Nonlinear Serial Dependence Research Articles

Dynamics of episodic transient correlations in currency exchange rate returns and their predictability

AbstractWe study the dynamics of the linear and non-linear serial dependencies in financial time series in a rolling window framework. In particular, we focus on the detection of episodes of statistically significant two- and three-point correlations in the returns of several leading currency exchange rates that could offer some potential for their predictability. We employ a rolling window approach in order to capture the correlation dynamics for different window lengths and analyze the distributions of periods with statistically significant correlations. We find that for sufficiently large window lengths these distributions fit well to power-law behavior. We also measure the predictability itself by a hit rate, i.e. the rate of consistency between the signs of the actual returns and their predictions, obtained from a simple correlation-based predictor. It is found that during these relatively brief periods the returns are predictable to a certain degree and the predictability depends on the selection of the window length.

Has split share structure reform improved the efficiency of the Chinese stock market?

Split share structure reform brings about fundamental changes to the Chinese stock market. This article compares the market efficiency before and after this reform. The generalized spectral derivative method is applied, which can capture linear and nonlinear serial dependence, and has stronger power against departures from market efficiency. The results show that although the markets were inefficient before the split share structure reform, they have reached the weak-form efficiency after that. This fundamental reform has improved the Chinese stock market efficiency.

Measuring Nonlinear Serial Dependencies Using the Mutual Information Coefficient

Construction, estimation and application of the mutual information measure have been presented in this paper. The simulations have been carried out to verify its usefulness to detect nonlinear serial dependencies. Moreover, the mutual information measure has been applied to the indices and the sector sub-indices of the Warsaw Stock Exchange.

A TEST OF THE GARCH(1, 1) SPECIFICATION FOR DAILY STOCK RETURNS

Daily financial returns (and daily stock returns, in particular) are commonly modeled as GARCH(1, 1) processes. Here we test this specification using new model evaluation technology developed by Ashley and Patterson that examines the ability of the estimated model to reproduce features of particular interest: various aspects of nonlinear serial dependence, in the present instance. Using daily returns to the CRSP equally weighted stock index, we find that the GARCH(1, 1) specification cannot be rejected; thus, this model appears to be reasonably adequate in terms of reproducing the kinds of nonlinear serial dependence addressed by the battery of nonlinearity tests used here.

IDENTIFYING NONLINEAR SERIAL DEPENDENCE IN VOLATILE, HIGH-FREQUENCY TIME SERIES AND ITS IMPLICATIONS FOR VOLATILITY MODELING

In this article, we show how tests of nonlinear serial dependence can be applied to high-frequency time series data that exhibit high volatility, strong mean reversion, and leptokurtotis. Portmanteau correlation, bicorrelation, and tricorrelation tests are used to detect nonlinear serial dependence in the data. Trimming is used to control for the presence of outliers in the data. The data that are employed are 161,786 half-hourly spot electricity price observations recorded over nearly a decade in the wholesale electricity market in New South Wales, Australia. Strong evidence of nonlinear serial dependence is found and its implications for time series modeling are discussed.

Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?

Nonlinear models, especially threshold autoregressive [TAR] and exponential smooth transition autoregressive [ESTAR] classes, are widely applied for modeling real exchange rates in order to examine the validity of purchasing power parity [PPP]. Even though the nonlinear models are theoretically well-motivated, some of the recent findings cast doubts on their relevance for real exchange rates. In particular, the nonlinear models do not necessarily yield improved out-of-sample forecasts over linear models and add little value in resolving the well-documented PPP puzzle. Utilizing a nonparametric entropy measure of dependence proposed by Granger et al. (2004), we show, in this study, that the real exchange rates from four major countries had exhibited quite strong nonlinear serial dependence, which linear autoregressive models fail to replicate. Furthermore, the nonlinear TAR and ESTAR models estimated for the real exchange rates also have some difficulty in generating significant serial dependence structure actually observed in the data. Overall, other nonlinear models than the currently entertained TAR and ESTAR should be considered to study the dynamics of the real exchange rates.

The Weak-form Efficiency of Chinese Stock Markets

Motivated by the shortcomings of earlier Chinese efficiency studies, the present paper re-examines the weak-form efficiency of Shanghai and Shenzhen Stock Exchanges. Specifically, our adopted methodologies mitigate the confounding effect of thin trading on return autocorrelation, detect both linear and nonlinear serial dependencies in the adjusted returns series, and capture the persistence of dependency structures over time. The result shows that the adjusted returns series from both markets follow a random walk for long periods of time, only to be interspersed with brief periods of strong linear and/or nonlinear dependency structures. This suggests that there are certain time periods when new information is not fully reflected into stock prices. Another interesting finding is that the existence of serial dependencies in both the Shanghai and Shenzhen Stock Exchanges follows one another closely after October 1997. It indicates that both markets respond in a similar way to influences from political, economic, social and institutional changes.

Weak-form market efficiency and nonlinearity: evidence from Middle East and African stock indices

This study examines the existence of nonlinear serial dependence in five stock markets in the Middle East and Africa. The results from the application of a battery of nonlinearity tests reveal that after removing all short-term linear dependence, the stock returns still contain predictable nonlinearities that contradict the unpredictable criterion of weak-form efficient markets hypothesis.

Are Chinese stock markets efficient? Further evidence from a battery of nonlinearity tests

Given that the efficiency of the Chinese stock markets was empirically examined in extant literature using statistical tests that are designed to uncover linear correlations of price changes, the obtained statistical inferences of efficiency/inefficiency are on very shaky grounds as highlighted in a recent article by Saadi et al. (2006). Motivated by this concern, the present article re-examines the efficiency of the A- and B-shares markets in Shanghai and Shenzhen Stock Exchanges (SHSE and SZSE) using a battery of nonlinearity tests. The empirical investigation reveals strong evidence of nonlinear serial dependence in the underlying returns generating processes for all indices even after removing linear serial correlations from the data, hence, contradicting the unpredictable criterion of weak-form efficient market hypothesis. Theoretically, these results are not surprising given the fact that investors in the Chinese stock markets trade like noise traders, who purely speculate and treat the market like a casino.

A New Bispectral Test for NonLinear Serial Dependence

Nonconstancy of the bispectrum of a time series has been taken as a measure of non-Gaussianity and nonlinear serial dependence in a stochastic process by Subba Rao and Gabr (1980) and by Hinich (1982), leading to Hinich's statistical test of the null hypothesis of a linear generating mechanism for a time series. Hinich's test has the advantage of focusing directly on nonlinear serial dependence—in contrast to subsequent approaches, which actually test for serial dependence of any kind (nonlinear or linear) on data which have been pre-whitened. The Hinich test tends to have low power, however, and (in common with most statistical procedures in the frequency domain) requires the specification of a smoothing or window-width parameter. In this article, we develop a modification of the Hinich bispectral test which substantially ameliorates both of these problems by the simple expedient of maximizing the test statistic over the feasible values of the smoothing parameter. Monte Carlo simulation results are presented indicating that the new test is well sized and has substantially larger power than the original Hinich test against a number of relevant alternatives; the simulations also indicate that the new test preserves the Hinich test's robustness to misspecifications in the identification of a pre-whitening model.

Nonlinear behaviour of emerging market bonds spreads: the Latin American case

In this article we check for nonlinear behaviour of the 10 most important Latin American emerging market bonds spreads. Applying the Hinich portmanteau bicorrelation test, the BDS test and the Engle LM test, we observe systematic nonlinear structure in the spreads series. Our results suggest that the nonlinear serial dependencies are episodic in nature. All the stock returns series (with the exception of Mexico) are characterized by few brief periods of highly significant nonlinearity, followed by long time periods in which the returns follow a pure noise process. Our findings support the idea that, even in this well informed and sophisticated market, the weak-form of the efficient market hypothesis cannot be supported.

Sectoral impact of shocks: empirical evidence from the Malaysian stock market

The present study adopts the framework of Lim et al. (2006) who conjectured that the existence of nonlinear serial dependencies is due to shocks that unsettled the market and caused large deviations from equilibrium. Specifically, this article extends the investigation to shed further light on whether different economic sectors of the Malaysian stock market are subjected to the same shocks effects. The results reveal that the Russian crisis, negative economic outlook, unorthodox capital control measures, increased political tension, uncertainty over Central Limit Order Book issue, and the imposition of repatriation levy, have sent shock waves throughout the domestic stock market.

Nonlinear serial dependence and the weak-form efficiency of Asian emerging stock markets

The objective of this paper is to re-examine the weak-form efficiency of 10 Asian emerging stock markets. Using a battery of nonlinearity tests, the statistical results reveal that all the returns series still contain predictable nonlinearities even after removing linear serial correlation from the data. The next stage of sub-sample analysis using the Hinich [Hinich, M., 1996. Testing for dependence in the input to a linear time series model. Journal of Nonparametric Statistics 6, 205–221] bicorrelation test shows that the 10 Asian series follow a pure noise process for long periods of time, only to be interspersed with brief periods of strong nonlinear dependence. The exploratory investigation found that the cross-country differences in nonlinear departure from market efficiency can be explained by market size and trading activity, while the transient burst of nonlinear periods in each individual market can be attributed largely to the occurrence of economic and political events.

Financial crisis and stock market efficiency: Empirical evidence from Asian countries

This paper empirically investigates the effects of the 1997 financial crisis on the efficiency of eight Asian stock markets, applying the rolling bicorrelation test statistics for the three sub-periods of pre-crisis, crisis, and post-crisis. On a country-by-country basis, the results demonstrate that the crisis adversely affected the efficiency of most Asian stock markets, with Hong Kong being the hardest hit, followed by the Philippines, Malaysia, Singapore, Thailand and Korea. However, most of these markets recovered in the post-crisis period in terms of improved market efficiency. Given that the evidence of nonlinear serial dependencies indicates equilibrium deviation resulted from external shocks, the present findings of higher inefficiency during the crisis are not surprising as in the chaotic financial environment at that time, investors would overreact not only to local news, but also to news originating in the other markets, especially when the news events were adverse.

Ranking market efficiency for stock markets: A nonlinear perspective

The present paper demonstrates, via a rolling sample approach, that the stylized fact of nonlinear dependence in stock returns is quite localized in time, suggesting that market efficiency evolves over time. Given that the rolling sample framework is able to detect periods of efficiency/inefficiency, the relative efficiency of stock markets can easily be assessed by comparing the total time windows these markets exhibit significant nonlinear serial dependence. It was found that the US market is the most efficient while Argentine is at the end of the ranking.

Events that Shook the Market: An Insight from Nonlinear Serial Dependencies in Intraday Returns

The present study proposes the use of nonlinear serial dependencies in the returns series for assessing market responses to new information. Unlike the standard event study methodology, this paper advocates a reserve form that let data analysis to first detect those periods with significant nonlinearity, and then identify whether their occurrences can be associated with major economic or political events. Our proposed research framework involves the application of the Hinich (1996) portmanteau bicorrelation test statistic in a moving time windows setting. Using the Malaysian stock market as a case study, our empirical application is able to detect not only the presence of nonlinear serial dependencies in the KLCI intraday ten-minute returns, but also the time periods when they occurred. The next stage of event-matching managed to identify major events that unsettled the local stock market in all cases except one. In particular, the Russian crisis, the unorthodox capital control measures and the Brazilian crisis are found to be responsible for the short burst of nonlinear behavior. However, the paper noted that factors that shook the market need not be news announcement in the media. It could be due to, among others, rumors, speculations, expectations, or worries prevail in the investment communities.

Evaluating the Effectiveness of State-Switching Time Series Models for U.S. Real Output

Two types of state-switching models for U.S. real output have been proposed: models that switch randomly between states and models that switch states deterministically, as in the threshold autoregressive model of Potter. These models have been justified primarily on how well they fit the sample data, yielding statistically significant estimates of the model coefficients. Here we propose a new approach to the evaluation of an estimated nonlinear time series model that provides a complement to existing methods based on in-sample fit or on out-of-sample forecasting. In this new approach, a battery of distinct nonlinearity tests is applied to the sample data, resulting in a set of p-values for rejecting the null hypothesis of a linear generating mechanism. This set of p-values is taken to be a “stylized fact” characterizing the nonlinear serial dependence in the generating mechanism of the time series. The effectiveness of an estimated nonlinear model for this time series is then evaluated in terms of the congruence between this stylized fact and a set of nonlinearity test results obtained from data simulated using the estimated model. In particular, we derive a portmanteau statistic based on this set of nonlinearity test p-values that allows us to test the proposition that a given model adequately captures the nonlinear serial dependence in the sample data. We apply the method to several estimated state-switching models of U.S. real output.

Episodic nonlinearity in Latin American stock market indices

This letter applies the Hinich portmanteau bicorrelation test jointly with the windowed testing procedure to detect nonlinear behaviour in the rate of returns series for seven Latin American stock market indices. Our results suggest that the nonlinear serial dependencies are episodic in nature. All the stock returns series are characterized by few brief periods of highly significant nonlinearity, followed by long time periods in which the returns follow a pure noise process. Our findings help explain why there are difficulties in forecasting asset returns.

Comments on “A critical investigation on detrending procedures for nonlinear processes”

We agree that either mistaking a stochastic trend for a deterministic trend (or vice-versa) is consequential for unit root tests and for tests of nonlinear serial dependence. In addition, we comment that similar results obtain for ordinary parameter inference in simple linear models. In particular, we note that detrending stochastically trended data with a deterministic polynomial or by applying the Hodrick–Prescott filter yields notably mis-sized hypothesis tests, even with a sample length of 200 observations. Interestingly, we further find that these size distortions persist even with stationary—albeit highly persistent—data.

The cross-sectional and cross-temporal universality of nonlinear serial dependencies: Evidence from world stock indices and the Taiwan Stock Exchange

This paper studies a variety of world financial market indices to determine how widespread the phenomenon of nonlinear serial dependency is, and then, by studying a relatively financially isolated market, the Taiwan Stock Exchange of the 1980s, examines more closely the extent to which nonlinearity appears to be an inherent feature of financial trading behavior. Nonlinearity is found to be a cross-sectionally universal phenomenon, existing within all the markets studied and within the vast majority of individual stocks traded on the Taiwan Stock Exchange. However, closer examination of the nonlinearity via a windowed testing procedure reveals that such dependencies do not appear to be cross-temporally universal; rather, the data seem to be characterized by relatively few brief episodes of extremely strong dependencies that are followed by longer stretches of relatively quiet behavior. Thus, the modeling of the extant nonlinearity appears to be problematic at best.