# An examination of structural change and nonlinear dynamics in emerging equity markets.

ABSTRACT

Recent equity market collapses in many emerging nations have made many of these markets the subject of much concern. Several emerging nations underwent a dramatic overhaul of their financial infrastructure in the 1990s as a result of radical changes in regulatory attitudes. This study uses nonlinear dynamics to examine whether such regime changes have made these capital markets more efficient in recent years. This study examines ten emerging countries' equity markets, i.e. Argentina, Chile, Jordan, Korea, Malaysia, Mexico, Philippines, Taiwan, Thailand, and Turkey using daily data covering the periods 1988-1992 and 1999-2003. Informational efficiency for each examined stock market over each examined subperiod is gauged by the extent of stochastic and deterministic nonlinear predictability inherent in the market. Results indicate that the hypothesized financial regime changes during the 1990's have had no conclusive impact on the examined nonlinear predictability of these markets. The good news is that no compelling evidence was uncovered to suggest that any of the examined markets have become less informationally efficient over the ensuing period.

INTRODUCTION

Recent equity market collapses in many emerging nations have made many of these markets the subject of much concern. Several emerging nations underwent a dramatic overhaul of their financial infrastructure in the 1990s as a result of radical changes in regulatory attitudes, sometimes shaped by external pressures applied from creditor nations and the International Monetary Fund (IMF) (Radelet and Sachs, 1998; Dornbush and Werner, 1994). Have such regime switches made these capital markets more efficient in recent years? This study will seek to determine whether nonlinear predictability of emerging markets have changed due to these regime switches. While there has been much investigation of nonlinear dynamics and chaos in the capital markets of the developed world (e.g., see Hsieh, 1995; Kohers et al., 1997; Pandey et al., 1998), examinations of nonlinear dynamics in emerging markets have been limited in scope to stochastic nonlinearities (Sewel et al., 1993) or to sporadic coverage (Barkoulas and Travlos, 1998). Some recent literature has focused on regime switching models to explain exchange rates (Van Norden, 1996) and capital market integration (Bekaert and Harvey, 1995). Some studies (e.g., Guillermo and Mishkin, 2003) have tried to explore the impact of currency regime switches on capital markets. Moving beyond currency regimes, the intent of this study is to explore the equity market impact of regime shifts in the broader financial infrastructure of emerging countries, such as the ones mentioned in Radlett and Sachs (1998). Hence this study examines emerging country equity markets before and after apparent regime changes using nonlinear dynamics, both stochastic and deterministic, in order to ascertain the predictability of these markets in these separate periods.

DATA AND METHODOLOGY

This study will examine the Morgan Stanley Capital International Markets (MSCI) daily stock index returns from ten emerging markets (i.e., Argentina, Chile, Jordan, Korea, Malaysia, Mexico, Philippines, Taiwan, Thailand, and Turkey) for evidence of the existence of nonlinear processes under various financial infrastructure regimes. This data set consists of daily index values in each country's local currency, the observations span from the origin (base) date of the index, the earliest date, starting from Jan 4, 1988 to December 31, 2003. These indexes, representing market-weighted price averages, were retrieved from Datastream database and are compiled by Morgan Stanley Capital International Perspective (MSCI) of Geneva, Switzerland. These indices represent emerging stock markets worldwide for which data was available on a consistent and reliable basis. The Morgan Stanley Capital International indexes are considered performance measurement benchmarks for global stock markets and are accepted benchmarks used by global portfolio managers as well as researchers (e.g., Cochran et al., 1993). Each one of the country indexes is composed of stocks that broadly represent the stock compositions in the different countries. To avoid the possibility that any detected systematic pattern is due to foreign exchange rate developments, the various national stock markets are measured in terms of their respective local currencies.

The sample period examined in this study extends from 1988 through 2003. However, the intermediate period 1993-1998 is hypothesized to be a period of structural change in the financial infrastructure of many emerging markets as enumerated in Radelet and Sachs (1998) and Dornbush and Werner (1994). The intent of this study is to examine the impact of these structural shifts in nonlinear dynamics inherent in the equity markets of these emerging nations. Hence the overall time frame is also subdivided into two subperiods of approximately equal length, that is 1988-1992 and 1999-2003, and the data sample is then examined for stationary nonlinear dynamics across the two subperiods.

Since the intent of this study is to investigate nonlinear dynamics, prior to proceeding with their examination for nonlinearity, each index returns series is filtered for linear correlations using autoregressive models of order p denoted AR (p) of the form:

[Y.sub.t] = [[theta].sub.0] + [P.summation over (i=1) [[phi].sub.i] [Y.sub.t-1] + [[omega].sub.t]

where [[omega].sub.t] is a random error term uncorrelated over time, while [phi] = ([[phi].sub.?], [[phi].sub.2] ..., [[phi].sub.n]) is the vector of autoregressive parameters. The lags (or order, p) used in the autoregressions for the appropriate model are determined via the Akaike Information Criterion (AIC) (Akaike 1974).

In examining the efficiency of financial markets, the first step lies in testing for the randomness of security or portfolio returns. Such an approach was adopted in earlier studies of market efficiency using linear statistical theory and very general nonparametric procedures. Examinations of chaotic dynamics have revealed that deterministic processes of a nonlinear nature can generate variates that appear random and remain undetected by linear statistics. Hence, this study employs tests that have recently evolved from statistical advances in chaotic dynamics. One of the more popular statistical procedures that has evolved from recent progress in nonlinear dynamics is the BDS statistic, developed by Brock et al. (1991), which tests whether a data series is independently and identically distributed (IID).

The BDS statistic, which can be denoted as [W.sub.m,T([member of])] is given by

[W.sub.m,T]([epsilon])= [square root of T] [[C.sub.m,T]([epsilon])-[C.sub.1,T][([epsilon]).sup.m]] [??] [[sigma].sub.m,T]([epsilon])

where:

T = the number of observations,

[member of] = a distance measure,

m = the number of embedding dimensions,

C = the Grassberger and Procaccia correlation integral, and

[[sigma].sup.2] = a variance estimate of C.

For more details about the development of the BDS statistic, see Brock et al. (1991). Simulations in Brock et al. (1991) demonstrate that the BDS statistic has a limiting normal distribution under the null hypothesis of independent and identical distribution (IID) when the data series is sufficiently large (over 500 observations). The use of the BDS statistic to test for independent and identical distribution of pre-whitened data has become a widely used and recognized process (e.g., Hsieh, 1991, 1993, 1995; Kohers et al., 1997; Pandey et al., 1998; Sewell et al., 1993). After data has been pre-whitened and nonstationarity is ruled out, the rejection of the null of IID by the BDS statistic points towards the existence of some form of nonlinear dynamics.

Rejection of the null hypothesis of IID by the BDS statistic is not considered evidence of the presence of chaotic dynamics. Other forms of nonlinearity, such as nonlinear stochastic processes, could also drive such results. In addition, structural shifts in the data series can be a significant contributor to the rejection of the null.

In order to minimize the possibility of stochastic nonlinearity affecting the results of tests for chaotic dynamics, a series of stochastic filters are employed. As there is a wide range of identified stochastic processes in existence, no exhaustive filter exists for the general class of stochastic nonlinear processes. The alternative is to fit stochastic models to the data and capture the residuals. If these are IID, we know that stochastic nonlinearity explains away all the nonlinearity identified by the BDS statistics of pre-whitened data series.

However, since it is possible to construct an infinite number of stochastic models, fitting each model to the pre-whitened data is an impossible task to undertake. Fortunately, prior research indicates that Generalized Autoregressive Conditional Heteroskedasticity (Engel, 1982) model of the first order, i.e., GARCH (1,1) is able to explain away the latent stochastic nonlinearity in a wide range of financial time-series (e.g., Brock et al., 1991; Errunza et al., 1994; Hsieh 1993, 1995; Sewell et al., 1996). Bera and Higgins (1993) provide an extensive survey of the application of GARCH models to the studies of many financial assets. Hence it is imperative, that any pre-whitened financial series exhibiting non-IID behavior be subjected to filters for the GARCH (1,1) process first.

The GARCH process may be described as:

[y.sub.t] = [[beta].sub.0] + [m.summation over (i=1) [[beta].sub.i][x.sub.t-i] + [[epsilon].sub.t]

where [[epsilon].sub.t] (conditional on past data) is normally distributed with mean zero and variance [h.sub.t] such that:

[h.sub.t] = [omega] + [q.summation over (i=1)] [[alpha].sub.i] [[epsilon].sup.2.sub.t-i] + [p.summation over (j=1)] [[gamma].sub.j] [[h.sub.t-j]

Hence the GARCH series becomes and iterative series where past conditional variances feed into future values of the series [x.sub.t] and the solution is obtained when the computing algorithm achieves convergence. The GARCH (1,1) series is a GARCH model estimated with values of p = q =1 in the above scheme.

The GARCH(1,1) model is fitted to each data series and the residuals captured in the filtering process. If this conditional heteroskedasticity model explains any observed non-IID behavior of the data series, one can be certain that stochastic nonlinearity is the contributing factor.

If the data sets examined pass the abovementioned stochastic filter and still displays non-IID behavior as per recomputed BDS statistics, then one can employ tests specifically aimed at detecting chaotic nonlinearity latent in the datasets. The test for chaos employed in this study is the third moment test (Brock et al., 1991; Hsieh 1989, 1991).

Hsieh (1989, 1991) and Brock et al. (1991) developed the third moment test to specifically capture mean-nonlinearity in a given series. Briefly stated, this test uses the concept that mean-nonlinearity implies additive autoregressive dependence, whereas variance-nonlinearity implies multiplicative autoregressive dependence. Using this notion and exploiting its implications, Hsieh (1989, 1991) constructed a test that examines the third order moments of a given series. Additive dependencies will lead to some of these third order moments being correlated. By its construction, this test will not detect variance nonlinearities.

The third order sample correlation coefficients are computed as:

[r.sub.(xxx)] (i,j) = [1/T [summation] [x.sub.t] [x.sub.t-1] [x.sub.t-j]] / [[1/T [summation] [x.sup.2.sub.t]].sup.1.5]

where:

[r.sub.(xxx)] (i,j) = the third order sample correlation coefficient of [x.sub.t] with [x.sub.t-I] and [x.sub.t-j]

T = the length of the data series being examined.

Hsieh (1991) developed the estimates of the asymptotic variance and covariance for the combined effect of these third order sample correlation coefficients which can be used to construct a [chi square] statistic to test for the significance of the joint influence of the [r.sub.(xxx)] (i,j)'s for specific values of j, such that 1 [less than or equal to] I [less than or equal to] j. If the [chi square] statistics for relatively low values of j are significant, this outcome would be a strong indicator of the presence of mean-nonlinearity in the examined series. As chaotic determinism is a form of mean-nonlinearity, the third moment test provides strong evidence of the presence of chaos.

Hence, the methodology employed follows a sequential series of steps where each country's index values are used to compute returns using differenced logs. Next, each returns series is then filtered for latent linearity by fitting it with an appropriate autoregressive model and capturing the residuals. The appropriate lag lengths for constructing these autoregressive models are determined by employing the Akaike Information Criterion. These filtered data series are then be tested for nonlinear dynamics by employing the BDS statistics. Rejection of the null of IID for stationary data indicates the presence of nonlinear dynamics. To ensure that the results from the above step is not merely an artifact of nonstationarity of the examined index returns series, the BDS test is conducted on subsets of the larger data set. If the BDS test results for the subsets are not consistent with those for the entire data set, then nonstationarity of the data sets will taint the results of tests for nonlinearity employed in subsequent steps. Hence those returns series will not be examined further in this study.

Each index returns series is then filtered for latent GARCH effects by employing the popular GARCH(1,1) model. If the residuals of the pre-whitened returns series fitted with the above models do not reject the null of IID, as per recomputed BDS statistics, one may conclude that the source of the observed nonlinear behavior is stochastic nonlinearity. The series for which non-IID behavior of pre-whitened returns are not explained by either nonstationarity of data or via the examined stochastic influences, are then tested for deterministic nonlinearity (chaos) using the Third Moments test.

RESULTS

Since all tests for nonlinear dynamics are also sensitive to inherent linearities, each examined series is filtered for linear autocorrelation before tests for nonlinear dynamics are applied. The order of the linear filter applied is determined by the Akaike Information Criterion (AIC), (Akaike, 1974). Table 1 presents the autoregressive lags used to filter each examined equity index return series for each of the subperiods studied. As mentioned before, the two subperiods examined are before the hypothesized structural change (1988-1992) and after (1999-2003).

Table 2 presents the computed BDS statistics for the sample subperiod 1, 1988-1992. The BDS statistics used in this study report computed statistics of each data series for dimensions m = 2, ..., 10 and the distance measure [epsilon] = 0.5 F and 1.00 F. A lower [epsilon] value represents a more stringent criteria since points in the m-dimensional space must be clustered closer together to qualify as being "close" in terms of the BDS statistic. The BDS statistic has an intuitive explanation. For example, a positive BDS statistic indicates that the probability of any two m histories, ([x.sub.t], [x.sub.t-1], ..., [x.sub.t-m+1]) and ([x.sub.s], [x.sub.s-1], ..., [x.sub.s-m+1]), being close together is higher than what would be expected in truly random data. In other words, some clustering is occurring too frequently in an m-dimensional space. Thus, some patterns of stock return movements are taking place more frequently than is possible with truly random data.

In this study, the values of m examined go only as high as 10. Two reasons dictate the choice of 10 as the highest dimension analyzed. First, with m = 10, only about 130 non-overlapping 10 history points exist in each examined return series. Examining a higher dimensionality would restrict the confidence in the computed BDS statistic. Second, the interest of this study lies only in detecting low-dimensional nonlinearity. High-dimensional nonlinear dynamics is, for all practical purposes, just as good as IID behavior where index predictability is concerned.

As noted in the Table 2, all reported BDS statistics reject the null of independent and identical distribution (IID). Hence it is possible that some nonlinearities exist in all examined equity indices during the 1988-92 subperiod. A similar examination of BDS statistics for the 1999-2003 subperiod in Table 3 shows that except for the Korean equity index, all examined indices still exhibit possible signs of nonlinear influences.

Given the plethora of evidence in existence that points towards the existence of stochastic nonlinearites in equity markets (e.g., Brock et al., 1991; Errunza et al., 1994; Hsieh ,1993, 1995; Sewell et al., 1996), a stochastic GARCH(1,1) model is employed to filter the pre-whitened returns. These GARCH filtered series are examined again using the BDS statistics. As noted from Tables 4 and 5, the GARCH(1,1) filters do not significantly alter the outcomes observable from the reported BDS statistics. Hence, commonly observed stochastic influences do not seem to affect the examined emerging market equity indices.

The results of the third moments test are presented in Table 6. This table shows the [x.sup.2] statistics for a combined test of the significance of all examined three moment correlations [r.sub.(xxx)](i,j) up to a certain lag length. Where 1 [less than or equal to] I [less than or equal to] j [less than or equal to] 5, the [x.sup.2] statistic has 15 degrees of freedom. When 1 [less than or equal to] I [less than or equal to] j [less than or equal to] 10, the [x.sup.2] statistic has 55 degrees of freedom. As one may observe from Table 6, the [x.sup.2.sub.15] statistics for the Thai index returns series is significant at the 1% level, where as the [x.sup.2.sub.55] statistics for equity indices of Jordan, Taiwan and Turkey are significant at a minimum of 5% level. These results suggest that the Thai index returns is highly likely to be influenced by low-dimensional chaos, whereas the chaotic determinism driving the index returns of Jordan, Taiwan and Turkey is somewhat higher dimensional. These observations suggest that during the 1988-1992 subperiod, index returns of Thailand, Jordan, Taiwan and Turkey were driven by nonlinear deterministic processes. The low dimensionality of chaos in the Thai index indicates a greater degree of predictability than the somewhat higher dimensionality of chaos driving the equity indexes of Jordan, Taiwan and Turkey.

Results of the three moments tests for the sample subperiod 1999-2003 presented in Table 7 indicate low dimensional chaos driving the index returns of Mexico and Philippines and a somewhat higher dimensional chaos in index returns of Chile. These results indicate that the hypothesized structural changes may have made the markets of Philippines, Mexico and Chile more predictable. However, it remains unclear that this possible predictability is economically exploitable.

CONCLUSIONS AND IMPLICATIONS

Overall, the results of this study indicate that the period of structural instability during the mid 1990s has rendered the equity market of Korea driven more by a random process. The Korean equity market exhibits IID behavior during the second subperiod examined and hence it exhibits no signs of predictability. During this latter subperiod, post hypothesized structural change, the markets of Thailand, Jordan, Taiwan and Turkey have become less predictable, while the stock markets of Chile, Mexico and Philippines, somewhat more predictable. Overall, the results are mixed and do not lead us to a very conclusive determination of a structural shift in emerging equity markets caused by recent changes in the financial infrastructure in these markets. Any observed predictability is implied by the existence of low dimensional nonlinear determinism, or chaos, in these markets. From a practical standpoint, such observed predictability may be too costly to implement and may generate returns of insufficient magnitude to overcome transactions costs. Hence, even in these instances, one may not be able to confirm any instances of market inefficiency. Moreover, since one does not observe any consistent pattern of change in the nonlinear dynamics of examined markets before and after the hypothesized structural overhaul of financial markets in emerging countries, one is unable to discern any material impact on the efficiency of these financial markets.

The good news is that, for the most part, no compelling evidence was uncovered in this study to suggest that any of the examined markets have become less informationally efficient as a result of the overhaul of the financial infrastructure in these economies. Future studies should aim at examining the multivariate impact of key macroeconomic factors affected by the changing financial environment in these emerging markets, and their varying contribution to equity market efficiency.

REFERENCES

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Brock, W., W. Dechert, B. Lebaron & J.A. Scheinkman (1997). A Test for Independence Based on the Correlation Dimension. Econometrics Reviews, 15, 197-235.

Brock, W., D. Hsieh & B. Lebaron (1991). Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. Cambridge, MA: MIT Press.

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Vivek K. Pandey, University of Texas at Tyler

Recent equity market collapses in many emerging nations have made many of these markets the subject of much concern. Several emerging nations underwent a dramatic overhaul of their financial infrastructure in the 1990s as a result of radical changes in regulatory attitudes. This study uses nonlinear dynamics to examine whether such regime changes have made these capital markets more efficient in recent years. This study examines ten emerging countries' equity markets, i.e. Argentina, Chile, Jordan, Korea, Malaysia, Mexico, Philippines, Taiwan, Thailand, and Turkey using daily data covering the periods 1988-1992 and 1999-2003. Informational efficiency for each examined stock market over each examined subperiod is gauged by the extent of stochastic and deterministic nonlinear predictability inherent in the market. Results indicate that the hypothesized financial regime changes during the 1990's have had no conclusive impact on the examined nonlinear predictability of these markets. The good news is that no compelling evidence was uncovered to suggest that any of the examined markets have become less informationally efficient over the ensuing period.

INTRODUCTION

Recent equity market collapses in many emerging nations have made many of these markets the subject of much concern. Several emerging nations underwent a dramatic overhaul of their financial infrastructure in the 1990s as a result of radical changes in regulatory attitudes, sometimes shaped by external pressures applied from creditor nations and the International Monetary Fund (IMF) (Radelet and Sachs, 1998; Dornbush and Werner, 1994). Have such regime switches made these capital markets more efficient in recent years? This study will seek to determine whether nonlinear predictability of emerging markets have changed due to these regime switches. While there has been much investigation of nonlinear dynamics and chaos in the capital markets of the developed world (e.g., see Hsieh, 1995; Kohers et al., 1997; Pandey et al., 1998), examinations of nonlinear dynamics in emerging markets have been limited in scope to stochastic nonlinearities (Sewel et al., 1993) or to sporadic coverage (Barkoulas and Travlos, 1998). Some recent literature has focused on regime switching models to explain exchange rates (Van Norden, 1996) and capital market integration (Bekaert and Harvey, 1995). Some studies (e.g., Guillermo and Mishkin, 2003) have tried to explore the impact of currency regime switches on capital markets. Moving beyond currency regimes, the intent of this study is to explore the equity market impact of regime shifts in the broader financial infrastructure of emerging countries, such as the ones mentioned in Radlett and Sachs (1998). Hence this study examines emerging country equity markets before and after apparent regime changes using nonlinear dynamics, both stochastic and deterministic, in order to ascertain the predictability of these markets in these separate periods.

DATA AND METHODOLOGY

This study will examine the Morgan Stanley Capital International Markets (MSCI) daily stock index returns from ten emerging markets (i.e., Argentina, Chile, Jordan, Korea, Malaysia, Mexico, Philippines, Taiwan, Thailand, and Turkey) for evidence of the existence of nonlinear processes under various financial infrastructure regimes. This data set consists of daily index values in each country's local currency, the observations span from the origin (base) date of the index, the earliest date, starting from Jan 4, 1988 to December 31, 2003. These indexes, representing market-weighted price averages, were retrieved from Datastream database and are compiled by Morgan Stanley Capital International Perspective (MSCI) of Geneva, Switzerland. These indices represent emerging stock markets worldwide for which data was available on a consistent and reliable basis. The Morgan Stanley Capital International indexes are considered performance measurement benchmarks for global stock markets and are accepted benchmarks used by global portfolio managers as well as researchers (e.g., Cochran et al., 1993). Each one of the country indexes is composed of stocks that broadly represent the stock compositions in the different countries. To avoid the possibility that any detected systematic pattern is due to foreign exchange rate developments, the various national stock markets are measured in terms of their respective local currencies.

The sample period examined in this study extends from 1988 through 2003. However, the intermediate period 1993-1998 is hypothesized to be a period of structural change in the financial infrastructure of many emerging markets as enumerated in Radelet and Sachs (1998) and Dornbush and Werner (1994). The intent of this study is to examine the impact of these structural shifts in nonlinear dynamics inherent in the equity markets of these emerging nations. Hence the overall time frame is also subdivided into two subperiods of approximately equal length, that is 1988-1992 and 1999-2003, and the data sample is then examined for stationary nonlinear dynamics across the two subperiods.

Since the intent of this study is to investigate nonlinear dynamics, prior to proceeding with their examination for nonlinearity, each index returns series is filtered for linear correlations using autoregressive models of order p denoted AR (p) of the form:

[Y.sub.t] = [[theta].sub.0] + [P.summation over (i=1) [[phi].sub.i] [Y.sub.t-1] + [[omega].sub.t]

where [[omega].sub.t] is a random error term uncorrelated over time, while [phi] = ([[phi].sub.?], [[phi].sub.2] ..., [[phi].sub.n]) is the vector of autoregressive parameters. The lags (or order, p) used in the autoregressions for the appropriate model are determined via the Akaike Information Criterion (AIC) (Akaike 1974).

In examining the efficiency of financial markets, the first step lies in testing for the randomness of security or portfolio returns. Such an approach was adopted in earlier studies of market efficiency using linear statistical theory and very general nonparametric procedures. Examinations of chaotic dynamics have revealed that deterministic processes of a nonlinear nature can generate variates that appear random and remain undetected by linear statistics. Hence, this study employs tests that have recently evolved from statistical advances in chaotic dynamics. One of the more popular statistical procedures that has evolved from recent progress in nonlinear dynamics is the BDS statistic, developed by Brock et al. (1991), which tests whether a data series is independently and identically distributed (IID).

The BDS statistic, which can be denoted as [W.sub.m,T([member of])] is given by

[W.sub.m,T]([epsilon])= [square root of T] [[C.sub.m,T]([epsilon])-[C.sub.1,T][([epsilon]).sup.m]] [??] [[sigma].sub.m,T]([epsilon])

where:

T = the number of observations,

[member of] = a distance measure,

m = the number of embedding dimensions,

C = the Grassberger and Procaccia correlation integral, and

[[sigma].sup.2] = a variance estimate of C.

For more details about the development of the BDS statistic, see Brock et al. (1991). Simulations in Brock et al. (1991) demonstrate that the BDS statistic has a limiting normal distribution under the null hypothesis of independent and identical distribution (IID) when the data series is sufficiently large (over 500 observations). The use of the BDS statistic to test for independent and identical distribution of pre-whitened data has become a widely used and recognized process (e.g., Hsieh, 1991, 1993, 1995; Kohers et al., 1997; Pandey et al., 1998; Sewell et al., 1993). After data has been pre-whitened and nonstationarity is ruled out, the rejection of the null of IID by the BDS statistic points towards the existence of some form of nonlinear dynamics.

Rejection of the null hypothesis of IID by the BDS statistic is not considered evidence of the presence of chaotic dynamics. Other forms of nonlinearity, such as nonlinear stochastic processes, could also drive such results. In addition, structural shifts in the data series can be a significant contributor to the rejection of the null.

In order to minimize the possibility of stochastic nonlinearity affecting the results of tests for chaotic dynamics, a series of stochastic filters are employed. As there is a wide range of identified stochastic processes in existence, no exhaustive filter exists for the general class of stochastic nonlinear processes. The alternative is to fit stochastic models to the data and capture the residuals. If these are IID, we know that stochastic nonlinearity explains away all the nonlinearity identified by the BDS statistics of pre-whitened data series.

However, since it is possible to construct an infinite number of stochastic models, fitting each model to the pre-whitened data is an impossible task to undertake. Fortunately, prior research indicates that Generalized Autoregressive Conditional Heteroskedasticity (Engel, 1982) model of the first order, i.e., GARCH (1,1) is able to explain away the latent stochastic nonlinearity in a wide range of financial time-series (e.g., Brock et al., 1991; Errunza et al., 1994; Hsieh 1993, 1995; Sewell et al., 1996). Bera and Higgins (1993) provide an extensive survey of the application of GARCH models to the studies of many financial assets. Hence it is imperative, that any pre-whitened financial series exhibiting non-IID behavior be subjected to filters for the GARCH (1,1) process first.

The GARCH process may be described as:

[y.sub.t] = [[beta].sub.0] + [m.summation over (i=1) [[beta].sub.i][x.sub.t-i] + [[epsilon].sub.t]

where [[epsilon].sub.t] (conditional on past data) is normally distributed with mean zero and variance [h.sub.t] such that:

[h.sub.t] = [omega] + [q.summation over (i=1)] [[alpha].sub.i] [[epsilon].sup.2.sub.t-i] + [p.summation over (j=1)] [[gamma].sub.j] [[h.sub.t-j]

Hence the GARCH series becomes and iterative series where past conditional variances feed into future values of the series [x.sub.t] and the solution is obtained when the computing algorithm achieves convergence. The GARCH (1,1) series is a GARCH model estimated with values of p = q =1 in the above scheme.

The GARCH(1,1) model is fitted to each data series and the residuals captured in the filtering process. If this conditional heteroskedasticity model explains any observed non-IID behavior of the data series, one can be certain that stochastic nonlinearity is the contributing factor.

If the data sets examined pass the abovementioned stochastic filter and still displays non-IID behavior as per recomputed BDS statistics, then one can employ tests specifically aimed at detecting chaotic nonlinearity latent in the datasets. The test for chaos employed in this study is the third moment test (Brock et al., 1991; Hsieh 1989, 1991).

Hsieh (1989, 1991) and Brock et al. (1991) developed the third moment test to specifically capture mean-nonlinearity in a given series. Briefly stated, this test uses the concept that mean-nonlinearity implies additive autoregressive dependence, whereas variance-nonlinearity implies multiplicative autoregressive dependence. Using this notion and exploiting its implications, Hsieh (1989, 1991) constructed a test that examines the third order moments of a given series. Additive dependencies will lead to some of these third order moments being correlated. By its construction, this test will not detect variance nonlinearities.

The third order sample correlation coefficients are computed as:

[r.sub.(xxx)] (i,j) = [1/T [summation] [x.sub.t] [x.sub.t-1] [x.sub.t-j]] / [[1/T [summation] [x.sup.2.sub.t]].sup.1.5]

where:

[r.sub.(xxx)] (i,j) = the third order sample correlation coefficient of [x.sub.t] with [x.sub.t-I] and [x.sub.t-j]

T = the length of the data series being examined.

Hsieh (1991) developed the estimates of the asymptotic variance and covariance for the combined effect of these third order sample correlation coefficients which can be used to construct a [chi square] statistic to test for the significance of the joint influence of the [r.sub.(xxx)] (i,j)'s for specific values of j, such that 1 [less than or equal to] I [less than or equal to] j. If the [chi square] statistics for relatively low values of j are significant, this outcome would be a strong indicator of the presence of mean-nonlinearity in the examined series. As chaotic determinism is a form of mean-nonlinearity, the third moment test provides strong evidence of the presence of chaos.

Hence, the methodology employed follows a sequential series of steps where each country's index values are used to compute returns using differenced logs. Next, each returns series is then filtered for latent linearity by fitting it with an appropriate autoregressive model and capturing the residuals. The appropriate lag lengths for constructing these autoregressive models are determined by employing the Akaike Information Criterion. These filtered data series are then be tested for nonlinear dynamics by employing the BDS statistics. Rejection of the null of IID for stationary data indicates the presence of nonlinear dynamics. To ensure that the results from the above step is not merely an artifact of nonstationarity of the examined index returns series, the BDS test is conducted on subsets of the larger data set. If the BDS test results for the subsets are not consistent with those for the entire data set, then nonstationarity of the data sets will taint the results of tests for nonlinearity employed in subsequent steps. Hence those returns series will not be examined further in this study.

Each index returns series is then filtered for latent GARCH effects by employing the popular GARCH(1,1) model. If the residuals of the pre-whitened returns series fitted with the above models do not reject the null of IID, as per recomputed BDS statistics, one may conclude that the source of the observed nonlinear behavior is stochastic nonlinearity. The series for which non-IID behavior of pre-whitened returns are not explained by either nonstationarity of data or via the examined stochastic influences, are then tested for deterministic nonlinearity (chaos) using the Third Moments test.

RESULTS

Since all tests for nonlinear dynamics are also sensitive to inherent linearities, each examined series is filtered for linear autocorrelation before tests for nonlinear dynamics are applied. The order of the linear filter applied is determined by the Akaike Information Criterion (AIC), (Akaike, 1974). Table 1 presents the autoregressive lags used to filter each examined equity index return series for each of the subperiods studied. As mentioned before, the two subperiods examined are before the hypothesized structural change (1988-1992) and after (1999-2003).

Table 2 presents the computed BDS statistics for the sample subperiod 1, 1988-1992. The BDS statistics used in this study report computed statistics of each data series for dimensions m = 2, ..., 10 and the distance measure [epsilon] = 0.5 F and 1.00 F. A lower [epsilon] value represents a more stringent criteria since points in the m-dimensional space must be clustered closer together to qualify as being "close" in terms of the BDS statistic. The BDS statistic has an intuitive explanation. For example, a positive BDS statistic indicates that the probability of any two m histories, ([x.sub.t], [x.sub.t-1], ..., [x.sub.t-m+1]) and ([x.sub.s], [x.sub.s-1], ..., [x.sub.s-m+1]), being close together is higher than what would be expected in truly random data. In other words, some clustering is occurring too frequently in an m-dimensional space. Thus, some patterns of stock return movements are taking place more frequently than is possible with truly random data.

In this study, the values of m examined go only as high as 10. Two reasons dictate the choice of 10 as the highest dimension analyzed. First, with m = 10, only about 130 non-overlapping 10 history points exist in each examined return series. Examining a higher dimensionality would restrict the confidence in the computed BDS statistic. Second, the interest of this study lies only in detecting low-dimensional nonlinearity. High-dimensional nonlinear dynamics is, for all practical purposes, just as good as IID behavior where index predictability is concerned.

As noted in the Table 2, all reported BDS statistics reject the null of independent and identical distribution (IID). Hence it is possible that some nonlinearities exist in all examined equity indices during the 1988-92 subperiod. A similar examination of BDS statistics for the 1999-2003 subperiod in Table 3 shows that except for the Korean equity index, all examined indices still exhibit possible signs of nonlinear influences.

Given the plethora of evidence in existence that points towards the existence of stochastic nonlinearites in equity markets (e.g., Brock et al., 1991; Errunza et al., 1994; Hsieh ,1993, 1995; Sewell et al., 1996), a stochastic GARCH(1,1) model is employed to filter the pre-whitened returns. These GARCH filtered series are examined again using the BDS statistics. As noted from Tables 4 and 5, the GARCH(1,1) filters do not significantly alter the outcomes observable from the reported BDS statistics. Hence, commonly observed stochastic influences do not seem to affect the examined emerging market equity indices.

The results of the third moments test are presented in Table 6. This table shows the [x.sup.2] statistics for a combined test of the significance of all examined three moment correlations [r.sub.(xxx)](i,j) up to a certain lag length. Where 1 [less than or equal to] I [less than or equal to] j [less than or equal to] 5, the [x.sup.2] statistic has 15 degrees of freedom. When 1 [less than or equal to] I [less than or equal to] j [less than or equal to] 10, the [x.sup.2] statistic has 55 degrees of freedom. As one may observe from Table 6, the [x.sup.2.sub.15] statistics for the Thai index returns series is significant at the 1% level, where as the [x.sup.2.sub.55] statistics for equity indices of Jordan, Taiwan and Turkey are significant at a minimum of 5% level. These results suggest that the Thai index returns is highly likely to be influenced by low-dimensional chaos, whereas the chaotic determinism driving the index returns of Jordan, Taiwan and Turkey is somewhat higher dimensional. These observations suggest that during the 1988-1992 subperiod, index returns of Thailand, Jordan, Taiwan and Turkey were driven by nonlinear deterministic processes. The low dimensionality of chaos in the Thai index indicates a greater degree of predictability than the somewhat higher dimensionality of chaos driving the equity indexes of Jordan, Taiwan and Turkey.

Results of the three moments tests for the sample subperiod 1999-2003 presented in Table 7 indicate low dimensional chaos driving the index returns of Mexico and Philippines and a somewhat higher dimensional chaos in index returns of Chile. These results indicate that the hypothesized structural changes may have made the markets of Philippines, Mexico and Chile more predictable. However, it remains unclear that this possible predictability is economically exploitable.

CONCLUSIONS AND IMPLICATIONS

Overall, the results of this study indicate that the period of structural instability during the mid 1990s has rendered the equity market of Korea driven more by a random process. The Korean equity market exhibits IID behavior during the second subperiod examined and hence it exhibits no signs of predictability. During this latter subperiod, post hypothesized structural change, the markets of Thailand, Jordan, Taiwan and Turkey have become less predictable, while the stock markets of Chile, Mexico and Philippines, somewhat more predictable. Overall, the results are mixed and do not lead us to a very conclusive determination of a structural shift in emerging equity markets caused by recent changes in the financial infrastructure in these markets. Any observed predictability is implied by the existence of low dimensional nonlinear determinism, or chaos, in these markets. From a practical standpoint, such observed predictability may be too costly to implement and may generate returns of insufficient magnitude to overcome transactions costs. Hence, even in these instances, one may not be able to confirm any instances of market inefficiency. Moreover, since one does not observe any consistent pattern of change in the nonlinear dynamics of examined markets before and after the hypothesized structural overhaul of financial markets in emerging countries, one is unable to discern any material impact on the efficiency of these financial markets.

The good news is that, for the most part, no compelling evidence was uncovered in this study to suggest that any of the examined markets have become less informationally efficient as a result of the overhaul of the financial infrastructure in these economies. Future studies should aim at examining the multivariate impact of key macroeconomic factors affected by the changing financial environment in these emerging markets, and their varying contribution to equity market efficiency.

REFERENCES

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Bekaert, Geert & Campbell R. Harvey (1995). Time-Varying World Market Integration. The Journal of Finance, 50 (20), 403-444.

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Barkoulas, J. & N. Travlos (1998). Chaos in an Emerging Capital Market? The Case of the Athens Stock Exchange. Applied Financial Economics, 8 (3), 231-43.

Brock, W., W. Dechert, B. Lebaron & J.A. Scheinkman (1997). A Test for Independence Based on the Correlation Dimension. Econometrics Reviews, 15, 197-235.

Brock, W., D. Hsieh & B. Lebaron (1991). Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. Cambridge, MA: MIT Press.

Cochran, S. J., R. H. DeFina & L. O. Mills (1993). International Evidence on the Predictability of Stock Returns. Financial Review, 28 (2), 1993, 159-180.

Dornbush, R. & A. Werner (1994). Mexico: Stabilization, Reform and No Growth. Brookings Papers on Economic Activity, 1994 (1), 253-297.

Engel, R. F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 987-1007.

Errunza, V., K. Hogan, Jr., O. Kini & P. Padmanabhan (1994). Conditional Heteroskedasticity and Global Stock Return Distributions. Financial Review, 29(3), 293-317.

Guillermo, A. C. & F. S. Mishkin (2003). The Mirage of Exchange Rate Regimes for Emerging Market Countries. The Journal of Economic Perspectives, 17(4), 99-118.

Hsieh, D. (1995). Nonlinear Dynamics in Financial Markets: Evidence and Implications. Financial Analysts Journal, 51(4), 55-62.

Hsieh, D. (1993). Implications of Nonlinear Dynamics for Financial Risk Management. Journal of Financial and Quantitative Analysis, 28(1), 41-64.

Hsieh, D. (1991). Chaos and Nonlinear Dynamics: Application to Financial Markets. Journal of Finance, 5, 1839-1877.

Hsieh, D. (1989). Testing for Nonlinear Dependence in Daily Foreign Exchange Rates. Journal of Business, 62(3), 339-368.

Ilinitch, Anne Y., Richard A. D'Aveni & Arie Y. Lewin (1996). New Organizational Forms and Strategies for Managing in Hypercompetitive Environments. Organization Science, 7(3), 211-220.

Kohers, T., V. Pandey & G. Kohers (1997). Using Nonlinear Dynamics to Test for Market Efficiency Among the Major US Stock Exchanges. The Quarterly Review of Economics and Finance, 37(2), 523-545.

Pandey, V., T. Kohers & G. Kohers (1998). Deterministic Nonlinearity in Major European Stock Markets and the U.S. The Financial Review, 33(1), 45-63.

Radelet, S. & J. D. Sachs (1998). The East Asian Financial Crisis: Diagnosis, Remedies, Prospects. Brookings Papers on Economic Activity, 1998(1), 1-74.

Sewell, S. P., S. R. Stansell, I. Lee & M. S. Pan (1993). Nonlinearities in Emerging Foreign Capital Markets. Journal of Business Finance and Accounting, 20(2), 237-248.

Van Norden, Simon (1996). Regime Switching as a Test for Exchange Rate Bubbles. Journal of Applied Econometrics, 11(3), 219-251.

Vivek K. Pandey, University of Texas at Tyler

Table 1: Autoregression Lags Used to Filter Returns on the Stock Markets Analyzed Country Autoregressive Stock Market Index Model Used: (Subperiod 1, Subperiod 2) Argentina AR(5), AR(1) Chile AR(3), AR(1) Jordan AR(2), AR(3) Korea AR(3), AR(2) Malaysia AR(3), AR(1) Mexico AR(7), AR(2) Philippines AR(1), AR(3) Taiwan AR(2), None Thailand AR(1), AR(1) Turkey AR(5), None NOTE: AR = Autoregressive model with (x) lags. Lags are determined via the Akaike Information Criterion (AIC). Subperiod 1: Daily observations from 1988-1992; Subperiod 2: 1999-2003. Table 2: BDS Statistics for Filtered Returns for Emerging Stock Markets Sample Subperiod 1: 1988-1992 Country Stock Market Index: e/[sigma] m Argentina Chile Jordan Korea 0.5 2 8.8727 8.2886 3.6639 5.901 0.5 3 12.1130 12.5900 5.2559 9.012 0.5 4 16.0930 16.2420 7.2941 11.655 0.5 5 21.6290 20.1130 8.6243 13.297 0.5 6 29.9260 25.4820 10.6150 14.811 0.5 7 40.8530 32.3830 13.3290 15.683 0.5 8 58.1560 42.0500 15.8360 16.000 0.5 9 86.1490 53.3320 18.2590 16.542 0.5 10 131.7700 66.5960 21.9850 18.025 1 2 10.4220 7.9397 4.0167 7.122 1 3 12.5780 10.8060 5.2862 9.462 1 4 15.0290 13.1450 6.6094 11.362 1 5 17.3550 14.7010 7.4459 12.650 1 6 19.8820 16.4710 8.1532 13.718 1 7 22.3620 18.3910 8.9216 14.528 1 8 25.4680 20.4430 9.5589 15.303 1 9 29.7170 22.6090 10.2250 15.851 1 10 35.2480 25.3550 10.9550 16.850 e/[sigma] Malaysia Mexico Philippines 0.5 8.2574 9.3310 6.9320 0.5 9.7951 11.7330 9.9521 0.5 11.5850 14.2310 11.7590 0.5 13.0300 16.8520 13.7670 0.5 14.4850 19.5230 16.1740 0.5 16.1620 22.3940 19.7380 0.5 18.0770 27.1070 25.8450 0.5 20.4360 32.8200 36.5640 0.5 23.3570 41.1090 57.4490 1 9.4056 8.9309 6.5045 1 11.3050 10.8170 9.0120 1 12.6430 12.3220 10.1550 1 13.5940 13.7740 11.0680 1 14.5250 15.2110 12.2410 1 15.3370 16.4920 13.4900 1 16.3130 17.7740 15.1580 1 17.3450 18.6980 17.0270 1 18.5210 19.9070 19.2970 e/[sigma] Taiwan Thailand Turkey 0.5 8.1250 11.1850 12.8440 0.5 11.8140 14.2960 18.1580 0.5 15.2440 17.8340 22.3250 0.5 19.0440 21.8620 27.3360 0.5 24.9340 26.6530 35.1500 0.5 32.3740 32.5250 46.7310 0.5 40.7150 39.3350 60.1380 0.5 51.0340 47.1460 77.7310 0.5 68.6550 57.3360 99.0300 1 9.3970 12.4120 12.0540 1 13.3840 14.7290 15.9430 1 16.3160 16.5470 18.3840 1 18.8000 18.1190 20.7010 1 21.8340 19.8420 23.4310 1 25.5520 21.7030 27.0250 1 30.3070 23.4150 31.3600 1 36.2940 25.6310 36.6630 1 43.7790 28.1930 42.7190 NOTE: m = embedding dimension. Except where noted with *, all BDS statistics are significant at the 5% level. Table 3: BDS Statistics for Filtered Returns for Emerging Stock Markets Sample Subperiod 2: 1999-2003 Country Stock Market Index: e/[sigma] m Argentina Chile Jordan 0.5 2 5.4889 4.5514 4.8915 0.5 3 7.3548 5.5112 5.7258 0.5 4 8.4475 5.8131 6.4798 0.5 5 8.7866 6.6721 7.7796 0.5 6 9.7123 7.0271 8.8790 0.5 7 10.0140 7.3442 9.3009 0.5 8 10.6580 8.4612 10.343 0.5 9 10.6020 9.3171 11.926 0.5 10 9.0572 7.6701 13.846 1 2 6.5388 5.4693 4.6663 1 3 8.4945 6.5597 5.4627 1 4 9.5272 7.0808 5.7935 1 5 10.2910 7.8601 6.1573 1 6 11.0560 8.7478 6.1731 1 7 11.7730 9.4106 5.7996 1 8 12.8180 10.3410 5.4687 1 9 13.7160 11.2470 5.2873 1 10 14.9340 12.2360 4.9462 e/[sigma] Korea Malaysia Mexico Philippines 0.5 1.6234 * 7.9697 3.2922 1.4201 * 0.5 0.6716 * 10.0410 4.4196 2.2758 0.5 0.0139 * 12.1120 5.5476 3.5001 0.5 0.0286 * 15.0350 5.9605 4.3034 0.5 0.9903 * 18.1670 5.9340 4.6487 0.5 1.7033 * 21.8130 6.9197 4.8014 0.5 2.3763 28.5460 7.6257 5.7979 0.5 2.0715 37.3290 10.1850 6.0584 0.5 1.9225 * 51.9110 16.9000 7.7051 1 1.1945 * 8.3870 3.0938 2.3465 1 0.1567 * 10.5690 4.3891 3.5207 1 1.1177 * 11.8390 6.1041 4.7063 1 1.5894 * 13.4130 6.8335 5.4678 1 2.1041 14.8290 7.6016 6.0919 1 2.4849 16.4380 8.5162 6.5544 1 2.5978 18.3220 9.3126 7.0837 1 2.9086 20.5220 10.2910 7.4910 1 3.3555 23.2190 11.3480 7.7451 e/[sigma] Taiwan Thailand Turkey 0.5 1.2363 * 5.4060 3.3901 0.5 2.0039 6.4503 5.0194 0.5 2.1041 7.9052 5.6853 0.5 2.9906 8.8495 6.5085 0.5 3.8327 9.9777 8.3116 0.5 5.4745 11.2790 10.1120 0.5 5.4372 13.2970 10.2620 0.5 5.3961 12.5830 11.5290 0.5 4.5580 12.2390 13.0930 1 0.9722 * 6.0332 4.6278 1 1.9060 * 7.4018 6.1217 1 2.5185 8.5904 6.3347 1 3.2064 9.5520 6.9550 1 3.5727 10.0980 7.9020 1 3.9628 10.7300 8.7893 1 4.2297 11.7130 9.6186 1 4.4768 12.6110 10.1900 1 4.9235 13.3750 10.9970 NOTE: m = embedding dimension. Except where noted with *, all BDS statistics are significant at the 5% level. Table 4: BDS Statistics for Garch (1,1) Filtered Pre-Whitened Returns for Emerging Stock Markets Sample Subperiod 1: 1988-1992 Country Stock Market Index: e/[sigma] m Argentina Chile Jordan 0.5 2 8.8595 8.2900 3.6636 0.5 3 12.0970 12.5900 5.2568 0.5 4 16.0760 16.2430 7.2949 0.5 5 21.6080 20.1130 8.6252 0.5 6 29.8910 25.4870 10.6160 0.5 7 40.7990 32.3890 13.3310 0.5 8 58.0960 42.0590 15.8370 0.5 9 86.0540 53.3440 18.2600 0.5 10 131.6200 66.6120 21.9880 1 2 10.4230 7.9384 4.0167 1 3 12.5800 10.8050 5.2862 1 4 15.0310 13.1450 6.6094 1 5 17.3570 14.7010 7.4459 1 6 19.8840 16.4700 8.1532 1 7 22.3640 18.3910 8.9216 1 8 25.4680 20.4420 9.5589 1 9 29.7170 22.6080 10.2250 1 10 35.2480 25.3550 10.9550 e/[sigma] Korea Malaysia Mexico Philippines 0.5 5.9014 8.2577 9.3307 6.9760 0.5 9.0117 9.7962 11.7340 10.0650 0.5 11.6550 11.5850 14.2320 11.9080 0.5 13.2970 13.0310 16.8530 13.9130 0.5 14.8110 14.4830 19.5240 16.2900 0.5 15.6830 16.1610 22.3950 19.7540 0.5 16.0000 18.0740 27.1080 25.7890 0.5 16.5420 20.4330 32.8210 35.5900 0.5 18.0250 23.3540 41.1110 54.9080 1 7.1223 9.4055 8.9308 6.4707 1 9.4619 11.3050 10.8170 8.9641 1 11.3620 12.6430 12.3210 10.1160 1 12.6500 13.5930 13.7740 11.0110 1 13.7180 14.5250 15.2110 12.1040 1 14.5280 15.3370 16.4920 13.2770 1 15.3030 16.3120 17.7730 14.8240 1 15.8510 17.3450 18.6980 16.5510 1 16.8500 18.5210 19.9060 18.5900 e/[sigma] Taiwan Thailand Turkey 0.5 8.1228 11.1840 12.8450 0.5 11.8130 14.2960 18.1560 0.5 15.2440 17.8350 22.3310 0.5 19.0440 21.8610 27.3360 0.5 24.9340 26.6510 35.1500 0.5 32.3740 32.5230 46.7310 0.5 40.7150 39.3320 60.1370 0.5 51.0340 47.1430 77.7310 0.5 68.6550 57.3320 99.0300 1 9.3959 12.4120 12.0530 1 13.3830 14.7290 15.9420 1 16.3160 16.5470 18.3820 1 18.8000 18.1190 20.6990 1 21.8340 19.8420 23.4300 1 25.5520 21.7030 27.0220 1 30.3070 23.4150 31.3550 1 36.2940 25.6310 36.6560 1 43.7790 28.1930 42.7130 NOTE: m = embedding dimension. Except where noted with *, all BDS statistics are significant at the 5% level. Table 5: BDS Statistics for GARCH (1,1) Filtered Pre-whitened Returns for Emerging Stock Markets Sample Subperiod 2: 1999-2003 Country Stock Market Index: e/[sigma] m Argentina Chile Jordan 0.5 2 5.4873 4.5526 4.8881 0.5 3 7.3535 5.5121 5.7232 0.5 4 8.4462 5.8139 6.4774 0.5 5 8.7854 6.6728 7.7772 0.5 6 9.7111 7.0278 8.8764 0.5 7 10.0130 7.3450 9.2982 0.5 8 10.6570 8.4620 10.3400 0.5 9 10.6010 9.3180 11.9220 0.5 10 9.0558 7.6709 13.8420 1 2 6.5390 5.4693 4.6651 1 3 8.4950 6.5597 5.4619 1 4 9.5277 7.0808 5.7928 1 5 10.2910 7.8601 6.1567 1 6 11.0560 8.7478 6.1725 1 7 11.7740 9.4106 5.7990 1 8 12.8190 10.3410 5.4682 1 9 13.7170 11.2470 5.2868 1 10 14.9340 12.2360 4.9457 e/[sigma] Korea Malaysia Mexico Philippines 0.5 1.6232 * 7.9725 3.2964 1.4214 * 0.5 0.6704 * 10.0450 4.4227 2.2757 0.5 0.0130 * 12.1150 5.5550 3.5001 0.5 0.0278 * 15.0390 5.9784 4.3033 0.5 0.9911 * 18.1720 5.9555 4.6487 0.5 1.7040 * 21.8180 6.9185 4.8013 0.5 2.3771 28.5530 7.6243 5.7978 0.5 2.0723 37.3390 10.1830 6.0584 0.5 1.9233 * 51.9260 16.8970 7.7050 1 1.1935 * 8.3873 3.0932 2.3465 1 0.1584 * 10.5690 4.3880 3.5207 1 1.1190 * 11.8390 6.1040 4.7063 1 1.5905 * 13.4130 6.8332 5.4678 1 2.1051 14.8290 7.6011 6.0919 1 2.4859 16.4390 8.5154 6.5544 1 2.5987 18.3240 9.3112 7.0837 1 2.9096 20.5240 10.2890 7.4910 1 3.3564 23.2210 11.3490 7.7451 e/[sigma] Taiwan Thailand Turkey 0.5 1.2346 * 5.4103 3.3876 0.5 2.0039 6.4521 5.0166 0.5 2.1042 7.9051 5.6871 0.5 2.9906 8.8494 6.5063 0.5 3.8327 9.9776 8.3093 0.5 5.4745 11.2790 10.1100 0.5 5.4373 13.2970 10.2590 0.5 5.3962 12.5830 11.5260 0.5 4.5580 12.2380 13.0900 1 0.9724 * 6.0330 4.6227 1 1.9065 * 7.4017 6.1173 1 2.5194 8.5904 6.3315 1 3.2073 9.5521 6.9542 1 3.5735 10.0990 7.9015 1 3.9635 10.7300 8.7878 1 4.2304 11.7140 9.6167 1 4.4776 12.6130 10.1900 1 4.9243 13.3770 10.9950 Note: m = embedding dimension. Except where noted with *, all BDS statistics are significant at the 5% level. Table 6: Chi-Square statistics for the Influence of Three Moment Correlations for the Filtered Index Returns Sample Subperiod 1: 1988 - 1992 Lags(i,j) Statistic Argentina Chile 1 [less than or equal to] [chi square](15) 4 19.14 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] [chi square](55) 46 28.96 I [less than or equal to] j [less than or equal to] 10 Lags(i,j) Jordan Korea Malaysia 1 [less than or equal to] 22.72 1.74 16.22 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] 382.60 ** 25.21 15.25 I [less than or equal to] j [less than or equal to] 10 Lags(i,j) Mexico Philippines Taiwan 1 [less than or equal to] 17.61 21.52 6.81 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] 34.53 15.96 83.79 * I [less than or equal to] j [less than or equal to] 10 Lags(i,j) Thailand Turkey 1 [less than or equal to] 71.50 ** 2.14 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] 31.94 126.10 ** I [less than or equal to] j [less than or equal to] 10 ** Significant at the 1% level for a right-tailed test. * Significant at the 5% level. Table 7: Chi-Square statistics for the Influence of Three Moment Correlations for the Filtered Index Returns Sample Subperiod 2: 1999 - 2003 Lags(i,j) Statistic Argentina Chile 1 [less than or equal to] [chi square](15) 4.45 5.78 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] [chi square](55) 22.48 80.72 * I [less than or equal to] j [less than or equal to] 10 Lags(i,j) Jordan Korea Malaysia 1 [less than or equal to] 4.68 14.04 3.95 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] 29.12 16.40 12.86 I [less than or equal to] j [less than or equal to] 10 Lags(i,j) Mexico Philippines Taiwan 1 [less than or equal to] 57.14 ** 84.10 ** 3.64 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] 27.06 24.89 15.02 I [less than or equal to] j [less than or equal to] 10 Lags(i,j) Thailand Turkey 1 [less than or equal to] 10.99 2.58 I [less than or equal to] j [less than or equal to] 5 1 [less than or equal to] 13.99 26.39 I [less than or equal to] j [less than or equal to] 10 ** Significant at the 1% level for a right-tailed test. * Significant at the 5% level

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Author: | Pandey, Vivek K. |
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Publication: | Journal of International Business Research |

Geographic Code: | 1USA |

Date: | Jan 1, 2007 |

Words: | 6456 |

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