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 nonlinear dynamics, study of systems governed by equations in which a small change in one variable can induce a large systematic change; the discipline is more popularly known as chaos (see chaos theory). 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 19881992 and 19992003. Informational efficiency for each examined stock market over each examined subperiod is gauged by the extent of stochastic By guesswork; by chance; using or containing random values. stochastic  probabilistic and deterministic 1. (probability) deterministic  Describes a system whose time evolution can be predicted exactly. Contrast probabilistic. 2. (algorithm) deterministic  Describes an algorithm in which the correct next step depends only on the current state. nonlinear A system in which the output is not a uniform relationship to the input. nonlinear  (Scientific computation) A property of a system whose output is not proportional to its input. predictability inherent in the market. Results indicate that the hypothesized financial regime changes during the 1990's have had no conclusive Determinative; beyond dispute or question. That which is conclusive is manifest, clear, or obvious. It is a legal inference made so peremptorily that it cannot be overthrown or contradicted. 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 en·sue intr.v. en·sued, en·su·ing, en·sues 1. To follow as a consequence or result. See Synonyms at follow. 2. To take place subsequently. 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 IMF See: International Monetary Fund IMF See 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 sporadic /spo·rad·ic/ (sporad´ic) occurring singly; widely scattered; not epidemic or endemic. spo·rad·ic or spo·rad·i·cal adj. 1. Occurring at irregular intervals. 2. 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 Morgan Stanley Capital International (MSCI) This firm publishes a number of well known benchmarks, such as the MSCI World Index. 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 marketweighted price averages, were retrieved from Datastream database and are compiled by Morgan Stanley Capital International Perspective (MSCI) of Geneva Geneva, canton and city, Switzerland Geneva (jənē`və), Fr. Genève, canton (1990 pop. 373,019), 109 sq mi (282 sq km), SW Switzerland, surrounding the southwest tip of the Lake 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 19931998 is hypothesized to be a period of structural change in the financial infrastructure of many emerging markets as enumerated This term is often used in law as equivalent to mentioned specifically, designated, or expressly named or granted; as in speaking of enumerated governmental powers, items of property, or articles in a tariff schedule. 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 19881992 and 19992003, 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 Theta A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option. ].sub.0] + [P.summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over (i=1) [[phi].sub.i] [Y.sub.t1] + [[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 Akaike's information criterion, developed by Hirotsugu Akaike under the name of "an information criterion" (AIC) in 1971 and proposed in Akaike (1974), is a measure of the goodness of fit of an estimated statistical model. It is grounded in the concept of entropy. (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 BDS Statistic A statistic based upon the correlation integral which examines the probability that a purely random system could have the same scaling properties as the system under study. See: Correlation Integral. , developed by Brock brock n. Chiefly British A badger. [Middle English brok, from Old English broc, of Celtic origin.] et al. (1991), which tests whether a data series is independently and identically distributed (IID IID Imperial Irrigation District (California) IID Interface Identifier (Component Object Model) IID Ignition Interlock Device (automotive security system) ). 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 1. (mathematics) embedding  One instance of some mathematical object contained with in another instance, e.g. a group which is a subgroup. 2. (theory) embedding  (domain theory) A complete partial order F in [X > Y] is an embedding if dimensions, C = the Grassberger and Procaccia correlation integral Correlation Integral The probability that two points are within a certain distance from one another. Used in the calculation of the correlation dimension. , 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 null hypothesis, n theoretical assumption that a given therapy will have results not statistically different from another treatment. null hypothesis, n of independent and identical distribution (IID) when the data series is sufficiently large In mathematics, the phrase sufficiently large is used in contexts such as:
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 Stochastic models Liabilitymatching models that assume that the liability payments and the asset cash flows are uncertain. Related: Deterministic 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 BDS abbr. Bachelor of Dental Surgery BDS Bachelor of Dental Surgery BDS n abbr (= Bachelor of Dental Surgery) → título universitario BDS statistics of prewhitened data series. However, since it is possible to construct an infinite number infinite number a number so large as to be uncountable. Represented by 8, frequently obtained by 'dividing' by zero. of stochastic models, fitting each model to the prewhitened data is an impossible task to undertake. Fortunately, prior research indicates that Generalized gen·er·al·ized adj. 1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain. 2. Not specifically adapted to a particular environment or function; not specialized. 3. Autoregressive Conditional Heteroskedasticity Autoregressive Conditional Heteroskedasticity (ARCH) A nonlinear stochastic process, where the variance is timevarying, and a function of the past variance. ARCH processes have frequency distributions which have high peaks at the mean and fattails, much like fractal distributions. (Engel, 1982) model of the first order, i.e., GARCH GARCH Generalized Autoregressive Conditional Heteroskedasticity (1,1) is able to explain away the latent Hidden; concealed; that which does not appear upon the face of an item. For example, a latent defect in the title to a parcel of real property is one that is not discoverable by an inspection of the title made with ordinary care. stochastic nonlinearity in a wide range of financial timeseries (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 Financial assets Claims on real assets. . Hence it is imperative, that any prewhitened financial series exhibiting nonIID 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.ti] + [[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.ti] + [p.summation over (j=1)] [[gamma].sub.j] [[h.sub.tj] Hence the GARCH series becomes and iterative it·er·a·tive adj. 1. Characterized by or involving repetition, recurrence, reiteration, or repetitiousness. 2. Grammar Frequentative. Noun 1. series where past conditional variances feed into future values of the series [x.sub.t] and the solution is obtained when the computing computing  computer 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 nonIID behavior of the data series, one can be certain that stochastic nonlinearity is the contributing factor. If the data sets examined pass the abovementioned a·bove·men·tioned adj. Mentioned previously. n. The one or ones mentioned previously. stochastic filter and still displays nonIID 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 meannonlinearity in a given series. Briefly stated, this test uses the concept that meannonlinearity implies additive additive In foods, any of various chemical substances added to produce desirable effects. Additives include such substances as artificial or natural colourings and flavourings; stabilizers, emulsifiers, and thickeners; preservatives and humectants (moistureretainers); and autoregressive dependence, whereas variancenonlinearity 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 cor·re·late v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates v.tr. 1. To put or bring into causal, complementary, parallel, or reciprocal relation. 2. . 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.t1] [x.sub.tj]] / [[1/T [summation] [x.sup.2.sub.t]].sup.1.5] where: [r.sub.(xxx)] (i,j) = the third order sample correlation coefficient Correlation Coefficient A measure that determines the degree to which two variable's movements are associated. The correlation coefficient is calculated as: of [x.sub.t] with [x.sub.tI] and [x.sub.tj] T = the length of the data series being examined. Hsieh (1991) developed the estimates of the asymptotic variance and covariance Covariance A measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns vary inversely. for the combined effect of these third order sample correlation coefficients which can be used to construct a [chi square chi square (kī), n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies. ] statistic statistic, n a value or number that describes a series of quantitative observations or measures; a value calculated from a sample. statistic a numerical value calculated from a number of observations in order to summarize them. 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 meannonlinearity in the examined series. As chaotic determinism is a form of meannonlinearity, 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 To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer. 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 A distortion in an image or sound caused by a limitation or malfunction in the hardware or software. Artifacts may or may not be easily detectable. Under intense inspection, one might find artifacts all the time, but a few pixels out of balance or a few milliseconds of abnormal sound 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 taint an unpleasant odor and flavor in a human foodstuff of animal origin. Caused by the ingestion of the substance, commonly a plant such as Hexham scent, or while in storage, e.g. milk stored with pineapples, or as a result of animal metabolism, e.g. boar 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 prewhitened 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 nonIID behavior of prewhitened 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 Autocorrelation The correlation of a variable with itself over successive time intervals. Sometimes called serial correlation. 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 (19881992) and after (19992003). Table 2 presents the computed BDS statistics for the sample subperiod 1, 19881992. 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 mdimensional 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.t1], ..., [x.sub.tm+1]) and ([x.sub.s], [x.sub.s1], ..., [x.sub.sm+1]), being close together is higher than what would be expected in truly random data. In other words Adv. 1. in other words  otherwise stated; "in other words, we are broke" put differently , some clustering is occurring too frequently in an mdimensional 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 TO DICTATE. To pronounce word for word what is destined to be at the same time written by another. Merlin Rep. mot Suggestion, p. 5 00; Toull. Dr. Civ. Fr. liv. 3, t. 2, c. 5, n. 410. the choice of 10 as the highest dimension analyzed an·a·lyze tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es 1. To examine methodically by separating into parts and studying their interrelations. 2. Chemistry To make a chemical analysis of. 3. . First, with m = 10, only about 130 nonoverlapping 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 lowdimensional nonlinearity. Highdimensional 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 198892 subperiod. A similar examination of BDS statistics for the 19992003 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 plethora /pleth·o·ra/ (pleth´ahrah) 1. an excess of blood. 2. by extension, a red florid complexion.pletho´ric pleth·o·ra n. 1. 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 prewhitened 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 lowdimensional chaos, whereas the chaotic determinism driving the index returns of Jordan, Taiwan and Turkey is somewhat higher dimensional. These observations suggest that during the 19881992 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 19992003 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 dis·cern v. dis·cerned, dis·cern·ing, dis·cerns v.tr. 1. To perceive with the eyes or intellect; detect. 2. To recognize or comprehend mentally. 3. 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 mac·ro·ec·o·nom·ics n. (used with a sing. verb) The study of the overall aspects and workings of a national economy, such as income, output, and the interrelationship among diverse economic sectors. factors affected by the changing financial environment in these emerging markets, and their varying contribution to equity market efficiency. REFERENCES Akaike, H. (1974). A New Look at Statistical Model Identification. IEEE (Institute of Electrical and Electronics Engineers, New York, www.ieee.org) A membership organization that includes engineers, scientists and students in electronics and allied fields. Transactions on Automatic Control, 19(6), 716723. Bekaert, Geert & Campbell R. Harvey (1995). TimeVarying World Market Integration. The Journal of Finance, 50 (20), 403444. Bera, A. K. & M. L. Higgins (1993). ARCH Models: Properties, Estimation estimation In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator. and Testing. Journal of Economic Surveys, 7, 305366. Barkoulas, J. & N. Travlos (1998). Chaos in an Emerging Capital Market? The Case of the Athens Stock Exchange Athens Stock Exchange Greece's only major securities market. Greek language only. Athens Stock Exchange (ASE) Greece's principal stock exchange. . Applied Financial Economics, 8 (3), 23143. Brock, W., W. Dechert, B. Lebaron & J.A. Scheinkman (1997). A Test for Independence Based on the Correlation Dimension Correlation Dimension An estimate of the Fractal Dimension which measures the probability that two points chosen at random will be within a certain distance of each other, and examines how this probability changes as the distance is increased. . Econometrics econometrics, technique of economic analysis that expresses economic theory in terms of mathematical relationships and then tests it empirically through statistical research. Reviews, 15, 197235. Brock, W., D. Hsieh & B. Lebaron (1991). Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. Cambridge, MA: MIT MIT  Massachusetts Institute of Technology Press. Cochran, S. J., R. H. DeFina & L. O. Mills (1993). International Evidence on the Predictability of Stock Returns. Financial Review, 28 (2), 1993, 159180. Dornbush, R. & A. Werner (1994). Mexico: Stabilization Stabilization The action undertakes a country when it buys and sells its own currency to protect its exchange value. Actions registered competitive traders undertake by on the NYSE to meet the exchange requirement that 75% of their traded be stabilizing, meaning that sell orders , Reform and No Growth. Brookings Papers on Economic Activity, 1994 (1), 253297. Engel, R. F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 9871007. Errunza, V., K. Hogan hogan Dwelling of the Navajo Indians of Arizona and New Mexico. The hogan is roughly circular and constructed usually of logs, which are stepped in gradually to create a domed roof. , Jr., O. Kini & P. Padmanabhan (1994). Conditional Heteroskedasticity and Global Stock Return Distributions. Financial Review, 29(3), 293317. Guillermo, A. C. & F. S. Mishkin (2003). The Mirage of Exchange Rate Regimes for Emerging Market Countries. The Journal of Economic Perspectives, 17(4), 99118. Hsieh, D. (1995). Nonlinear Dynamics in Financial Markets: Evidence and Implications. Financial Analysts Journal, 51(4), 5562. Hsieh, D. (1993). Implications of Nonlinear Dynamics for Financial Risk Management. Journal of Financial and Quantitative Analysis Quantitative Analysis A security analysis that uses financial information derived from company annual reports and income statements to evaluate an investment decision. Notes: , 28(1), 4164. Hsieh, D. (1991). Chaos and Nonlinear Dynamics: Application to Financial Markets. Journal of Finance, 5, 18391877. Hsieh, D. (1989). Testing for Nonlinear Dependence in Daily Foreign Exchange Rates. Journal of Business, 62(3), 339368. 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), 211220. 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), 523545. Pandey, V., T. Kohers & G. Kohers (1998). Deterministic Nonlinearity in Major European Stock Markets and the U.S. The Financial Review, 33(1), 4563. Radelet, S. & J. D. Sachs (1998). The East Asian Financial Crisis: Diagnosis, Remedies, Prospects. Brookings Papers on Economic Activity, 1998(1), 174. 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), 237248. Van Norden, Simon (1996). Regime Switching as a Test for Exchange Rate Bubbles. Journal of Applied Econometrics, 11(3), 219251. Vivek K. Pandey, University of Texas at Tyler History The University of Texas at Tyler was originally founded in 1971 as Tyler State College. It was renamed Texas Eastern College in 1975, and then joined the University of Texas System in 1979. 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 19881992; Subperiod 2: 19992003. Table 2: BDS Statistics for Filtered Returns for Emerging Stock Markets Sample Subperiod 1: 19881992 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: 19992003 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 PreWhitened Returns for Emerging Stock Markets Sample Subperiod 1: 19881992 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 Prewhitened Returns for Emerging Stock Markets Sample Subperiod 2: 19992003 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: ChiSquare 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 righttailed test. * Significant at the 5% level. Table 7: ChiSquare 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 righttailed test. * Significant at the 5% level 

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