Nevertheless, for the period of China's slowdown, the results change considerably. Unlike India which appears the only country among BRICS driven by high frequency components (IMF1), South Africa joined China, Brazil and Russia and become significantly sensitive to slowly fluctuating components (IMFs 5 _ 6).

Figure 2 .

 2 Figure 2. The Euclidean distance via hierarchical clustering method Panel A: Period of rapid China's growth Panel B: Period of China's slowdown China

  describe signals with time-varying features have surfaced in the literature, though two have gained large popularity in the analysis of complex systems: the wavelet transform and the empirical mode decomposition. It is important to point out the appropriateness of both techniques for the analysis of nonstationary and nonlinear signals. Accordingly, Kijewski-Correa and Kareem (2006, 2007) affirmed the capability of the Empirical Mode Decomposition and the Wavelet decomposition (WD) to properly detect the instantaneous frequency of signals of constant and time-varying frequency in the presence of noise. Given this consideration, We utilize the WD as an alternative technique to ascertain the robustness of the EMD results. Using WD, we separate data into various frequency components, and then we examine each component with resolution matched to its time-scale. With wavelet transform, one selects a set of basis signal components and thereafter determines the parameters for each of these signals such that their aggregate will compose the original signal.

  function f (x) can be symbolized by the superposition of daughters ψ a,b of father wavelet φ mother wavelet ψ . Father wavelet represents the smooth part of the signal (or low frequency band), while the mother wavelet represents the volatile part (or high frequency), denoted as:

  the smooth behavior of the signal at a specific time scale. The coefficients k j d , represent deviations from the trend.

  To test noncausality hypothesis, we start by the fact that t

															t ε ~	nid	(	0	,	σ	2	);	the functional form of
															x does not cause t y if the
	past values of t x does not contain any information about t y that is already contained in the
	past values of	t y itself.
		y	t	f	(	y	t	1	,	,	y	t	q	,	) . t

*

f is unknown but we assume that is adequately represents the causal relationship between t x and . t y

Table 1 . Descriptive statistics of return series

 1 al. 2014[START_REF] Mensi | Asymmetric Linkages between BRICS Stock Returns and Country Risk Ratings: Evidence from Dynamic Panel Threshold Models[END_REF] 5 . The data for gold prices, which are measured in USD per ounce, were downloaded /fred.stlouisfed.org/series/VIXCLS).Table1provides the descriptive statistics of the daily returns for the period of rapid China's growth (Panel A, Table1) and the period of China's growth slowdown (Panel B, Table1). We clearly show that the average returns are positive for all the return series over the two periods under study. Importantly, all the stock markets in question become much more volatile during the period of China economic downturn. The greatest volatility of the different BRICS equities is confirmed by Figure A.1.We begin our analysis by employing some standard techniques (VECM and standard Granger causality test) for the two investigated periods: period of China's rapid growth and in the wake of China's economic slowdown. The idea here is to have a case of benchmarking to compare the VECM and the Granger causality results with the new methods (in particular, causality testing-based EMD and causality testing-based Wavelet decomposition 6 ). To proceed, we have, first, applied Ng-Perron[START_REF] Ng | Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power[END_REF] unit root test to examine whether the variables are stationary in the level or first difference form. The obtained outcomes indicate that almost all the considered variables show unit root behavior at level and appear stationary at 1 st difference with intercept and trend (TableA.1, Appendix). Due not Using VECM, we show that both short-and long-term linkages among BRICS equities are statistically significant prior to the Chinese crisis (Table2, Panel A). This result remains supported for the second period (Table2, Panel B). A sharp heterogeneity is found with respect to BRICS stock markets reactions over China's rapid growth period. In particular, the linkages seem strong for Brazil, followed by Russia and India and finally South Africa. Similar hierarchy is found during the China's slowdown period, but these links appear more pronounced compared to the period prior to the onset of Chinese crisis.

	from	the	website	of	the	Federal	Reserve	Bank	of	St.	Louis
	(https://fred.stlouisfed.org/series/GOLDAMGBD228NLBM); Likewise for the VIX index
	(https:/

(Appendix). The skewness coefficients are negative and the kurtosis coefficients are above three for all return series and over the two periods, indicating that the probability distributions of the return series under study are skewed and leptokurtic, thereby rejecting normality which is also confirmed by the Jarque-Bera statistics (J-B).

having information about structural breaks stemming in the time series, Ng-Perron unit root findings may be biased. To solve this limit, we carry out de-trended Zivot and Andrews (1992)'s structural break unit test to determine the integrating orders of the variables in the presence of structural breaks. We note that, for the two periods investigated, all the variables are stationary at specific levels showing structural breaks

(Table A.1, Panels A and B, Appendix)

. Then, we apply the VECM model and the standard Granger causality test in order to test if China's slowdown exacerbates risk spillovers among BRICS equities.

Table 2 . VECM: The dependence structure between China and the remaining BRICS markets

 2

		Panel A: Period of China rapid growth		Panel B: Period of China's slowdown
		STR_Brazil STR_Russia STR_India STR_South	STR_Brazil STR_Russia STR_India STR_South
				Africa				Africa
	D(STR_Chinat-1)	0.234***	0.168**	0.110***	0.051***	0.304***	0.162***	0.142***	0.094**
		(0.0000)	(0.0043)	(0.0000)	(0.0004)	(0.0000)	(0.0002)	(0.0009)	(0.0032)
	D(goldt-1)	-0.054**	0.039***	-0.062***	0.008*	-0.163**	-0.041*	0.083	-0.061*
		(0.0092)	(0.0000)	(0.0000)	(0.0415)	(0.0093)	(0.0311)	(0.2452)	(0.0981)
	D(VIXt-1)	-0.018*	-0.023**	-0.064**	-0.023	-0.049*	-0.092**	-0.078*	-0.063**
		(0.067)	(0.0051)	(0.0081)	(0.5412)	(0.0105)	(0.0067)	(0.0513)	(0.0091)
	STR_Chinat-1	0.431**	0.303**	0.276***	0.184**	0.509***	0.411***	0.336**	0.229**
		(0.0056)	(0.0018)	(0.0007)	(0.0011)	(0.0006)	(0.0008)	(0.0010)	(0.0014)
	goldt-1	0.111**	-0.076*	-0.065**	0.102***	-0.171**	-0.109*	0.147	0.094
		(0.0041)	(0.0818)	(0.0053)	(0.0000)	(0.0023)	(0.0813)	(0.2061)	(0.1542)
	VIXt-1	-0.064**	-0.096*	-0.055***	0.082	-0.051**	-0.087**	-0.059*	-0.088*
		(0.0091)	(0.0510))	(0.0004)	(0.1356)	(0.0067)	(0.0016)	(-0.0410)	(0.0514)
	ECTt-1	-0.026*	-0.039**	-0.091***	-0.100***	-0.081***	-0.088***	-0.073**	-0.065**
		(0.0504)	(0.0010)	(0.0000)	(0.0004)	(0.0000)	(0.0000)	(0.0019)	(0.0026)
	R-squared	0.73	0.67	0.71	0.64	0.69	0.68	0.59	0.46
	Adj. R-squared	0.68	0.54	0.69	0.52	0.51	0.64	0.38	0.39
	Note: (.): p-value; p-value<0.01: ***; p-value<0.05: **; p-value<0.

Table 3 . Standard Granger causality test: The dependence structure between China and the remaining BRICS markets

 3

	Panel A: Period of China rapidgrowth	Panel B: Period of China'sslowdown
	STR_Brazil STR_Russia STR_India STR_SouthAfrica STR_Brazil STR_Russia STR_India STR_SouthAfrica
	STR_China 0.0014**	0.0003*** 0.0000*** 0.0002***	0.0010**	0.0027**	0.0014** 0.0009***
	Note: (.): the p-value; p-value<0.01: ***; p-value<0.05: **; p-value<0.1

Table 4 . Interpretation of scales-based on EMD

 4

	modes	Panel A: Period of rapid China's growth	Panel B: Period of China's slowdown
	IMF1		Short-run: less than two months (60 days)
	IMF2	Short-run: less than two months (60 days)
	IMF3		Medium-run: above two months (60 days)
	IMF4	Medium-run: above two months (60 days)	and less than one year (365 days)
	IMF5	and less than one year (365 days)
	IMF6		Long-run: above one year (365 days)
	IMF7	Long-run: above one year (365 days)	___
	IMF8		___
		On various time-scales, distinct modes may behave differently, due to hidden factors
	driving the focal stock markets. Table

Table 5 . IMFs features

 5

		Panel A: Period of rapid China's growth			Panel B: Period of China's slowdown
		Mean	Pearson	Kendall	variance as % of	Mean	Pearson	Kendall	variance as % of
		period	correlation	correlation	the	sum	of	period	correlation	correlation	the	sum	of
					(IMFs+residue)				(IMFs+residue)
						China
	IMF1	0.93	0.111*	0.078**		5.01%		0.96	0.051	0.026		1.36%
	IMF2	0.99	0.061	0.052		1.34%		1.93	0.072	0.070*		1.56%
	IMF3	1.15	0.081*	0.059		1.11%		3.48	0.098***	0.83**		2.65%
	IMF4	4.34	0.094***	0.080***		2.06%		6.68	0.173***	0.148**		24.16%
	IMF5	9.11	0.069**	0.051		3.19%		13.71	0.232**	0.209***		31.67%
	IMF6	16.07	0.206*	0.196***		16.14%		17.91	0.189**	0.176**		15.13%
	IMF7	21.38	0.292***	0.284***		28.29%		___	___	___		___
	IMF8	26.72	0.115**	0.092**		18.18%		___	___	___		___
	Residue		0.251***	0.244***		23.91%			0.311**	0.268**		23.41%
						Brazil
	IMF1	1.03	0.126***	0.085**		1.91%		1.42	0.111**	0.107**		4.56%
	IMF2	2.11	0.091*	0.081**		2.55%		2.72	0.188**	0.132**		11.42%
	IMF3	5.32	0.059*	0.032		2.42%		4.15	0.046	0.031		2.91%
	IMF4	8.91	0.168***	0.149**		9.11%		8.42	0.060*	0.042		2.52%
	IMF5	12.24	0.171***	0.162***		11.23%		16.79	0.183***	0.172**		16.93%
	IMF6	19.86	0.328***	0.311***		18.72%		24.83	0.252**	0.238**		42.11%
	IMF7	24.10	0.251**	0.242***		17.73%		___	___	___		___
	IMF8	27.16	0.229**	0.217**		19.91%		___	___	___		___
	Residue		0.183***	0.176***		16.41%			0.186***	0.174**		20.98%
						Russia
	IMF1	1.51	0.071*	0.059*		0.88%		1.23	0.091*	0.072*		7.73%
	IMF2	1.76	0.088*	0.043		0.94%		1.83	0.072*	0.066		6.11%
	IMF3	6.09	0.082*	0.036		0.91%		6.71	0.104**	0.088*		8.92%
	IMF4	14.38	0.178**	0.159*		14.89%		8.52	0.092**	0.083**		5.11%
	IMF5	16.09	0.283**	0.261**		17.06%		13.91	0.181***	0.172***		18.32%
	IMF6	18.32	0.206***	0.183**		16.91%		19.27	0.236***	0.214**		23.34%
	IMF7	25.11	0.410***	0.379***		21.34%		___	___	___		___
	IMF8	27.36	0.196**	0.177**		18.02%		___	___	___		___

Note: *, **, ***: Correlations are significant at the levels of 0.01, 0.05 and 0.1, respectively (2-tailed).

Table 6 . Correlations and variance of components

 6

		Panel A: Period of rapid China's growth	Panel B: Period of China's slowdown
		Pearson	Kendall	variance as %	Pearson	Kendall	variance as %
		correlation	correlation	of the sum of	correlation	correlation	of the sum of
				IMFs			IMFs
				China
	High frequency	0.178**	0.159**	7.46%	0.133***	0.127**	2.92%
	component
	Low Frequency	0.511***	0.492***	62.61%	0.361**	0.324**	46.8%
	component
	Trend component	0.412**	0.386***	23.91%	0.303***	0.256**	23.41%
				Brazil
	High frequency	0.087*	0.079*	6.88%	0.156***	0.141**	15.98%
	component
	Low Frequency	0.421***	0.389***	56.36%	0.324*** 0.278***	59.04%
	component
	Trend component	0.176**	0.161**	16.41%	0.194**	0.186**	20.98%

Note: ***: Correlations are significant at the levels of 0.01, 0.05 and 0.1, respectively (2-tailed)

Table 7 . Scale-by-scale causality among China and BRICS stock returns

 7

	Panel A: Period of rapid China's growth		Panel B: Period of China's slowdown
	Time-	Brazil	Russia	India	South	Time-	Brazil	Russia	India	South
	scales				Africa	scales				Africa
					7.1. Unconditional analysis
	Short					Short
	scales					scales
	IMF1	0.3981	0.5119	0.1462	0.0043**	IMF1	0.4321	0.3146	0.0013**	0.0138*
	IMF2	0.2276	0.2081	0.0003***	0.0018**	IMF2	0.4015	0.2275	0.0029**	0.1014
	IMF3	0.2451	0.3410	0.0012**	0.0009***
	Medium					Medium
	scales					scales
	IMF4	0.6134	0.2344	0.2289	0.1567	IMF3	0.3210	0.1963	0.0162*	0.0111*
	IMF5	0.5542	0.5203	0.3016	0.1810	IMF4	0.2072	0.2048	0.0303*	0.0048**
	Long					Long
	scales					scales
	IMF6	0.0000***	0.0068**	0.3651	0.2867	IMF5	0.1093	0.0091**	0.8012	0.4985
	IMF7	0.0003***	0.0073**	0.4218	0.4155	IMF6	0.0046*	0.0068**	0.7146	0.6371
	IMF8	0.0016**	0.0107	0.2910	0.3762
	Residue 0.0001*** 0.0039**	0.0017**	0.1483	Residue	0.0001***	0.0026**	0.0044**	0.0015**
					7.2. Conditional analysis
	Short					Short
	scales					scales
	IMF1	0.1968	0.2671	0.0019**	0.1335	IMF1	0.6134	0.2678	0.0135*	0.0067**
	IMF2	0.4031	0.1342	0.0018**	0.0167*	IMF2	0.5592	0.1432	0.0108*	0.0013**
	IMF3	0.2264	0.2053	0.0000***	0.0098**
	Medium					Medium
	scales					scales
	IMF4	0.1051	0.2627	0.3358	0.2156	IMF3	0.2981	0.4267	0.0118*	0.0029**
	IMF5	0.0918*	0.3178	0.2094	0.2378	IMF4	0.3415	0.5039	0.0092**	0.0034**
	Long					Long
	scales					scales
	IMF6	0.1263	0.4567	0.5011	0.9172	IMF5	0.0023**	0.0003***	0.1652	0.4360
	IMF7	0.1029	0.0006**	0.4327	0.5429	IMF6	0.0046**	0.1012	0.1832	0.3782
	IMF8	0.0114*	0.0000**	0.2289	0.6039
	Residue 0.0003*** 0.0001***	0.0073**	0.0061**	Residue	0.0002*** 0.0000***	0.0010**	0.0017**
		Note: The table reports the p-values; *, ** or *** denote that the null hypothesis is rejected at the 10%, 5% or
		1% significant level, respectively.

Table 8 . Wavelet decomposition results: Scale-by-scale causality among China and BRICS stock returns

 8

	Panel A: Period of rapid China's growth		Panel B: Period of China's slowdown
	Time-	Brazil	Russia	India	South	Time-	Brazil	Russia	India	South
	scales				Africa	scales				Africa
					8.1. Unconditional analysis
	Short					Short
	scales					scales
	WD1	0.2871	0.2136	0.0010**	0.0004***	WD1	0.1158	0.1972	0.0107*	0.0092**
	WD2	0.1543	0.1852	0.0006***	0.0010**	WD2	0.1264	0.2341	0.0068**	0.0188*
	Medium					Medium
	scales					scales
	WD3	0.3451	0.2575	0.2289	0.1726	WD3	0.1874	0.2431	0.0093**	0.1142
	WD4	0.4872	0.2914	0.2095	0.1193	WD4	0.1932	0.2185	0.0061**	0.0032**
	Long					Long
	scales					scales
	WD5	0.0000*** 0.0001***	0.1568	0.1952	WD5	0.0012**	0.0007***	0.4415	0.2093
					8.2. Conditional analysis
	Short					Short
	scales					scales
	WD1	0.1546	0.1542	0.0003***	0.0110*	WD1	0.3255	0.2411	0.0093**	0.0134*
	WD2	0.2029	0.1098	0.0000***	0.0091**	WD2	0.2091	0.2356	0.0214*	0.1142
	Medium					Medium
	scales					scales
	WD3	0.1164	0.3110	0.1146	0.4561	WD3	0.1022	0.1092	0.0008***	0.0113*
	WD4	0.0711*	0.3452	0.1283	0.4781	WD4	0.3154	0.1076	0.0001***	0.0034**
	Long					Long
	scales					scales
	WD5	0.0024**	0.0013**	0.4177	0.3015	WD5	0.0001***	0.0014**	0.4155	0.3890
		Notes: WD1: less than 30 days; WD2: within 30 and 60 days; WD3: within 60 and 120 days; WD4: within 120
		and 240 days; WD5: more than 240 days; The table reports the p-values; *, ** or *** denote that the null
		hypothesis is rejected at the 10%, 5% or 1% significant level, respectively.

Table 9 . Scale-by-scale causality among China and BRICS stock returns (weekly data)

 9

		Panel A: Period of rapid China's growth			Panel B: Period of China's slowdown
	Time-	Brazil	Russia	India	South	Time-	Brazil	Russia	India	South
	scales				Africa	scales				Africa
				9.1. Unconditional analysis
	Short					Short
	scales					scales
	IMF1	0.6785	0.6934	0.0345*	0.0411*	IMF1	0.7645	0.6245	0.0057**	0.0086**
	IMF2	0.2459	0.2345	0.0089**	0.0096**	IMF2	0.5234	0.7542	0.0130*	0.0171*
	IMF3	0.3872	0.9510	0.2345	0.4308
	Medium					Medium
	scales					scales
	IMF4	0.5274	0.4663	0.5582	0.8156	IMF3	0.5484	0.4785	0.0413*	0.0023**
	IMF5	0.6178	0.7102	0.7239	0.6723	IMF4	0.2297	0.7213	0.0059**	0.2159
	Long					Long
	scales					scales
	IMF6	0.0036**	0.0513*	0.9568	0.3908	IMF5	0.0014**	0.5437	0.7312	0.8261
	IMF7	0.0219*	0.4567	0.7635	0.3156	IMF6	0.0213*	0.0006***	0.6273	0.3345
	IMF8	0.5062	0.3351	0.3061	0.6126
	Residue	0.0013**	0.0404*	0.0065**	0.4867	Residue	0.0035**	0.0000***	0.0156*	0.0094**
					9.2. Conditional analysis
	Short					Short
	scales					scales
	IMF1	0.3211	0.3286	0.2345	0.0234*	IMF1	0.9124	0.3219	0.0035**	0.0154*
	IMF2	0.2879	0.5081	0.0039**	0.0045**	IMF2	0.6754	0.1092	0.0184*	0.0068**
	IMF3	0.5672	0.5672	0.0004***	0.9515
	Medium					Medium
	scales					scales
	IMF4	0.3891	0.7100	0.4138	0.2216	IMF3	0.2563	0.6789	0.0251*	0.0073**
	IMF5	0.5023	0.2879	0.2545	0.5004	IMF4	0.8954	0.6430	0.0574*	0.0216*
	Long					Long
	scales					scales
	IMF6	0.0114*	0.4567	0.3561	0.3456	IMF5	0.0000***	0.0022**	0.5671	0.8467
	IMF7	0.0076**	0.0012**	0.3867	0.3267	IMF6	0.0011**	0.0008***	0.4498	0.6524
	IMF8	0.0032**	0.0048**	0.2961	0.1876
	Residue	0.0010** 0.0000***	0.0156*	0.0515*	Residue	0.0000***	0.0029**	0.0004***	0.0121*
		Note: The table reports the p-values; *, ** or *** denote that the null hypothesis is rejected at the 10%, 5% or
		1% significant level, respectively.

  Several Years of rapid economic growth have notably increased China's standing in the world. Over the last decade, it accounted for a fifth of the total growth in global exports and imports, and played a potential role in supporting demand during times of distress including the eurozone's financial crisis. Given the emergence of China as a key driver of the global economy, the China's slowing economy is sending shock waves through its trading partners around the world. The present research attempts to assess whether the deepening Chinese slowdown intensifies uncertainty spillovers among China and the remaining BRICS (Brazil, Russia, India, and South Africa) stock markets. Since the co-movement or the causality between stock markets during times of rising uncertainty may mask the irregularities we want to identify, we carry out flexible econometric techniques that are designed to extract essential hidden features from data. This sets our study apart from other literature on the issue. Appendix) reports the statistics of the average annual exports to China and imports from China to the rest of BRICS from 2000 to 2018. Over this period, Brazilian exports to China averaged 59.34 USD billion, followed by Russia (47.12 USD billion), then India (31.91 USD billion) and finally South Africa (8.92 USD billion). It is also well noticeable that Russia and Brazil are the major importers of Chinese goods, followed by India and South Africa.Regarding Chinese foreign direct investments (FDI) into BRICS countries, Brazil and Russia appear better positioned than India and South Africa (see FigureC.2, Appendix).

	Specifically, we conduct a multi-scale analysis based on empirical mode decomposition and
	wavelet approach.
	What appears interesting from the obtained results is the heterogeneity in terms of the
	significance of risk spillovers. Even though China's slowdown exerts wider influence (long-
	run) on Brazilian and Russian markets, its impact on Indian and South African equities seems
	relatively moderate (i.e., supported in the short-run). Whatever the models used (causality
	testing-based EMD or wavelets) and whatever the periods investigated (China's rapid growth

or China's slowdown), these findings remain fairly robust, with modest changes in terms of significance. These results seem intuitive since we respect the same hierarchy when considering the intensity of trade and foreign direct investment relationships. Figure C.1

(

  Wherelk and hk are respectively the low-pass and high-pass filter coefficients.

	ψ	(	x	)	=	2	h ∑ φ k	(	2	x	-	k		).	(a.2)
										k
	l k		=		2 1	∫	φ	(	t	)	φ	(	2	t	-	k	)	dt	;	h k	=	2 1 ∫	ψ	(	t	)	φ	(	2	t	-	k	)	dt	.
	A wavelet decomposition of a function	f	( x	)	can be defined as a sequence of projections into
	father			and					mother					wavelets k J s , , k J d , ,…,d k , 1 ,	expressed	as	follows:
	s	J	,	k		≈	∫	φ	J	,	k	(	t		)		f		(	t	)	dt	(a.3)
	d	j	k		≈	∫		j	k	t		f			t		dt

Table C .2. Sectoral distribution of the BRICS stock market indices (in percent)

 C

	Sectors	Brazil	Russia	India	South Africa
		Cyclical sectors
	-Oil and raw materials	50.2	60.2	1.4	2.0
	-Financials and Banks	21.9	9.7	2.6	46.0
	-Industrial and manufacturing	6.3	6.1	9.1	8.3
	-Information technology	-	3.2	47.0	2.9
	Total	78.4	79.2	60.1	59.2
		Non-cyclical sectors
	-Consumer goods	9.5	11.2	6.8	9.8
	-Telecommunications	4.3	4.1	10.4	7.0
	-Others	7.8	6.4	22.7	21.8
	Total	21.6	20.8	39.9	39.8

Sources: CME group, Bloomberg India-infoline (IIFL) websites.

We keep the same acronym throughout the rest of our study, even if it concerns only four countries.

Further control variables have been accounted for without fundamentally changing our findings. These variables include oil and iron prices. The results are available upon request.

We thank the Reviewer for the very careful review of our paper and for pointing out helpful comments and insightful remarks. A major revision of the paper has been carried out to take all of them into account.

For more details about wavelet decomposition, you can refer to Appendix B.

various rebalancing horizons. Holding diversified portfolio could play a significant role in palliating risk management and lightening the adverse risks, by allocating investments among distinct BRICS stocks that respond heterogeneously to China's growth slowdown.

Appendix

Appendix B. A brief overview on the wavelet decomposition

We explore the dynamic spillovers between China market and the remaining BRICS stock markets prior to and post-China growth's slowdown. For this purpose, we use a Wavelet

Transform operating on a data vector whose length is transformed into distinct vector of the same length. It is a technique that allows to properly separating data into different frequency components, and then analyzes each component with resolution matched to its time-scale. The wavelet approach aims at transforming the investigated time series to hierarchical structure by rigorous means of the wavelet transformations prompting a set of wavelet coefficients. This technique enables to simultaneously decompose a signal as a function of both time t and frequency f (period or scale a).

A wavelet series is a representation of a real or complex valued function by a specific orthonormal series generated by a wavelet transform. Using the wavelet decomposition, the

The raw signals are then used as input for the wavelet analysis in order to find the energy distribution of each wavelet coefficient. A further step consists of testing the causality of each frequency band.