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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 1988-1992 and 1999-2003. 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/ (spo-rad´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 market-weighted 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 1993-1998 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 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 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.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 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:
is true for 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 A character that is all 0 bits. Also written as "NUL," it is the first character in the ASCII and EBCDIC data codes. In hex, it displays and prints as 00; in decimal, it may appear as a single zero in a chart of codes, but displays and prints as a blank space.  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 Stochastic models

Liability-matching 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 pre-whitened 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 pre-whitened 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 time-varying, and a function of the past variance. ARCH processes have frequency distributions which have high peaks at the mean and fat-tails, 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 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 Financial assets

Claims on real 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 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 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 a·bove·men·tioned  
adj.
Mentioned previously.

n.
The one or ones mentioned previously.
 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 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 (moisture-retainers); and
 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 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.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 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.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 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 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 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 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 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 (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 Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently
, 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 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 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 plethora /pleth·o·ra/ (pleth´ah-rah)
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 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 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.

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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.
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Greece's only major securities market. Greek language only.


Athens Stock Exchange (ASE)

Greece's principal stock exchange.
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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
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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.
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A security analysis that uses financial information derived from company annual reports and income statements to evaluate an investment decision.

Notes:
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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 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 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.
Publication:Journal of International Business Research
Geographic Code:1USA
Date:Jan 1, 2007
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