IV. DATA AND METHODOLOGY

Transcription

1 IV. DATA AND METHODOLOGY IV.1. DATA SELECTION As mentioned in the preceding chapter, empirical investigation of crisis contagion will yield a more conclusive result if performed across different asset markets. Some study also attempts to measure contagion across sectoral indices (Nagayasu, 2001). It is suggested that this type of empirical measurement will reveal a clear causality direction between different sectors or asset markets which appear to be the case in the crisis of 2008 (Longstaff, 2010). However, due to the international nature and the scope of this study, test and analysis are performed on cross-country linkages of the international equity market. This specific asset market is chosen because there is a strong empirical evidence of global stock market crash which was originated in the United States and then spread worldwide in Daily data from thirty-four international stock market indices and one global world index, all denoted in US dollars, are collected from Thomson One Banker 1. Indices denoted in US currency are selected due to the international context of this empirical measurement of contagion. For the sensitivity analysis purpose, one international stock market index is chosen and data in local currency from this market are also collected from Thomson One Banker. All data are collected over the period 22/12/ /03/2009, resulting in 30,744 total observations of daily price indices. Daily data is opted because it is in line with previous empirical measurement of contagion which is predominantly performed on highfrequency variables (Rigobon, 2001; Gagnon & Karolyi, 2003; Khan & Park, 2009). 1 See Appendix for list of markets included in the study

2 Furthermore, it has been put forward that contagion effects are less detectable when using less frequent data (Nagayasu, 2001; Leitão, Lobao, & Armada, 2008). The countries investigated in this study represent a cross-sectional data of developed, emerging and developing economies. Additionally, they are classified based on two factors. The first classification is based on geographical proximity to the United States, specifically: Africa, America, Asia, and Europe. The purpose of this classification is to illustrate the potential effect of regional proximity to the crisis country. The second classification is based on the macroeconomic similarities to the United States. For this purpose, countries are categorized into lower-middle income, upper-middle income and high income countries (The World Bank, 2010) Daily short-term money market interest rates are obtained from (Bloomberg, 2010) and the website of central bank of each economy whenever applicable 2. Interest rates are included in order to capture common shocks and/or monetary policy coordination (Forbes & Rigobon, 2002). Short-term money market interest rates included in this study are Federal Fund Overnight Rate for the United States and its equivalences for other economies. Daily short-term interest rates are obtained over the same period as that for market indices. Three periods are distinguished: tranquil, turmoil and full periods. Tranquil period is defined as the start of data collection until the week before the stock market crash in the United States on 06 October Meanwhile the time window for the turmoil period is defined as 06 October March The start of the high volatility period in 2008 is quite clear. Graphically, the sharp decline in stock indices can be seen around early October when the stock market in the United States crashed and other markets followed 2 See Appendix for list of the source for interest rates

3 suit (BBC News, 2008; Economist, 2008). However, the end of the crisis period in this study is somewhat arbitrary. The specification of the time window for the crisis period a priori is one of the limitations of this study. Study suggests that the power of correlation test for contagion is affected by large difference in sample sizes between tranquil and turmoil periods (Dungey & Zhumabekova, 2001). Another factor that we have to take into account is that the Fisher Transformation statistic which is calculated to achieve distribution approximate normality requires a sample size larger than 50 (Nuevo, 2005). Therefore, it is deemed reasonable to specify the turmoil period as 6 month long compared to 31 months of relatively low volatility period. In sensitivity analysis, the robustness of this time window will be tested. Shorter high volatility period will be investigated based on the premise that contagion in stock market returns is generally short-lived ( (Rigobon, 2001). The implications of the time window of crisis period will be discussed later. Empirical investigation of contagion using correlation test such as that applied in this study does not specifically measure the propagation mechanism. However, trade linkages are one of the important propagation mechanisms (Dungey, Fry, & Martin, 2006); therefore, a measure of bilateral trade linkage is calculated for each of the economy considered here and the results are presented for illustrative purpose only. Furthermore, Calvo (2000) argues that countries with more internationally-traded financial assets and more liquid markets should be more vulnerable to contagion; in other words, small and highly illiquid markets are likely to be under-represented in international portfolios to begin with, and as such, shielded from contagion. For that reason, market capitalization of each market is collected from (The World Bank) and tabulated in the following chapter.

4 IV.2. DATA TREATMENT Stock market returns are calculated from the indices series using the following simple method (Brooks, 2008): Eq. 1 Where R t refers the simple return at time t and p t denotes the asset price at time t. Although it has been suggested that heteroscedasticity problem can be solved by estimating the regression in a log-linear form, this simple return method is preferred because visual presentation of returns in log-linear form can be misleading in a way that it shows homoscedasticity although heteroscedasticity are present (Maddala, 2001). Furthermore, results from correlation tests perform with simple returns and those with continuously compounded (log) returns are found to be similar (Bradley & Taqqu, 2005). Two-day rolling average is calculated from the simple returns R t in order to control for the weekend effect and different time zones across markets (Lin, Engle, & Ito, 1994; Forbes & Rigobon, 2002). It is observed that there are several missing data in this study due to weekend and public holidays. This observation is categorized as Missing Not at Random (Tabachnick & Fidell, 2007). By researching literature on both financial econometrics and contagion, simply dropping observation with missing returns data due to nonsynchronization of trading days is a reasonable procedure (Hamao, Masulis, & Ng, 1990; Tabachnick & Fidell, 2007).

5 IV.3. PRELIMINARY ANALYSIS IV.3.1. DESCRIPTIVE STATISTICS After calculating the two-day moving average of simple returns for each market and dropping the missing observations due to weekends and bank holidays in market j and USA market, preliminary analysis of the data is carried out. The following descriptive statistics of each sample are calculated: mean, standard deviation, standard error of the mean, skewness coefficient (Sk), standard error of the skewness, coefficient of kurtosis (Kr) and standard error of kurtosis. Arithmetic mean or the average of returns is the most common measure of central tendency and the sample mean can be calculated as (Berenson, Levine, & Krehbiel, 2009): Eq. 2 Where denotes the two-day rolling average of simple returns and T is the total observation in each market. Standard deviation of sample is a measure of the average dispersion of observation points around their mean and is represented by the following formula (Berenson, Levine, & Krehbiel, 2009): Eq. 3 Skewness coefficient (Sk) is the third central moment which measures the extent to which a distribution of random variables is non-symmetrical with respect to its means

6 (Brooks, 2008). The estimated skewness coefficient for the returns data in this study is calculated as (Tsay, 2005): Eq. 4 Where. Kurtosis coefficient (Kr) is the fourth central moment which is a measure of how fat the tails of the distributions are (Brooks, 2008). This statistic is calculated as (Tsay, 2005): Eq. 5 IV.3.2. STATISTICAL TESTS Any inferences to be made regarding these descriptive statistics result from statistical tests. The significance of each of the sample statistics is examined by performing the following parametric tests. Applying Central Limit Theorem, the t-tests for each of the distribution parameter is calculated since the sample size for each market is large ( > 30) (Berenson, Levine, & Krehbiel, 2009). The purpose of performing t-test for the sample mean is to check whether the estimated value is an adequate presentation of its population counterpart. The t- statistic for sample mean is (Berenson, Levine, & Krehbiel, 2009): Eq. 6 Where is the standard error of the sample mean and μ is the population mean. The null hypothesis here is whether the sample mean is significant:

7 Eq. 7 This is a two-tailed test and we reject the null hypothesis if the t-test value is bigger than the positive critical value or lower than the negative critical value for the chosen level of significance. With intention to maintain consistency, the significance level selected for all tests performed in this study is α = 5% and the critical value for two-tailed test at this level of significance is ± 1.96 (Berenson, Levine, & Krehbiel, 2009) As for the skewness coefficient, its t-statistic is calculated as (Tsay, 2005): Eq. 8 Where is the standard error of the skewness coefficient. Normal distribution has skewness coefficient Sk = 0 which signifies a symmetrical distribution (Berenson, Levine, & Krehbiel, 2009). Therefore the hypothesis tested here is whether the return distribution is not significantly skewed, i.e. whether the coefficient is not significantly different from zero (Tsay, 2005): Eq. 9 Similar to t-test for sample means, this is also a two-tailed test with critical values ± 1.96 at α = 5% and similar procedure of testing decision. A normal distribution has kurtosis coefficient Kr = 3 (Patterson, 2000). Therefore the t-test for the kurtosis coefficient is performed using the following test statistic (Tsay, 2005): Eq. 10

8 Where is the standard error of the kurtosis coefficient. The null hypothesis tested here is the absence of excess kurtosis (Tsay, 2005): Eq. 11 This is a two-tailed test with the same critical values and similar procedure of testing decision as the previous t-tests. Skewness and kurtosis coefficients indicate whether the sample distribution conform or deviate from a Gaussian distribution. A Gaussian or normal distribution is not skewed and is defined to have a coefficient of kurtosis of 3 (Brooks, 2008). There are several tests of normality such as normal probability plot, Anderson-Darling normality test, and the Jarque-Bera (JB) test (Gujarati & Porter, 2009). The latter is selected in this study as a joint test statistic to measure the departure from normality. The JB statistic is calculated as follows (Tsay, 2005): Eq ): With the null hypothesis of normality (Rachev, Mittnik, Fabozzi, Focardi, & Jasic, Eq. 13 The JB statistic is asymptotically -distributed with 2 degree of freedom (Tsay, 2005). The critical value of -distribution for 5% is 5.99 (Siegel A. F., 2003). We reject the null hypothesis of normality if the JB statistic of the sample is larger than the critical value for the chosen level of significance.

9 IV.3.3. SIMPLE CORRELATION COEFFICIENT Simple correlation coefficient here refers to the coefficient determined from the two-day rolling average returns of market j and that of USA. This coefficient measures the relative strength of linear relationship between two random variables and can be calculated using the following formula (Berenson, Levine, & Krehbiel, 2009): Eq. 14 Where indicate the sample estimation of the correlation coefficient and the superscript j and US denote the parameters of market j and USA, respectively. The significance of the calculated coefficient is tested with the test statistic defined as (Berenson, Levine, & Krehbiel, 2009): Eq. 15 Where is the standard error of the sample correlation coefficient. The null hypothesis here is that there is no correlation between the pair of market returns (Berenson, Levine, & Krehbiel, 2009): Eq. 16 This is a two-tailed test with t-statistic follows a t-distribution with (T 2) degrees of freedom. (Berenson, Levine, & Krehbiel, 2009). IV.4. METHODOLOGY The definition of contagion applied in this study is that of very restrictive classification, also known as shift-contagion. Although it is somewhat limiting, it provides

10 direct framework for contagion testing by simply comparing linkages between two markets during tranquil times to those observed directly after a shock (Forbes & Rigobon, 2002). Another advantage of defining shift-contagion is the circumvention of having to directly measure and differentiate between the various propagation mechanisms which are extremely difficult to measure and quantify (Forbes & Rigobon, 2002). Cross-market linkages investigated in this study are measured through correlation coefficient between asset returns specifically that of stock market returns. Time series data such as stock market returns are afflicted by problems of simultaneous equation, omitted variables, conditional and unconditional heteroscedasticity, serial correlation, non-linearity and non-normality problems (Rigobon, 2001). Assuming away the last two problems, this study describe and perform empirical measurement of shift-contagion in international equity market using correlation analysis, adjusted for serial correlation, conditional heteroscedasticity and omitted variables. It is also worth noting that the exogeneity of the USA market is determined a priori. All of the empirical tests in this study are performed as pair-wise multivariate analysis between market j and USA market. The underlying assumption is that the United States is designated as the epicenter of the crisis and any change in the cross-market linkages is presumed to be caused by the shock originated in this country. In other words, we define that the endogenous variable to be estimated is the return of market other than the United States and the exogenous, i.e. predetermined variable (Maddala, 2001) is the return of USA market.

11 IV.4.1. SERIAL- AND CROSS-CORRELATION TEST Serial correlation is the correlation of market returns with its past values (Brooks, 2008). On the other hand, cross-correlation refers to the correlations between return of market i at time t ( ) with the past values of market j ( ) (Tsay, 2005). If both types of correlation are found to be significant, it justifies the application of linear time series analysis to handle the non-stationarity in the returns data. The joint test for both serial- and cross-correlations is a multivariate-version of the Ljung-Box statistic calculated as (Tsay, 2005): Eq. 17 Where: m = the number of covariate k = the lag order = 1,...,p T = the sample size tr(a) = the trace of the matrix A = the sum of the diagonal elements of A = the inverse of the covariance matrix at time t (lag p = 0) = the transpose of lag-k cross-covariance matrix With null hypothesis that there is no serial- and cross-correlations: Eq. 18 follows asymptotically distribution with degrees of freedom (Tsay, 2005). The rejection of null hypothesis indicates the presence of significance serial- and cross-

12 correlation between the two markets necessitating the application of multivariate time series model to obtain the stationary residuals (Gujarati & Porter, 2009), i.e. detrended returns in this case. Each of the lag-k cross-covariance matrices in Equation 25 can be calculated by multiplying the matrix with the transpose of past values matrix. Meanwhile lag(0) covariance matrix is the product multiplied by its transpose. Formulation of variancecovariance matrix can be found in the following section (Equation 39). IV.4.2. EMPIRICAL MODEL For illustration purpose, the estimation method for the factor model as described in Equation 2-3 is Ordinary Least Square (OLS). Therefore, the empirical model to be fitted in order to test for the changes in the propagation mechanism described in the aforementioned theoretical model is (Rigobon, 2001): Eq. 19 Eq. 20 The conditional expectation of market j given is (Patterson, 2000): Eq. 21 With conditional variance of market j given is (Patterson, 2000; Tsay, 2005): Eq. 22 By assuming the exogeneity of USA market, the variance of US market is: Eq. 23

13 With conditional covariance between market j and USA market defined as (Patterson, 2000): Eq. 24 Thus the conditional correlation between the two markets is calculated as (Rigobon, 2001): Eq. 25 However, the structural model in Equation 26 above cannot be consistently estimated because (Dungey & Fry, 2000; Rigobon, 2001). In order to circumvent this problem and to remove any non-stationarity pervasive in time series data, a reduced-form of Vector Autoregressive (VAR) model is built to filter any serial- and crosscorrelation in the returns. This model is specified according to Forbes and Rigobon (2002): Eq. 26 Where: Eq. 27 Eq. 28 refers to the stock market return in the United States (as the crisis country) and is the stock market returns in market j. Similarly, denotes the daily short-term interest rate in the United States and refers to that of market j. refers to the transposed vector of market returns in each set of pair-wise market analysis. and are vector of lags. Finally, denotes the vector of reduced-form disturbances, often

14 referred to as innovation, which is assumed to be weakly stationary, i.e. it is a sequence of serially uncorrelated random vectors with mean zero and covariance matrix (Tsay, 2005). Specifically, with lag order defined as p = 3, the multivariate analysis in this study can be described as: Eq. 29 This type of equation is called a reduced-form equation since we do not directly estimate the contemporaneous linear dependence between the two random variables and (Tsay, 2005). The advantage of applying this reduced-form VAR is the ease of estimation using Ordinary Least Square (OLS) separately on each equation (Tsay, 2005; Brooks, 2008). Another advantage of VAR model applied for the calculation of the conditional correlation is that all dependent variables are endogenous (Brooks, 2008). The exogeneity of the USA returns is implied in the structural equation which can be obtained using the Cholesky decomposition 3. Nevertheless, due to the time constraint the structural equation of each pair of the markets analyzed in this study is not produced. The main purpose of this study is to calculate the conditional correlation between the markets; therefore 3 See for example: (Corsetti, Pericoli, & Sbracia, 2005; Tsay, 2005; Greene, 2008)

15 transformation of reduced-form model into the structural equation is not deemed necessary. IV.4.3. LAG ORDER IDENTIFICATION Appropriate number of lags must be specified to capture the serial- and crosscorrelation (Maddala, 2001; Gujarati & Porter, 2009). There are several information criteria available to determine the order p of an autoregressive model which based on likelihood estimation method (Tsay, 2005). In this study the number of lags are arbitrarily determined at p = 3. It has been shown in previous study that different lag order does not change the conclusion of the hypothesis test (Forbes & Rigobon, 2002). In the sensitivity analysis model of different lag order will be applied to test the robustness of this specification. IV.4.4. CONDITIONAL CORRELATION COEFFICIENT We specify D as a m x m diagonal matrix consisting of the standard deviations of (i = 1,,m) and m denotes the number of the dependent variables in the multivariate analysis model. The concurrent or lag-zero cross-correlation matrix of is defined as (Tsay, 2005): Eq. 30 Specifically, the (i, j)th element of is: Eq. 31 This correlation is referred to as a concurrent or contemporaneous correlation coefficient because it is the correlation of the two series at time t (Tsay, 2005). The

16 covariance is shown by the off-diagonal element of the covariance matrix of which can be estimated as (Tsay, 2005): Eq. 32 Where and simply signify the estimated covariance matrix and regression residuals, respectively, of a VAR(p) model. IV.4.5. ESTIMATION METHOD For a each of the specified VAR(3) model in this multivariate analysis, the conditional least squares method, which starts with the 4-th observation (t = p+1), is used to estimate the parameters. For example, conditioning on the first 3 observations of USA market, we have: Eq. 33 And the fitted model is: Eq. 34 Where t = p + 1 (t = 4),, T and the hat denotes the estimate of the parameters The estimated residuals of regression are (Tsay, 2005): Eq. 35 The series is called the reduced-form disturbances, from which we obtain the covariance matrix according to Equation 39.

17 Essentially, assuming that the rational expectation of investors can be captured by the mean return equation described by the VAR(3) model applied here, each series of market return is regressed on its past values, the past values of its covariate and lagged interest rates from both markets. This procedure is also carried out to filter any autocorrelation within and across markets which are pervasive time-series data. After conditioning each market return on these common factors, the contemporaneous linkages, i.e. comovement of market j and the market of the crisis country are therefore revealed by correlation analysis of the estimated residuals (Loretan & Phillips, 1994; Valdés, 1997; Cont, 2001; Cizeau, Potters, & Bouchaud, 2001; Dungey & Zhumabekova, 2001; Pritsker, 2001; Bradley & Taqqu, 2005; Khan & Park, 2009). The calculation of conditional correlation coefficients is performed for the three periods defined in this study: full, tranquil and turmoil periods. The significance of each of the conditional correlation coefficient is tested using the formula in Equation 22 with the null hypothesis stated in Equation 23. As for the regression analysis, t-test for each of the OLS parameters is performed with test statistic calculated as (Berenson, Levine, & Krehbiel, 2009): Eq. 36 Where: Eq. 37 And to simplify the denotation: = the dependent variable of the regression (i.e. and )

18 = the OLS estimated value of = the explanatory variable of the regression (,, etc.) = the average value of the explanatory variable = the i-th OLS estimated parameter (i = 1,., q) = the population parameter of i-th explanatory variable q = number of explanatory variables Krehbiel, 2009): This parametric test is carried out with the null hypothesis (Berenson, Levine, & Eq. 38 Additionally, the joint F test of the multiple regression parameters is performed with the statistic defined as (Berenson, Levine, & Krehbiel, 2009): Eq. 39 The null hypothesis tested for this test statistic is (Maddala, 2001): Eq. 40 Finally, as a measure of the explanatory power of the regression model, the coefficient of determination is calculated as (Berenson, Levine, & Krehbiel, 2009): Eq. 41

19 IV.4.6. MODEL CHECKING If the fitted model is adequate, the residual series should behave as a white noise (Tsay, 2005), that is is a sequence of independent and identically distributed (i.i.d) random variables with finite mean and variance. To test for the stationarity of the residuals, the Durbin-Watson (DW) test is calculated to examine whether the error terms and are correlated, i.e. first-order autocorrelation between each residual and the residual for the previous time period (Berenson, Levine, & Krehbiel, 2009). The DW statistic is defined as (Maddala, 2001): Eq. 42 Where and are the estimated residuals for period t and t - 1, respectively. The rule of thumb is that when the DW statistic approaches DW = 2, the residuals are not correlated (Berenson, Levine, & Krehbiel, 2009). In this study, DW statistics for each of the reducedform disturbances are produced using SPPS. Another assumption that is necessary to be tested is the equal variance of regression residuals (Berenson, Levine, & Krehbiel, 2009). There are several tests with the null hypothesis of homoscedasticity, i.e. equal variance, namely the likelihood ratio test, Goldfeld and Quandt test, and Breusch and Pagan test (Maddala, 2001). Due to time constraint and software availability, the test selected to detect the presence of heteroscedasticity in regression residuals is the Levene test which is which is a preferable test of variance equality when the normality assumption is questionable (Breyfogle, 2003). With limited time at hand, test for residuals heteroscedasticity is performed only on one market, namely residuals from regression of the pair-wise analysis for full period of Australia-USA markets. The producer of calculating Levene test statistic is as follows:

20 sample with size T is divided into n subgroup where is the sample size of the i-th subgroup (i = 1,, n) (NIST/SEMATECH). The Levene test statistic (LW) is formulated as (NIST/SEMATECH): Eq. 43 Where: group median of the overall median of the median of the i-th subgroup Krehbiel, 2009): The null hypothesis of Levene test is (NIST/SEMATECH; Berenson, Levine, & Eq. 44 The test statistic follows F-distribution with degrees of freedom (T n) for numerator and (n 1) for denominator. IV.4.7. ADJUSTMENT FOR HETEROSCEDASTICITY Due to the inherent heteroscedasticity of asset returns, the conditional correlation coefficients are conditional on market volatility (Forbes & Rigobon, 2002), i.e. estimates of cross-market correlation coefficients tend to increase and be biased upwards during a crisis. Forbes and Rigobon (2002) suggest that it is necessary to calculate unconditional

21 correlation coefficients to adjust for this bias. The adjusted correlation coefficient is defined as (Forbes & Rigobon, 2002) Eq. 45 Where δ is the relative increase of volatility in crisis country, which can be expressed as (Forbes & Rigobon, 2002): Eq. 46 Var is the variance of USA market during the crisis period and Var is its counterpart for the relatively more tranquil times, which is calculated from the full sample period. IV.4.8. HYPOTHESES TESTING There are two set of hypotheses testing conducted in this study. In the first test, the heteroscedasticity-adjusted (unconditional) correlation coefficients are tested by comparing the coefficient from the high volatility period to that estimated from full sample with the null hypothesis of no contagion (Dungey & Zhumabekova, 2001): Eq. 47 Eq. 48 The null hypothesis in this study slightly differs from that employed by Forbes and Rigobon (Forbes & Rigobon, 2002; Dungey, Fry, Gonzales-Hermosillos, & Martin, 2005). In order to clearly indicate that there is a significant increase in the correlation coefficient, a one-tailed test is performed with test statistic follows t-distribution at 5% level of significance. The rejection of the null hypothesis clearly indicates significant increase in the

22 cross-market linkages, i.e. contagion. The test statistics of the correlation coefficients is calculated as (Dungey, Fry, Gonzales-Hermosillos, & Martin, 2005): Eq. 49 Where is the unconditional correlation coefficient in turmoil period and is the coefficient measured for full periods. and denote the total number of observation for crisis and full sample respectively. Calculating the test statistics as fisher transformation is recommended in order to achieve distribution which is closer to normal (Bradley & Taqqu, 2005). The Fisher transformation ( ) of correlation test statistic is (Dungey, Fry, Gonzales-Hermosillos, & Martin, 2005): Eq. 50 However, it has been suggested that a stronger test is to estimate VAR model for tranquil and turmoil period and test the null hypothesis of whether the unadjusted (conditional) correlation coefficient are significantly different (Dungey & Zhumabekova, 2001): Eq. 51 Eq. 52 Where and are the unconditional correlation coefficient for tranquil and crisis period respectively. With the fisher transformation: Eq. 53

23 next chapter. Both set of hypotheses are tested in this study and the results are reported in the IV.4.9. EXOGENEITY ASSUMPTION The exogeneity assumption of the United States as the crisis country can be tested using Granger-Causality test. It is a statistical device to examine the causality relationship between two variables based on the premise that the future cannot cause the present or the past (Maddala, 2001). If the event A occurs after event B, it is implied that A cannot cause B. Basically in Granger-Causality test of the structural equation, the lead-lag relationship between the two variables and is examined. In other words, the test is conducted to see whether the two variables are contemporaneous or whether is not preceded by the endogenous variable. The series fails to Granger-cause if in a regression of on lagged and lagged, the coefficient of the latter are zero (Brooks, 2008). This test can be easily performed by examining the t test of OLS parameters from the regression for the US market of each of the VAR(3) model. IV.5. SENSITIVITY ANALYSIS Lastly, the robustness of the model is then tested by changing the parameters of the study. The sensitivity analysis is performed on three variables: lag order, common factor and time window. As mentioned previously, the lag order p = 3 applied in this study is determined arbitrarily. Therefore the first sensitivity analysis of the model is performed on lag order. The analysis is carried out by increasing the lag order to p = 5 and by decreasing the lag order to p =1.

24 Another set of sensitivity analysis is performed on the common factor applied in this study. We check whether different common factors applied in the model will affect the results of correlation analysis. This is done by replacing the lagged values of interest rates with those of another common factor. In this study, a global index MSCI World is selected and employed to replace interest rates in order to filter fundamentals from the returns. Additionally, by assuming that the USA market is the sole global factor, for each set of VARs equation, lagged interest rates from both markets are removed and regression for market j is performed only on its past values and past values of USA market. Additionally, the sensitivity of the model toward the currency on which the indices are denoted is also performed. Finally two different time windows for tranquil and turmoil periods are specified and additional regression are conducted to test whether the model is affected by different sample size and the specification of the crisis period.