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Arabian Journal of Business and Management Review
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Integration and Volatilitys Persistence in Emerging and Developed countries: Impulse Responses and Multivariate DCC GARCH

Abdelkafi ZS1* and Khoufi W2

1Faculty of Economics and Management of Sfax, University of Sfax, Sfax, Tunisia

2High Institute of Commercial Studies of Sfax, University of Sfax, Sfax, Tunisia

*Corresponding Author:
Abdelkafi ZS
Faculty of Economics and Management of Sfax
University of Sfax, Sfax, Tunisia
Tel: +251215454
E-mail: [email protected]

Received date: May 15, 2017; Accepted date: June 14, 2017; Published date: June 21, 2017

Citation: Abdelkafi ZS, Khoufi W (2017) Integration and Volatility’s Persistence in Emerging and Developed Countries: Impulse Responses and Multivariate DCC GARCH. Arabian J Bus Manag Review 7: 301. doi: 10.4172/2223-5833.1000301

Copyright: © 2017 Abdelkafi ZS, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Abstract

The financial sectors have significant direct and indirect effects on the real economy because they are responsible for saving mobilization and credit allocation. So as to maximize their utility and well manage potential risks, stockholders and investors can use various financial products. If the financial sector is healthy, credit should become more available and the cost of finance should be more affordable. Up to this point, little is known about how stock markets, exchange rates and crude oil respond to financial stress shock. This paper uses monthly stock indexes, exchange rates and crude oil prices data from April 2003 until December 2014 to test and model the international markets’ integration, short term shock and volatility persistence in both emerging and developed countries. Trivariate DCC GARCH model and impulse responses show several interdependences and integration between international stock markets, exchange rates and crude oil.

Keywords

Impulse response; DCC GARCH (1,1); Short term persistence shock; Integration; Volatility’s persistence

Introduction

The international financial markets have become closely integrated since regulations and barriers have been gradually removed over the past years so that people in different parts of the world can invest into the markets of other countries. This provides investors an opportunity to optimize portfolios by higher returns and lower risk. But, this makes the financial markets become more dependent to each other and the system more complex. However, over the last few decades international financial markets have experienced a succession of serious crisis of different causes and origins. For example, the 2007-2009 global financial crisis, which originated in the United States was sparked by the subprime real estate crisis, and then turned into a world financial crisis. Most of these crises are characterized by high volatility and contagion [1]. Moreover, recent studies suggest that crises (subprime crisis and sovereign debt) stoked greater correlations between the world’s financial markets, in particular in periods of high and extreme volatility, and thus lowered the diversification benefit potential from investing in traditional stocks.

The highly volatility and widespread contagion have prompted investors to consider alternative investment instruments as a part of diversified portfolios in order to be used as a hedge to diversify away the increasing risk in the stock markets. Since the early 2000s, commodities have emerged as an additional asset class beside traditional ones such as stocks and bonds. Many researchers, using data from before the 2000s, have found a little negative return correlation between commodity and stock returns. Return correlations among commodities in different sectors have also been found to be small. Moreover, several papers have reported decreasing movements of return correlations between commodities and stocks at least before the recent financial crisis. These characteristics of commodity returns implied an opportunity for diversification and, thus, have attracted investors worldwide. Therefore, various instruments based on commodity indices have attracted billions of dollars of investment from institutional investors and wealthy individuals. The increasing presence of index investors precipitated a fundamental process of “financialization” amongst commodities markets, through which commodity prices became more correlated with prices of financial assets and with each other. As a result, time-varying correlations between commodity and traditional assets are becoming an important issue. These relationships imply that these markets share an equilibrium that links prices in the long run.

The modeling of the co-movements of oil with exchange rate and stock indexes both in emerging and developed economies simultaneously has so far received little attention in the financial literature. Yet, it is a subject of considerable importance for the pricing, risk management, and optimization of portfolios composed of different sectors.

Modeling the volatility dynamics between oil and other assets is an important and timely topic to study because recent developments in increased integration between financial markets and the “financialization” of commodity markets are providing investors with new ways to diversify; hedge and risk manage their investment portfolios. To date, most of the research on volatility dynamics and correlations and hedge ratios between oil and other assets has used multivariate GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models like BEKK [1] (Baba, Engle, Kraft, and Kroner), DCC (Dynamic Conditional Correlation) [1]. Estimating multivariate GARCH models on large data sets poses challenges. For example, the BEKK model can have a poorly behaved likelihood function which makes estimation difficult, especially for models with more than two variables. The VECH model has a large number of free parameters which makes it impractical for models with more than two variables. The basic problem is that as the number of estimated parameters increases, the likelihood function flattens making optimization very difficult, or in some cases impossible. Restricted correlation models, like Constant Conditional Correlation (CCC), Dynamic Conditional Correlation (DCC) or Asymmetric DCC (ADCC) are designed to address some of the problems encountered with BEKK and VECH type models and still retain analytical tractability for large data sets. One of the biggest challenges in multivariate GARCH modeling is finding a tradeoff between generality and feasibility, a tradeoff that is often referred to as “The curse of dimensionality”.

This paper makes several important contributions to the literature. First, while many existing studies are interested in dynamic correlations between stock markets and exchange rates, this current paper investigates from DCC type models for both emerging and developed economies (stock indexes and exchange rates) with energy sector (crude oil). This provides a more complete understanding of how international financial markets suffer from volatility’s persistence.

We emphasize that our investigation uses a more varied and relevant data set to construct for emerging and developed financial markets.

The following sections of the paper set out the relevant literature, empirical methodology, data, empirical results and the conclusions.

Relevant Literature

Energy is an important input into the economics of the world. Large modification in energy commodity price can influence regional and global economic and financial performance. The price of energy commodities is subject to major swings over time, particularly tied to the overall business cycle. When demand for a commodity like oil exceeds production capacity, the price will rise quite sharply as both demand and supply are fairly inelastic in the short run. Since the early 2000s, prices for the majority of energy commodities have more than tripled and have set record highs. Energy market has become increasingly volatile and risky. For this reason, studying the relationships between exchange rates, stock markets and energy prices have become an extremely crucial issue for central governments, businesses and corporations.

Tuhran et al. [2] suggest that “an oil price increase will also have an effect on a country’s wealth by a transfer of income from oil importing to oil exporting countries through a shift in the terms of trade thus; inevitably, exchange rates are also expected to change”. These facts make it necessary to understand the crude oil price dynamics and its impacts on international stock markets and exchange rates in emerging and developed countries. Financial globalization presents new challenges in understanding the effects of the oil prices on international markets.

We recognize that GARCH models are widely used to model asset price volatility dynamics. In this context, using Multivariate DCC GARCH (1,1), volatility’s persistence and dynamic correlations are our focus in this paper. His estimate bivariate GARCH models using weekly data from January 1998 to December 2009 in order to investigate volatility spillovers between oil and stock market sectors in the US and Europe. They find evidence of a spillover effect from oil to stock markets in Europe and a bidirectional spillover effect between oil and US stock market sectors. His estimate bivariate GARCH models over the period 2005 to 2010 to determine return and volatility transmission between oil prices and stock markets in the Gulf Cooperation Council (GCC) countries.

He uses multivariate GARCH (1,1) models to investigate volatility dynamics between the stock prices of clean energy companies, technology companies and oil prices over the period January 1, 2001 to December 31, 2010. The stock prices of clean energy companies correlate more highly with technology stock prices than with oil prices.

During the recent past decade, financial markets have been suffered from global financial crisis (GFC) caused by the bursting of the US mortgage bubble. The literature shows that while the value of US dollar is decreasing, the value of several countries national currency is increasing during crisis period. As a consequence, dramatic movements in one foreign exchange market imply a powerful impact on markets throughout the world. Kodres and Pritsker [3] posit that “the pattern and severity of financial contagion depends on markets' sensitivities to shared macroeconomic risk factors, and on the amount of information asymmetry in each market”. Information asymmetries play an important role in increasing the effect of contagion. Lhost [4] highlights that “Because emerging countries have higher levels of asymmetric information than developed markets, it is expected that they are more influenced by contagion than developed ones”. He test the existence of contagion phenomenon during the US subprime crisis for six developed and ten emerging stock markets by applying DCC Model. They conclude that contagion is strong between US and the developed and emerging countries during the subprime crisis. Hwang et al. [5] examine the contagion effects of the U.S. subprime crisis on international stock markets using a DCC-GARCH model on 38 country data. Results suggest evidence of financial contagion not only in emerging markets but also in developed ones. The hypothesis of constant variance is too restrictive. Bollerslev [6] introduces a GARCH model, designed to allow for more flexibility in the lag structure. He concludes that the GARCH formulation better matches the data than the classic ARCH framework presented by Bollerslev [6]. Based on Bollerslev [6] findings, other research proposes alternative types of GARCH models. As a result, the literature is very rich in terms of different innovative techniques to model conditional variances. Using the multivariate DCC-GARCH specification from January 1988 to September 2009, Filis [7] finds that the conditional variances of oil and stock prices do not differ for oil-importing and oil-exporting economies. Recently, Choi and Hammoudeh [8] extend the time-varying correlations analysis by considering commodity prices of Brent oil, WTI oil, copper, gold and silver, and the S&P 500 index from January 2, 1990 to May 1, 2006. They show that commodity correlations have increased since 2003, limiting hedging substitutability in portfolios. Modeling the comovement of stock market returns is a challenging task. Ling and Dhési [9] posit that “the conventional measure of market interdependence, known as the Pearson correlation coefficient, is a symmetric, linear dependence metric, suitable for measuring dependence in multivariate normal distributions”. However, correlations may be nonlinear and time-varying as showing by Ling and Dhési [9]. In order to better understand financial markets interdependences, econometric methods are applied such as Vector Autoregressive models (VAR) (Gilmoreand and McManus [10]; Cho and Parhizgari [11] and, Ling and Dhési [9]) and regime switching models, Schwender [12]. We note that the GARCH models gained a lot of popularity. There are several MGARCH models, of which the DCC-GARCH (Dynamic Conditional Correlation GARCH) models have greatly increased in popularity. The both advantages of this specification are the flexibility of univariate GARCH models and the simplicity of parametric correlation in the model; Swaray and Hammad [13]. The literature shows that GARCH models are widely considered for measuring the financial risk. DCC models calculate the correlation between the asset returns as a function of their past volatility and the correlations among them. This specification uses the recent past information for estimating the present correlation between series. DCC model’s estimation is achieved in two steps so as to simplify the estimation of the time varying correlation matrix. It was introduced by Engle [1] and its specifications will be discussed in the next section.

Since the development of the ARCH and GARCH models by Engle [1] and Bollerslev [14], a significant literature has focused on using these specifications to model the volatility. In this case, our research focuses on the interdependencies between international stock markets, crude oil and exchange rates. It makes several important contributions to the recent literature on financial interdependence from the existence literature which largely focuses on testing contagion between stock markets.

First, this paper tests the existence of interdependence between different stock markets, exchange rates and crude oil. Second, it aims to answer the question of whether emerging markets are more vulnerable to financial crisis than developed markets during the analyzed period. This research aims to answer these questions: i) Does impulse response allow detecting integration between financial markets? ii) To what extent emerging and developed countries prove volatility’s persistence and interdependences? throughout the following sections.

Data

Our data are composed of monthly returns relative to stock market indices, exchange rates and crude oil for seven developed economies (Australia, Canada, France, Japan, New Zealand Switzerland and United Kingdom) and eight emerging countries (Brazil, Chile, China, Mexico, Malaysia, Philippines, Russia and South Africa). The period is chosen between April 2003 and December 2014. This choice is motivated by the inclusion of two important events: the Subprime crisis and that of sovereign debt in Europe.

Model Specification: Multivariate DCC GARCH (1,1)

Bollerslev [14] introduced the model dynamic conditional correlations, the DCC-GARCH, enabling the matrix of conditional correlations vary over time. This model is a generalization of CCCGARCH model of Bollerslev [14]:

rtt + εt (1)

(2)

Ht=Dt Rt Dt (3)

where:

rt: n x 1 vector yields of n active at time t,

μt: n x 1 vector of expected returns of assets at time t,

εt: n x 1 vector of errors with E [εt]=0 and cov [εt]=Ht,

Ht: n × n matrix of εt conditional variances at time t,

Dt: n x n diagonal matrix of conditional standard deviation of εt at time t,

Rt: n × n matrix of conditional correlations at time t,

?t: n x 1 vector errors with E [?t]=0 and E [?t ?t ']=ln.

This is an estimation model in two stages. The first step is to estimate the conditional variance with univariate GARCH for each series. In the second step, the standardized residuals are used (obtained in the first step) to estimate the parameters of the dynamic correlations’ matrix. This specification includes conditions allowing the covariance matrix to be positive definite at all times and the covariance to be stationary.

Analogously to the CCC-GARCH model, the matrix Ht is divided into two matrices, Dt and Rt. Dt matrix parameters derived from univariate GARCH estimated for each series:

In the previous phase, the univarite GARCH may be of different orders, which enables the analysis of sets with different numbers of delays. The Rt matrix, that of conditional correlations standardized residuals, it is now dynamic.

To ensure that Ht is positive, it is necessary that also the matrix Rt be positive since Ht=Dt Rt Dt. The matrix Dt is always positive because therefore its parameters are always positive. It must also ensure that the Rt elements are ≤ 1 because there are the correlations. To ensure that Rt is positive, this matrix is decomposed into two matrices:

Rt=Qt*-1 Qt Qt*-1 (5)

(6)

The Qt matrix must be positive so that is also the Rt. In the previous equation, Qt=Cov [εtε't]=E [εtε't], either the unconditional covariance standardized residuals obtained by univariate GARCH. Note that αDcc and βDcc are scalar. The following conditions must be met for Ht is positive definite:

αDCC ≥ 0 (7)

βDCC ≥ 0 (8)

αDCC + βDCC ? 1 (9)

The general structure of DCC dynamic correlation (p, q) is as follows:

The advantages of DCC GARCH are direct modeling of the variance and the covariance and its flexibility. However, it also has limitations: the likelihood function becomes complicated when the number of variables is greater than or equal to 3 and the conditional correlation matrix must be positive for all t. The number of variables is limited to 3 in our investigation. This model will examine transfers of volatility between stock indexes, exchange rates and crude oil.

DCC GARCH (1, 1) Model estimation

We assume that εt standardized residuals have a Gaussian distribution, the estimation method is maximum likelihood. The likelihood function for is

(11)

The parameters of Ht, θ, are divided into two groups: (?1, ?2, ?3,…,?k ,δ)=(?, ψ).

The elements of ?i correspond to the parameters of the univariate GARCH of the ith series or ?i=(αo, α1, i, αPi i, β1i, βQii ...) and ψ elements to parameters of the dynamic correlation of structure (αDCC, βDCC). Rt matrix in the log-likelihood is replaced by an identity matrix h which gives the log quasi-likelihood of the first step.

The log-likelihood is derived as follows:

(12)

(13)

(14)

According to Engle (2002), the log-likelihood is the sum of a term volatility and correlation term, the settings in Dt are then rated by θ and Rt parameters are noted by ?.

L (θ, ?)=Lv (θ) + Lc (θ, ?) (15)

Where the portion of the volatility is:

And part of the correlation is:

In the first stage, θ it is estimated by maximizing θ *=arg max θ Lv (θ), and in the second step, ? it is estimated by maximizing ? *=arg max Lc (θ, ?).

First step: We maximize the results found in eqn. (14). Rt is replaced by an identity matrix In, giving

The first term of eqn. (18) is constant, we will maximize only:

We get as an estimator:

θ*=arg max θ Lv (θ). (20)

Second step: Once the estimate of the first completed step that of the second step is done using the likelihood function:

Since we maximize only the correlations settings, it is only the terms log |Rt| and that will be used, we can simplify the likelihood function:

The resulting estimator is expressed as follows:

?*=arg? max Lc (θ, ?) (23)

Under general conditions, the likelihood estimator will be consistent and asymptotically normal:

(24)

Statistical Test

Descriptive statistics

In developed countries, crude oil provides the maximum monthly return followed by Japanese and French stock markets. The developed exchange markets have maximum yields between 2% and 3%. The minimum monthly returns are represented by the Australian Dollar. All markets have a negative skewness coefficient indicating that they experience more negative impacts than positive shocks. The kurtosis demonstrates that all series show leptokurtic distribution. The Jarque- Bera test emphasizes the rejection of the normality assumption for all series. Standard deviation coefficient shows that Australian Dollar and crude oil are the most volatile (Tables 1a and 1b).

Developed Countries
  Australia Canada France Japan
  ASX AUD/USD CRUDE OIL SPTSX CAD/USD CRUDE OIL CAC EUR/USD CRUDE OIL NIKKEI JPY/USD CRUDE OIL
Mean 0.002022 -0.070335 0.001348 0.002565 0.0006 0.0013 0.001731 0.000223 0.0013 0.0024 -0.0001 0.0016
Median 0.006069 -0.060637 0.007375 0.005273 0.0010 0.0073 0.005513 0.000420 0.0073 0.0028 -0.0005 0.0077
Maximum 0.030640 0.032609 0.112988 0.046141 0.0268 0.1129 0.052316 0.027411 0.1129 0.0525 0.0256 0.1129
Minimum -0.0588 -0.215711 -0.171477 -0.08057 -0.0416 -0.1714 -0.06307 -0.030466 -0.1714 -0.1181 -0.031 -0.1714
Std. Dev. 0.0166 0.062933 0.039791 0.016979 0.0089 0.0397 0.020741 0.010621 0.0397 0.0248 0.0103 0.0397
Skewness -1.02074 -0.151284 -0.774236 -1.49802 -0.501 -0.7742 -0.67036 -0.109192 -0.7742 -1.0278 -0.0391 -0.7968
Kurtosis 4.134924 1.955682 4.889736 7.914288 5.9536 4.8897 3.805965 3.377191 4.8897 6.1382 3.3044 4.9691
Jarque-Bera 32.27947 6.994377 35.31580 195.9982 57.557 35.315 14.47858 1.123955 35.315 82.685 0.5806 37.701
Probability 0.0000 0.0302 0.0000 0.0000 0.0000 0.0000 0.0007 0.5700 0.0000 0 0.748 0
Sum 0.2871 -9.9875 0.1914 0.3642 0.0869 0.1914 0.245786 0.0317 0.1914 0.3402 -0.0039 0.238
Sum SqDev. 0.0389 0.5584 0.2232 0.040649 0.0113 0.2232 0.060656 0.0159 0.2232 0.0861 0.015 0.2209
Observations 142 142 142 142 142 142 142 142 142 141 141 141
  New-Zealand Switzerland United-Kingdom      
  DJNZ NZD/USD CRUDE OIL SUI CHF/USD CRUDE OIL FTSE GBP/USD CRUDE OIL      
Mean 0.00101 0.00086 0.00160 0.002199 0.001206 0.001348 0.001911 -4.93E-05 0.0013      
Median 0.00358 0.00208 0.00737 0.004451 0.001093 0.007375 0.004057 0.000407 0.0073      
Maximum 0.03452 0.03233 0.11298 0.046058 0.031945 0.112988 0.036046 0.039206 0.1129      
Minimum -0.05588 -0.03931 -0.17147 -0.05223 -0.044472 -0.17147 -0.06061 -0.045133 -0.171477      
Std. Dev. 0.01482 0.01300 0.03960 0.015846 0.011085 0.039791 0.016620 0.011182 0.039791      
Skewness -0.92055 -0.49081 -0.79257 -0.57228 -0.194004 -0.77423 -0.73483 -0.477867 -0.774236      
Kurtosis 4.688782 3.56908 5.05233 3.955885 4.410505 4.889736 4.244054 5.299941 4.889736      
Jarque-Bera 35.36927 7.29554 38.1069 13.15699 12.66212 35.31580 21.93654 36.70200 35.31580      
Probability 0.000000 0.02604 0.00000 0.001390 0.001780 0.000000 0.000017 0.000000 0.000000      
Sum 0.138294 0.11714 0.21802 0.312254 0.171212 0.191486 0.271361 -0.006998 0.191486      
Sum SqDev. 0.029685 0.02283 0.21175 0.035405 0.017327 0.223247 0.038947 0.017631 0.223247      
Observations 136 136 136 142 142 142 142 142 142      

Table 1a: Descriptive Statistics (Developed countries).

Emerging Countries
  Brazil Chile China Malaysia
  BOVESPA BRL/USD CRUDE OIL IPSA CLP/USD CRUDE OIL SHANGHAI CNY/USD CRUDE OIL KLCI MYR/USD CRUDE OIL
Mean 0.004360 0.000692 0.001348 0.004083 0.000540 0.001348 0.002207 0.000880 0.002359 0.003153 0.000192 0.001348
Median 0.005251 0.003194 0.007375 0.002814 0.001072 0.007375 0.003005 0.000642 0.007794 0.004472 0.000409 0.007375
Maximum 0.062767 0.062732 0.112988 0.064782 0.948460 0.112988 0.105328 0.008979 0.112988 0.055169 0.776076 0.112988
Minimum -0.123761 -0.072783 -0.17148 -0.04373 -0.918314 -0.17148 -0.12281 -0.006689 -0.17148 -0.07172 -0.778219 -0.17148
Std. Dev. 0.028746 0.019291 0.039791 0.019891 0.136502 0.039791 0.036550 0.002139 0.039058 0.016409 0.092740 0.039791
Skewness -0.612384 -0.673448 -0.77424 0.146046 0.024824 -0.77424 -0.536863 0.376010 -0.7957 -0.5264 -0.040935 -0.77424
Kurtosis 4.702699 5.371653 4.889736 3.132959 39.00378 4.889736 4.444475 5.639254 5.166791 6.179169 70.44148 4.889736
Jarque-Bera 26.02883 44.01330 35.31580 0.609395 7669.626 35.31580 18.89647 43.93197 42.16047 66.35835 26911.13 35.31580
Probability 0.000002 0.000000 0.000000 0.737347 0.000000 0.000000 0.000079 0.000000 0.000000 0.000000 0.000000 0.000000
Sum 0.619180 0.098281 0.191486 0.579722 0.076648 0.191486 0.308926 0.123224 0.330312 0.447686 0.027232 0.191486
Sum Sq Dev. 0.116511 0.052471 0.223247 0.055787 2.627211 0.223247 0.185686 0.000636 0.212046 0.037967 1.212705 0.223247
Obs 142 142 142 142 142 142 140 140 140 142 142 142
  Mexico Philippines Russia South-Africa
  IPC MXN/USD CRUDE OIL PSEI PHP/USD CRUDE OIL RTSI RUB/USD CRUDE OIL FTSSA ZAR/USD CRUDE OIL
Mean 0.005918 -0.001134 0.001348 0.005683 0.000671 0.001603 0.002193 -0.002175 0.001348 0.005582 -0.001447 0.001603
Median 0.007785 0.000239 0.007375 0.010563 0.000995 0.007375 0.008619 0.000490 0.007375 0.006574 9.58E-05 0.007375
Maximum 0.053760 0.920887 0.112988 0.060582 0.923572 0.112988 0.115888 0.925042 0.112988 0.050332 0.042438 0.112988
Minimum -0.085412 -0.924959 -0.17148 -0.1196 -0.924741 -0.17148 -0.195058 -0.92021 -0.17148 -0.06528 -0.07326 -0.17148
Std. Dev. 0.021532 0.144744 0.039791 0.024494 0.147134 0.039605 0.045029 0.144177 0.039791 0.019612 0.015907 0.039605
Skewness -0.754545 0.006947 -0.77424 -1.09276 -0.02351 -0.79257 -0.871867 0.111257 -0.77424 -0.46443 -0.678069 -0.79257
Kurtosis 4.667342 35.89300 4.889736 7.102445 34.87812 5.052334 5.241478 35.83094 4.889736 4.046521 5.341291 5.052334
Jarque-Bera 29.92285 6401.537 35.31580 122.4372 5758.562 38.10695 47.71692 6377.694 35.31580 11.09529 41.48427 38.10695
Probability 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.003897 0.000000 0.000000
Sum 0.840377 -0.161092 0.191486 0.772841 0.091285 0.218024 0.311444 -0.308859 0.191486 0.759194 -0.196777 0.218024
Sum Sq Dev. 0.065373 2.954084 0.223247 0.080993 2.922534 0.211751 0.285891 2.930987 0.223247 0.051924 0.034159 0.211751
Obs 142 142 142 136 136 136 142 142 142 136 136 136

Table 1b: Descriptive Statistics (Emerging countries).

Descriptive statistics analysis, in emerging countries, highlights that the maximum monthly return is provided by Russia followed by China. Chile and Russia are the emerging countries whose exchange rates represent the maximum monthly return. Stock markets presenting the minimum returns are Russia and Brazil. For exchange rates, those with the minimum monthly returns are Mexico and Philippines. The kurtosis exceeding the critical value (3) indicates the presence of fat tails at all series: all series show an excess of kurtosis, this finding is consistent with the empirical literature which postulates that financial data is leptokurtic.

Correlation matrices

By examining the correlation matrices for each country, we detect that for emerging economies, the strongest correlation for the pair [stock index -exchange rate] is recorded in Brazil (59.224%), the lowest in Chile (20.942%). The correlation provided by the pair [Stock Index- Crude Oil] emphasizes that Russia (60.218%), followed by South Africa have the highest value, the least important is registered in China (7.345%). The pair of variables [Crude-Oil-Exchange Rate] suggests that the largest correlation is presented by Brazil (35.521%), followed by South Africa (32. 155%), the lowest level in Chile (1.354%) (Table 2).

Emerging countries Developing countries
Brazil Australia
  BOVESPA BRL/USD CRUDE OIL   ASX AUD/USD CRUDE OIL
BOVESPA 1 0.59224 0.42364 ASX 1 -0.08166 0.38584
BRL/USD 0.59224 1 0.35521 AUD/USD -0.08166 1 0.0478
CRUDE OIL 0.42364 0.35521 1 CRUDE OIL 0.38584 0.0478 1
Chile Canada
  IPSA CLP/USD CRUDE OIL   SPTSX CAD/USD CRUDE OIL
IPSA 1 -0.20942 0.25869 SPTSX 1 0.34086 0.56687
CLP/USD -0.20942 1 0.01354 CAD/USD 0.34086 1 0.44653
CRUDE OIL 0.25869 0.01354 1 CRUDE OIL 0.56687 0.44653 1
China France
  SHANGHAI CNY/USD CRUDE OIL   CAC EUR/USD CRUDE OIL
SHANGHAI 1 -0.02529 -0.07345 CAC 1 0.22507 0.31045
CNY/USD -0.02529 1 0.13117 EUR/USD 0.22507 1 0.32592
CRUDE OIL -0.07345 0.13117 1 CRUDE OIL 0.31045 0.32592 1
Malaysia Japan
  KLCI MYR/USD CRUDE OIL   NIKKEI JPY/USD CRUDEOIL
KLCI 1 -0.05855 0.35911 NIKKEI 1 -0.40612 0.34294
MYR/USD -0.05855 1 0.07879 JPY/USD -0.40612 1 -0.11593
CRUDE OIL 0.35911 0.07879 1 CRUDEOIL 0.34294 -0.11593 1
Mexico New-Zealand
  IPC MXN/USD CRUDE OIL   DJNZ NZD/USD CRUDE OIL
IPC 1 -0.08497 0.302743 DJNZ 1 0.28086 0.11807
MXN/USD -0.08497 1 0.15796 NZD/USD 0.28086 1 0.31348
CRUDE OIL 0.30274 0.15796 1 CRUDE OIL 0.11807 0.31348 1
Philippines Switzerland
  PSEI PHP/USD CRUDE OIL   SMI CHF/USD CRUDE OIL
PSEI 1 0.00123 0.32273 SUI 1 -0.10732 0.17824
PHP/USD 0.00123 1 0.13146 CHF/USD -0.10732 1 0.18139
CRUDE OIL 0.32273 0.13146 1 CRUDE OIL 0.17824 0.18139 1
Russia United-Kingdom
  RTSI RUB/USD CRUDE OIL   FTSE GBP/USD CRUDE OIL
RTSI 1 0.0816 0.60218 FTSE 1 0.26061 0.35816
RUB/USD 0.0816 1 0.16572 GBP/USD 0.26061 1 0.45884
CRUDE OIL 0.60218 0.16572 1 CRUDE OIL 0.35816 0.45884 1
South Africa        
  FTSSA ZAR/USD CRUDE OIL        
FTSSA 1 0.25305 0.46902        
ZAR/USD 0.25305 1 0.32155        
CRUDE OIL 0.46902 0.32155 1        

Table 2: Correlation Matrices.

The developed countries show that the correlation between [Stock Index -Crude Oil] is strong in Canada (56.687%), followed by Australia, UK, Japan and in the last rank New Zealand (11.807%). Canada also ranks first with regard to the correlation between [Stock Index- Exchange Rate] among all countries. A strong negative correlation was detected between the Nikkei 225 and the Japanese Yen (-40%). Referring to correlations between Crude Oil and Exchange Rate, it appears that the UK provides the highest value (45.884%). In Japan, this value is negative (-11.59%).

This points out that the correlation increases during periods of high market volatility. When markets become more volatile, investors demand diversification. Investment strategies based on simple correlation estimation techniques do not work well during turbulent periods. Investors’ expectations may change drastically as a result of significant declines in the financial markets. They suppose that changes in correlations between financial markets explain the impact of shocks on the financial markets during periods of high turbulence. We can conclude that the channels through which the links and co-movements between active studied propagate are not limited to differences between investors and their investment horizons. He showed that crude oil was not correlated with stock indices until 2001. When this commodity begins to be used as a financial asset, the link between oil and other assets is reinforced. The most sensitive financial markets are stock markets and foreign exchange to the extent that any new information highlighted goes quickly, affecting both markets. In other words, when assessing a particular currency, the exporting country will lose its international competitiveness which will drop accordingly sales and profits and lower stock prices.

Stationary and unit root tests

Before studying the linkages between different markets, ADF and KPSS tests are applied to examine the properties of the different series. The null hypothesis of the ADF test is that the series has a unit root, while stationary is the null hypothesis in the KPSS test. We make a KPSS test as confirmation of the results of the ADF. But if the results of both tests are contradictory, then the KPSS is preferable (Table 3).

BRL/USD CRUDE OIL BOVESPA BRL/USD CRUDE OIL   ASX AUD/USD CRUDE OIL ASX
-12.04372 -9.176819 -9.947420 -12.28834 -9.440125 ADF -10.04791 -2.344378 -9.176819 -10.05000
 0.452880  0.226275  0.032387  0.028440  0.042957 KPSS  0.161291 1.105548  0.226275  0.105585
CLP/USD CRUDE OIL IPSA CLP/USD CRUDE OIL Canada SPTSX CAD/USD CRUDE OIL SPTSX
-11.44187 -9.176819 -10.57229 -11.43688 -9.440125 ADF -9.382410 -8.169653 -9.176819 -9.422546
 0.389202  0.226275  0.043526 0.364626  0.042957 KPSS  0.164110  0.362642  0.226275  0.076828
CNY/USD CRUDE OIL SHANGHAI CNY/USD CRUDE OIL France CAC EUR/USD CRUDE OIL CAC
-8.348339 -9.410863 -6.218562 -8.342802 -9.575016 ADF -10.36741 -8.653553 -9.176819 -10.32541
 0.219982  0.152052  0.064467  0.203884  0.029489 KPSS  0.185872  0.247991  0.226275  0.144824
MYR/USD CRUDE OIL KLCI MYR/USD CRUDE OIL Japan NIKKEI JPY/USD CRUDE OIL NIKKEI
-11.46338 -9.176819 -10.48809 -11.42985 -9.440125 ADF -9.777106 -9.107105 -9.103575 -9.741921
 0.500000  0.226275  0.044110 0.5  0.042957 KPSS  0.158755  0.385534  0.202563  0.158869
MXN/USD CRUDE OIL IPC MXN/USD CRUDE OIL New-Zealand DJNZ NZD/USD CRUDE OIL DJNZ
-9.821742 -9.176819 -10.69284 -9.793172 -9.440125 ADF -10.42849 -7.915530 -8.491656 -10.42678
 0.500000  0.226275  0.062199 0.5  0.042957 KPSS  0.232414  0.060046  0.260418  0.184185
PHP/USD CRUDE OIL PSEI PHP/USD CRUDE OIL United-Kingdom FTSE GBP/USD CRUDE OIL FTSE
-9.996257 -8.491656 -11.37446 -10.03446 -8.724203 ADF -11.83172 -10.29648 -9.176819 -11.80313
 0.500000  0.260418  0.061315 0.5  0.044831 KPSS  0.129519  0.109202  0.226275  0.093443
RUB/USD CRUDE OIL RTSI RUB/USD CRUDE OIL Switzerland SMI 25 CHF/USD CRUDE OIL SMI 25
-9.052151 -9.176819 -8.885822 -9.385980 -9.440125 ADF -8.980768 -10.28086 -9.176819 -8.974406
 0.404205  0.226275  0.041444 0.314669  0.042957 KPSS  0.190958  0.053635  0.226275  0.142308
ZAR/USD CRUDE OIL FTSSA ZAR/USD CRUDE OIL          
-8.785553 -8.491656 -12.20967 -8.844799 -8.724203          
 0.180774  0.260418  0.099807  0.053097  0.044831          

Table 3: Stationary and Unit Root Tests.

Lag length selection

Before performing the vector autoregression analysis, Schwarz's Bayesian Information Criterion (SBIC), the Akaike's Information Criterion (AIC) and the Log Likelihood tests are performed to determine the appropriate length of lags to be included in the model (Table 4).

Emerging countries   VAR (1) VAR (2) VAR 3) VAR (4) VAR (5) VAR (6) Developed countries VAR (1) VAR (2) VAR 3) VAR (4) VAR (5) VAR (6)
Brazil Log Likelihood 936.2018 943.4470 950.1492 953.3405 963.2876 967.8722 Australia 1040.687 1050.402 1060.755 1064.345 1069.116 1073.337
AIC -13.79406 -13.76787 -13.73357 -13.64687 -13.66101 -13.59511 -15.35354 -15.36422 -15.38440 -15.30366 -15.24054 -15.1692
SBIC -13.53455 -13.31373 -13.0848 -12.80347 -12.62298 -12.36244 -15.09403 -14.91008 -14.73563 -14.46026 -14.20251 -13.93654
Chile Log Likelihood 695.4817 705.7867 713.9441 725.4340 733.9083 738.9954 Canada 1120.487 1127.057 1133.359 1137.784 1147.272 1153.599
AIC -10.20122 -10.2207 -10.20812 -10.24528 -10.23744 -10.17904 -16.54458 -16.50831 -16.46804 -16.39976 -16.40705 -16.36715
SBIC -9.941712 -9.766558 -9.559351 -9.401882 -9.199404 -8.946372 -16.28507 -16.05417 -15.81927 -15.55636 -15.36902 -15.13449
China Log Likelihood 1127.869 1138.669 1142.686 1152.803 1157.136 1172.031 France 1032.563 1044.247 1047.167 1053.244 1060.500 1065.489
AIC -16.90711 -16.93437 -16.85887 -16.87581 -16.80509 -16.89441 -15.23228 -15.27234 -15.1816 -15.13797 -15.11195 -15.05207
SBIC  -16.64504 -16.47575 -16.20369 -16.02407 -15.7568 -15.64956 -14.97277 -14.8182 -14.53283 -14.29457 -14.07391 -13.81941
Malaysia Log Likelihood 772.3807 786.6040 792.2146 799.8924 811.4965 821.4411 Japan 998.7731 1006.060 1011.051 1014.636 1019.580 1029.441
AIC -11.34897 -11.42693 -11.37634 -11.3566 -11.39547 -11.40957 -14.83869 -14.81293 -14.75264 -14.67122 -14.61022 -14.62317
SBIC -11.08946 -10.97279 -10.72757 -10.5132 -10.35744 -10.17691 -14.57791 -14.35656 -14.10068 -13.82367 -13.56709 -13.38445
Mexico Log Likelihood 671.2953 683.6114 695.1736 708.5698 721.1771 728.6161 New-Zealand 746.8787 747.6061 752.1125 753.6102 755.2843 756.1222
AIC -9.840228 -9.889723 -9.927964 -9.99358 -10.04742 -10.02412 -11.57623 -11.5251 -11.53301 -11.49391 -11.45757 -11.40816
SBIC -9.580720 -9.435584 -9.279194 -9.150179 -9.009388 -8.791458 -11.44254 -11.30228 -11.22107 -11.09284 -10.96737 -10.82884
Philippines Log Likelihood 621.0703 634.5765 640.5277 652.6568 664.0489 675.0904 Switzerland 1048.463 1059.660 1066.029 1069.113 1073.127 1080.255
AIC -9.516724 -9.587133 -9.539495 -9.588387 -9.625764 -9.65766 -15.4696 -15.50239 -15.46313 -15.37482 -15.3004 -15.27247
SBIC -9.249346 -9.119222 -8.871051 -8.719409 -8.556253 -8.387618 -15.21009 -15.04825 -14.81435 -14.53142 -14.26237 -14.0398
Russia Log Likelihood 606.1361 618.2140 628.6473 636.8570 647.8585 657.7490 United-Kingdom 1058.179 1063.783 1068.785 1074.201 1077.316 1083.037
AIC -8.867703 -8.913642 -8.935034 -8.92324 -8.953112 -8.96640 -15.61461 -15.56393 -15.50425 -15.45077 -15.36293 -15.31398
SBIC -8.608195 -8.459503 -8.286264 -8.079838 -7.91508 -7.733741 -15.35510 -15.10979 -14.85548 -14.60737 -14.3249 -14.08132
South Africa Log Likelihood 942.1294 949.8957 955.5799 961.3040 966.1964 972.1832              
AIC -14.53327 -14.514 -14.46219 -14.411 -14.34682 -14.29974              
SBIC -14.26589 -14.04608 -13.79374 -13.54202 -13.27731 -13.02969              

Table 4: Lag length selection.

Results and Discussions

Impulse responses

The impulse response function illustrates the impact of innovation on the present and future values of other variables and helps to determine its magnitude and its depreciation.

We investigate the short-term causal relationships among the stock markets, exchange rates and crude oil belonging to eight emerging markets and seven developed economies through impulse response analyses in the two sub-periods. Huyghebaert and Lihong [15] posited that “A shock to the i-th variable not only directly affects the i-th variable but is also transmitted to all of the other endogenous variables through the dynamic (lag) structure of the VAR.

Our results reflect the severity of the last US recession (2007-2009) leading to a combination of similar expansionary fiscal and monetary policies both by the government and the US central bank. According to the theoretical model, current stock prices reflect the expected cash flows (earnings) discounted by the appropriate interest rate. The very low interest rates increase the discounted cash flow. The prices of commodities are rising, and foreign stocks still have more than US equities (Figures 1-15).

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Figure 1: Impulse Responses of Canada.

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Figure 2: Impulse Responses of New Zealand.

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Figure 3: Impulse Responses of Australia.

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Figure 4: Impulse Responses of France.

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Figure 5: Impulse Responses of United Kingdom.

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Figure 6: Impulse Responses of Suisse

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Figure 7: Impulse Responses of Figures 1-6.

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Figure 8: Immune Response of China.

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Figure 9: Immune Response of Malaysia.

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Figure 10: Immune Response of Brazil.

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Figure 11: Immune Response of Chile.

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Figure 12: Immune Response of Mexico.

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Figure 13: Immune Response of Philippines.

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Figure 14: Immune Response of Russia.

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Figure 15: Impulse responses (Emerging countries).

In developed countries, results show that the innovations of the ASX stock index’s realized volatility have spread to the exchange rate and crude oil. This result confirms the existence of ASX index’s volatility transmission effect to the Australian dollar and crude oil on the one hand and the significant influence of the index in other markets on the other hand. Moreover, it appears that the ASX index is influential since a rise in volatility increases uncertainty in the Australian dollar and crude oil. Shock to the crude oil leads to a negligible response from ASX stock index. Crude oil responds positively with a significant amplitude during five periods (shock on S&P/TSX). This important reaction from the Canadian dollar and crude oil reflects the degree of integration of these markets with the S&P/TSX stock index. S&P/TSX and the Canadian dollar are proving insensitive to shocks on crude oil whose reaction to its own impact is negligible (shock amortized after fourth month). In France, innovations of the CAC index’s realized volatility are spread to the Euro and crude oil. The Japanese stock market does not seem to have much influence that innovations can disrupt the movements of the other markets’ realized volatility. Thus, the analysis of the impulse response functions allowed seeing an important element characterizing the Japanese market, identified by the earlier literature on its evolution. Indeed, when the Nikkei 225 stock index undergoes a positive shock that is to say an increase in its realized volatility or other markets do not react or react briefly. So we end up this feature with the impulse response functions of the Japanese market compared to other markets from the perspective of the evolution of their volatilities. Only the New Zealand currency responds positively to its own shock. Following a shock on crude oil, the stock market remains insensitive and the exchange market reacts positively with smaller magnitude. The Swiss currency responds positively to its own shock; the reaction of the other two markets remains limited. For the UK, the three markets respond positively to shock exerted on the FTSE 100. The British stock market is influential since rising volatility increases uncertainty in other markets.

By examining the impulse responses’ functions corresponding to the emerging countries, it appears that the innovations of the realized volatility of BOVESPA have spread to the Brazilian Real and crude oil. It reflects the degree of integration of this stock index with the other two markets. The Brazilian currency and crude oil respond to them own shocks but other markets appear insensitive. The IPSA stock index responds positively to its own shock, the effect fades the fifth month. Crude oil and the Chilean Peso also respond positively but with limited magnitude: an increase in volatility of the IPSA index increases uncertainty in the other two markets. The crude oil’s response to its own shock, in Mexico, is important in comparison with that recorded at the stock and exchange markets. Following a shock on the South African stock market, all markets react positively but with different amplitudes. A shock on the South African Rand brings a significantly positive response in this market: stock market and crude oil react poorly. As part of Philippines, a shock on the PSEI results in positive and increasing amplitude: the other two markets react positively but in a smaller way. The Russian stock index reacts positively to its own shock during five periods but the Russian Ruble’s reaction remains small. The crude oil’s response is positively significant and the shock’s effect is damped after five months. This strong reaction (from crude oil) reflects the degree of integration of the two markets and the significant influence of the RTSI index on crude oil.

Trivariate DCC GARCH

For emerging countries, DCC model show that in South Africa, the three markets do not persist in the short term shock. Only the South African stock market have a high volatility persistence, β11=0.84 (significant at the 1% level), β22=-0.33 and β33=0.63 are not significant. BOVESPA and the Brazilian Real have highly significant volatility persistence. A persistence to short-term shock of the Brazilian stock market is detected. IPSA and the Chilean Peso persist in the short term shock. Also, this currency seems to have a highly significant persistence of volatility at the 10% level. In China, the Yuan and crude oil persist in the short term impact: they are sensitive to them own shocks. β11, β22 and β33 provide information on the volatility’s persistence in the three markets. The KLCI index and crude oil are able to persist to the short term shock and the crude oil has the highest level of volatility’s persistence. The Mexican Peso and crude oil persist in the short term shock. In Mexico, the three markets prove the volatility’s persistence. The Philippine Peso persists in the short term shock and all markets demonstrate a continued volatility. For Russia, all coefficients are significant demonstrating that the three markets persist in the short term shock. The Russian Ruble appears to have the highest level of volatility’s persistence (Table 5).

South Africa Brazil Chili China  
Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif
1.  FTSSA{1} 0.0318207 0.71403923 1.  BOVESPA{1} 0.17013416 0.11543648 1.  IPSA{1} 0.145861219 0.27060161 1.  SHANGHAI{1} 0.088179325 0.40780613
2.  ZAR/USD{1} 0.0991598 0.35393959 2.  BRL/USD{1} -0.0377044 0.80872861 2.  CLP/USD{1} 0.02385082 0.43170671 2.  CNY/USD{1} -0.16340516 0.92489757
3.  OIL{1} 0.0058397 0.89991034 3.  OIL{1} -0.01707536 0.80720926 3.  OIL{1} 0.020859199 0.75150605 3.  OIL{1} -0.13237434 0.08558781
4.  Constant 0.2681374 0.07211364 4.  Constant 0.37546981 0.15851718 4.  Constant 0.000470131 0.88559541 4.  Constant 0.134680132 0.72498174
5.  FTSSA{1} 0.051954 0.47476985 5.  BOVESPA{1} 0.05235037 0.55669985 5.  IPSA{1} 0.467484806 0.86143122 5.  SHANGHAI{1} -0.006246457 0.05481216
6.  ZAR/USD{1} 0.0873485 0.42758874 6.  BRL/USD{1} -0.10511585 0.38707595 6.  CLP/USD{1} -0.26776404 0.44153812 6.  CNY/USD{1} 0.555071793 0.00000018
7.  OIL{1} 0.0445765 0.38267066 7.  OIL{1} 0.04105585 0.50168844 7.  OIL{1} -0.05000616 0.97194413 7.  OIL{1} -0.001638167 0.64383693
8.  Constant -0.1331269 0.40900964 8.  Constant 0.11067546 0.49339271 8.  Constant 0.015697716 0.84975836 8.  Constant 0.036596522 0.02794139
9.  FTSSA{1} 0.064336 0.7011932 9.  BOVESPA{1} 0.11102162 0.44409514 9.  IPSA{1} 0.103800704 0.58864102 9.  SHANGHAI{1} 0.032192734 0.70183
10. ZAR/USD{1} 0.083616 0.69292174 10. BRL/USD{1} 0.09722597 0.58274758 10. CLP/USD{1} 0.033197068 0.9018973 10. CNY/USD{1} 2.361881397 0.11647408
11. OIL{1} 0.0982122 0.38612771 11. OIL{1} 0.02291785 0.82895505 11. OIL{1} 0.128153305 0.29995612 11. OIL{1} 0.036315032 0.75208557
12. Constant 0.0943436 0.80562558 12. Constant 0.43319061 0.19389736 12. Constant 0.001102102 0.80082093 12. Constant 0.365399166 0.2896888
13. C(1) 0.2700392 0.47556806 13. C(1) 14.62535065 0 13. C(1) 0.00042886 0.3470657 13. C(1) 0.820107817 0.24937176
14. C(2) 2.5678235 0.10191808 14. C(2) 7.40679154 0 14. C(2) 0.027770741 0.15136465 14. C(2) 0.002152903 0.13382878
15. C(3) 4.4667127 0.70348307 15. C(3) 5.73652425 0.32686434 15. C(3) 0.001765661 0.16567926 15. C(3) 2.476267552 0.18336831
16. A(1) 0.0475906 0.25618386 16. A(1) -0.05656677 0 16. A(1) 0.606012870 0.05196181 16. A(1) 0.183783016 0.12756446
17. A(2) 0.1068033 0.5089314 17. A(2) 0.01937335 0.27463757 17. A(2) 0.814477841 0.00112814 17. A(2) 0.724642636 0.00159835
18. A(3) 0.0212908 0.70971881 18. A(3) 0.1341881 0.27475248 18. A(3) 0.062958722 0.62314974 18. A(3) 0.266270842 0.07707399
19. B(1) 0.84090257 0.00000289 19. B(1) -0.79686833 0.00046391 19. B(1) -0.234600049 0.84478533 19. B(1) 0.767517744 0.00000001
20. B(2) -0.3313119 0.61612502 20. B(2) 0.98314939 0 20. B(2) 0.738459246 0.09776856 20. B(2) 0.520310284 0
21. B(3) 0.630317 0.49454593 21. B(3) 0.42537049 0.39571228 21. B(3) -0.240246759 0.74908328 21. B(3) 0.593702433 0.00000681
22. DCC(1) 0.06327032 0.03239649 22. DCC(1) 0.06253774 0.04301929 22. DCC(1) 0.035989147 0.03217624 22. DCC(1) 0.014279944 0.09713796
23. DCC(2) 0.91080342 0 23. DCC(2) 0.89023041 0 23. DCC(2) 0.930000000 0 23. DCC(2) 0.832123802 0.00210165
Malaysia Mexico Philippines Russia  
Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif
1.  KLCI{1} 0.0087403 0.94385376 1.  IPC{1} 0.11260507 0.29291968 1.  PSEI{1} -0.015377 0.89537036 1.  RTSI{1} 0.03916189 0.72318757
2.  MYR/USD{1} -0.0035949 0.9915046 2.  MXN/USD{1} -0.07758482 0.0000006 2.  PHP/USD{1} 0.0082661 0.87824218 2.  RUB/USD{1} -0.55246973 0.01355823
3.  OIL{1} -0.0140897 0.80236842 3.  OIL{1} -0.01054676 0.82636871 3.  OIL{1} -0.1053951 0.21828396 3.  OIL{1} 0.14814136 0.22993892
4.  Constant 0.0583958 0.77465856 4.  Constant 0.45537903 0.01544928 4.  Constant 0.8784177 0.00018775 4.  Constant 0.54055225 0.16468654
5.  KLCI{1} 0.1730827 0.94323318 5.  IPC{1} 0.26776586 0.00180297 5.  PSEI{1} 0.1635326 0.00950612 5.  RTSI{1} 0.0624923 0.00592521
6.  MYR/USD{1} -0.1217512 0.97870629 6.  MXN/USD{1} -0.04016343 0.00000031 6.  PHP/USD{1} -0.9488866 0 6.  RUB/USD{1} 0.25732379 0.01674113
7.  OIL{1} 0.5640573 0.50429999 7.  OIL{1} 0.22344264 0.02030417 7.  OIL{1} -0.0306731 0.38993338 7.  OIL{1} 0.05278114 0.00439761
8.  Constant 0.5963732 0.89282446 8.  Constant 0.48792904 0.18544069 8.  Constant -0.0978548 0.56465214 8.  Constant -0.02151123 0.76102043
9.  KLCI{1} 0.0646614 0.77432666 9.  IPC{1} 0.13089664 0.47026189 9.  PSEI{1} -0.0208697 0.89375297 9.  RTSI{1} 0.10137352 0.1809442
10. MYR/USD{1} -0.0359014 0.9070695 10. MXN/USD{1} -0.01135645 0.69526771 10. PHP/USD{1} -0.0178066 0.83676515 10. RUB/USD{1} -0.29503328 0.44009692
11. OIL{1} 0.0287158 0.82362679 11. OIL{1} 0.02723733 0.79946218 11. OIL{1} 0.0765339 0.50127668 11. OIL{1} -0.03604337 0.76605897
12. Constant 0.0998685 0.81415819 12. Constant 0.62890108 0.08977095 12. Constant 0.4669436 0.20239357 12. Constant 0.82884181 0.00648768
13. C(1) 0.7938909 0.55205432 13. C(1) 0.59981814 0.33419612 13. C(1) 0.8042429 0.27157926 13. C(1) 13.5897959 0.00000089
14. C(2) 0.1156673 0.49488093 14. C(2) 70.50912593 0 14. C(2) 0.8828022 0 14. C(2) 0.06878494 0.12904108
15. C(3) 0.9087585 0.27657497 15. C(3) 3.16771166 0.14356015 15. C(3) 0.5179632 0.09521576 15. C(3) 11.76055825 0.00000707
16. A(1) 0.2571602 0.06879045 16. A(1) 0.17609956 0.33086486 16. A(1) 0.1867726 0.14475492 16. A(1) 0.41338418 0.02750041
17. A(2) 0.0405188 0.95956084 17. A(2) 0.80334115 0 17. A(2) 0.3600676 0.04208539 17. A(2) 0.15350824 0.05752827
18. A(3) 0.2578423 0.05131426 18. A(3) 0.21548242 0.03224484 18. A(3) 0.230769 0.13132316 18. A(3) 0.45949579 0.00072648
19. B(1) 0.0257099 0.98765419 19. B(1) 0.67904374 0.01420698 19. B(1) 0.6985094 0.00075859 19. B(1) (-0.15273104) 0.01928048
20. B(2) 0.023211 0.98684171 20. B(2) (-98.003989) 0 20. B(2) (-0.9801491) 0 20. B(2) 0.72860712 0
21. B(3) 0.3559985 0.05256318 21. B(3) 0.57575065 0.00088495 21. B(3) 0.5601043 0.00043075 21. B(3) (-0.22018695) 0.06906002
22. DCC(1) 0.0258423 0.04655162 22. DCC(1) 0.02208179 0.00136266 22. DCC(1) 0.0198527 0.08281995 22. DCC(1) 0.01212974 0.03067851
23. DCC(2) 0.9523500 0 23. DCC(2) 0.81417119 0 23. DCC(2) 0.9531120 0 23. DCC(2) 0.82608523 0

Table 5a: Estimated coefficients of Trivariate DCC GARCH (1, 1) (Emerging markets).

Australia Canada France Japan
Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif
1.  ASX{1} 0.00698043 0.93743796 1.  S&P/TSX{1} 0.02487972 0.8216943 1.  CAC{1} 0.025946082 0.82188071 1.  NIKKEI{1} 0.165933603 0.16264113
2.  AUD/USD{1} -0.03800905 0.08907674 2.  CAD/USD{1} -0.109356969 0.32535046 2.  EUR/USD{1} 0.053291434 0.7953321 2.  JPY/USD{1} -0.054518925 0.81823881
3.  OIL{1} 0.16228245 0.00000103 3.  OIL{1} 0.005500988 0.9190925 3.  OIL{1} -0.057870661 0.36154644 3.  OIL{1} -0.096401721 0.14806245
4.  Constant -0.07525767 0.70168334 4.  Constant 0.001488328 0.36065772 4.  Constant 0.324237185 0.10557948 4.  Constant 0.003187578 0.12426751
5.  ASX{1} 0.14622689 0.0367881 5.  S&P/TSX{1} -0.041159258 0.49337789 5.  CAC{1} 0.076520258 0.07592063 5.  NIKKEI{1} -0.09265782 0.0423256
6.  AUD/USD{1} 0.97354033 0 6.  CAD/USD{1} 0.151732836 0.21337687 6.  EUR/USD{1} 0.092605082 0.2457856 6.  JPY/USD{1} 0.153983223 0.1627041
7.  OIL{1} 0.00317514 0.90409976 7.  OIL{1} -0.008084627 0.75432388 7.  OIL{1} 0.073936363 0.00152445 7.  OIL{1} 0.010751551 0.72486311
8.  Constant -0.06151411 0.75130466 8.  Constant 0.000509417 0.56775727 8.  Constant 0.000942201 0.99171082 8.  Constant -0.000045745 0.96466648
9.  ASX{1} -0.25113205 0.3027173 9.  S&P/TSX{1} 0.133576852 0.51019578 9.  CAC{1} 0.224764908 0.06513037 9.  NIKKEI{1} -0.010313873 0.95217345
10. AUD/USD{1} -0.11602194 0.01873198 10. CAD/USD{1} -0.237047287 0.56775444 10. EUR/USD{1} -0.344801154 0.32679479 10. JPY//USD{1} 0.15028568 0.7030313
11. OIL{1} 0.06112705 0.61140839 11. OIL{1} -0.016595268 0.90187171 11. OIL{1} -0.004507918 0.9725515 11. OIL{1} 0.010978943 0.9316048
12. Constant -0.15049867 0.75788547 12. Constant 0.003106159 0.4481235 12. Constant 0.709703355 0.05515279 12. Constant 0.006864857 0.04797507
13. C(1) 4.09704662 0.00006414 13. C(1) 0.00003337 0.44186758 13. C(1) 0.376196459 0.31391841 13. C(1) 0.000059653 0.30822337
14. C(2) 1.45314394 0.0000001 14. C(2) 0.000022538 0.46739126 14. C(2) 1.274694069 0.07972132 14. C(2) 0.000005924 0.09758755
15. C(3) 11.01343048 0.00559578 15. C(3) 0.000769383 0.36208257 15. C(3) 7.557775725 0.14598524 15. C(3) 0.001109466 0.02719682
16. A(1) 0.05626314 0.45623595 16. A(1) 0.050132477 0.29511689 16. A(1) 0.123305628 0.26237878 16. A(1) 0.086987184 0.14815371
17. A(2) 0.14764289 0.09084042 17. A(2) 0.134415422 0.5075526 17. A(2) -0.069412968 0.27014046 17. A(2) (-0.110628154) 0.02354371
18. A(3) 0.45458137 0.03758552 18. A(3) 0.106948321 0.15921111 18. A(3) 0.367625273 0.00779332 18. A(3) 0.309725863 0.05044055
19. B(1) (-0.85348512) 0.01098348 19. B(1) 0.802383843 0.00034831 19. B(1) 0.784384821 0.00001792 19. B(1) 0.806981361 0
20. B(2) -0.18294582 0.15182373 20. B(2) 0.551305791 0.3293037 20. B(2) -0.297929599 0.70162674 20. B(2) 0.999273313 0
21. B(3) -0.13963634 0.52037116 21. B(3) 0.342935116 0.58101252 21. B(3) 0.15668713 0.66782042 21. B(3) -0.076564461 0.82072217
22. DCC(1) 0.01957784 0 22. DCC(1) 0.024208297 0.03848425 22. DCC(1) 0.060482475 0.09285125 22. DCC(1) 0.039363032 0.06797204
23. DCC(2) 0.95042216 0 23. DCC(2) 0.913120000 0 23. DCC(2) 0.95005559 0 23. DCC(2) 0.939264059 0
New Zealand United-Kingdom Switzerland      
Variable Coeff Signif Variable Coeff Signif Variable Coeff Signif      
1.  DJNZ{1} 0.089498191 0.25683325 1.  FTSE100{1} -0.198879074 0.08028351 1.  SMI{1} 0.2774589 0.00253805      
2.  NZD/USD{1} 0.262881082 0.01225484 2.  GBP/USD{1} 0.057957445 0.67639169 2.  CHF/USD{1} 0.072595169 0.57848606      
3.  OIL{1} -0.037367432 0.24546968 3.  OIL{1} 0.136862312 0.00054632 3.  OIL{1} 0.007930551 0.82541764      
4.  Constant 0.115370779 0.41281257 4.  Constant 0.211545712 0.19589353 4.  Constant 0.169698842 0.23206262      
5.  DJNZ{1} 0.077730793 0.29693654 5.  FTSE100{1} 0.016926734 0.81882329 5.  SMI{1} 0.015887952 0.78510716      
6.  NZD/USD{1} 0.196875484 0.03494437 6.  GBP/USD{1} 0.041224597 0.76638509 6.  CHF/USD{1} -0.00259826 0.98416915      
7.  OIL{1} 0.052690715 0.060132 7.  OIL{1} 0.101203553 0.00047093 7.  OIL{1} 0.067157234 0.00455774      
8.  Constant 0.046027905 0.68830567 8.  Constant 0.011591361 0.92262972 8.  Constant 0.115860399 0.22563927      
9.  DJNZ{1} 0.11379359 0.63026367 9.  FTSE100{1} 0.099861503 0.70347843 9.  SMI{1} 0.28938055 0.1379255      
10. NZD/USD{1} -0.110017545 0.70330794 10. GBP/USD{1} -0.215555154 0.53903042 10. CHF/USD{1} -0.649127215 0.05815879      
11. OIL{1} 0.059433431 0.60403483 11. OIL{1} -0.029521272 0.7778197 11. OIL{1} 0.024480601 0.83591717      
12. Constant 0.491605095 0.18512804 12. Constant 0.59872545 0.06967272 12. Constant 0.558555081 0.12073177      
13. C(1) 3.787156471 0 13. C(1) 0.106682177 0.30299322 13. C(1) 3.822756461 0.00000001      
14. C(2) 0.243191527 0.58202064 14. C(2) 2.260964025 0 14. C(2) 0.243335387 0.41395721      
15. C(3) 4.196945384 0.12561777 15. C(3) 2.129428136 0.38186463 15. C(3) 2.212764386 0.12874235      
16. A(1) 0.086438517 0.00046678 16. A(1) 0.075430533 0.17373828 16. A(1) 0.079354739 0.26502233      
17. A(2) 0.051680061 0.55750062 17. A(2) 0.013221447 0.50247818 17. A(2) 0.153980147 0.15809259      
18. A(3) 0.241406601 0.02183995 18. A(3) 0.046185201 0.38653925 18. A(3) 0.191058236 0.01583022      
19. B(1) (0.999776500) 0 19. B(1) 0.873319601 0 19. B(1) (-0.869196795) 0.00000012      
20. B(2) 0.760800682 0.0526367 20. B(2) 0.999244782 0 20. B(2) 0.627912654 0.0589188      
21. B(3) 0.491583032 0.00959282 21. B(3) 0.755235060 0.00226697 21. B(3) 0.654615427 0.00000954      
22. DCC(1) 0.016013116 0.02681141 22. DCC(1) 0.019086186 0.08698273 22. DCC(1) 0.048858935 0.04419157      
23. DCC(2) 0.913280000 0 23. DCC(2) 0.932568400 0 23. DCC(2) 0.947922625 0.00000009      

Table 5b: Estimated coefficients of Trivariate DCC GARCH (1, 1) (Developed countries).

In developed economies, it appears that ASX stock index has highly significant volatility’s persistence. αDCC and βDCC (both significant at the 1% level) are equal to 0.019 and 0.98, respectively. These results are consistent with the empirical literature supporting that the αDCC coefficient is almost zero and βDCC approaches unity; Hammoudeh et al. [16]. The Australian currency and crude oil show persistence in the short term shock. They are sensitive to their own impacts. In Canada, only the S&P/TSX has a high level of volatility persistence. No persistence in short-term impact from the S&P/TSX, Canadian dollar and crude oil is recorded. The CAC 40 demonstrates the persistence of volatility. We report a lack of persistence in the short-term impact for both the CAC 40 and Euro. The crude oil, in France, persists in the short term shock: it is sensitive to its own shock. Nikkei and Yen have high levels of volatility persistence. The Japanese currency and crude oil persist in the short term shock. For New Zealand, all markets prove a high level of volatility’s persistence. The New Zealand stock index and crude oil persist in the short term shock. In the UK, it appears that the three markets do not persist in the short term shock. In contrast, there is persistence of volatility in the corresponding markets. In Switzerland, only the crude oil persists to short-term shock. β11, β22 and β33 are significant proving the continued volatility on the three markets. We underline that the statistical significance of the terms α and β provide evidence of volatility clustering.

Conclusion

Globalization as well as the deregulation of financial markets, all means that price volatility will remain a central feature of oil decades to come. Originally developed in finance, GARCH models have become indispensable in short-term volatility modeling of financial market prices, largely because they are very efficient at accommodating irregular periods of price volatility and tranquility that are characteristic of financial markets. Estimating GARCH models on large data sets is challenging because of “The curse of dimensionality” (which refers to the tradeoff between generality and feasibility). For some multivariate GARCH specifications, like BEKK, the number of free parameters grows rapidly as the number of variables increases making estimation infeasible for large data sets. Multivariate GARCH models like DCC GARCH offer analytically tractable ways to estimate Multivariate GARCH models on large data sets. DCC type multivariate GARCH models are becoming very popular. DCC captures 1) persistence in volatility and 2) correlation time-varying correlation, but does not capture spill-over effects in volatility nor is DCC closed under linear transformation. This paper presented an empirical application of a range of Multivariate DCC GARCH models and impulse response functions to monthly crude oil, exchange rates and stock markets from January 2003 to December 2014. Trivariate DCC GARCH estimated coefficients show, for emerging countries, short term and long term persistence shock in most markets. For developed economies, it appears also that most markets prove volatility’s persistence. Impulse response functions emphasize that the innovations of the ASX stock index’s realized volatility have spread to the exchange rate and crude oil. This result confirms the existence of ASX index’s volatility transmission effect to the Australian dollar and crude oil in the one hand and the significant influence of the index in other markets in the other hand. Moreover, it appears that the ASX index is influential since a rise in volatility increases uncertainty in the Australian dollar and crude oil. Besides, impulse response highlights that innovations of the CAC stock index’ s realized volatility are spread to the Euro and crude oil. The Japanese stock market does not seem to have much influence that innovations can disrupt the movements of the other markets’ realized volatility. Thus, the analysis of the impulse response functions allowed seeing an important element characterizing the Japanese market, identified by the earlier literature on its evolution. Indeed, when the Nikkei 225 stock index undergoes a positive shock that is to say an increase in its realized volatility or other markets do not react or react briefly by a decline in realized volatility. So we end up this feature with the impulse response functions of the Japanese market compared to other markets from the perspective of the evolution of their volatilities. For emerging countries, the innovations of the BOVESPA index’s realized volatility have spread to the Brazilian Real and crude oil. It reflects the degree of integration of this index with the other two markets. The strong reaction, from crude oil in Russia, reflects the degree of integration of the two markets and the significant influence of the RTSI index on crude oil. Our investigation revealed the interdependences and integration between financial markets both in emerging countries than in developed economies.

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