Test For Long-range Dependence Research Articles

Wavelet-domain test for long-range dependence in the presence of a trend

We propose a test to distinguish a weakly-dependent time series with a trend component, from a long-memory process, possibly with a trend. The test uses a generalized likelihood ratio statistic based on wavelet domain likelihoods. The trend is assumed to be a polynomial whose order does not exceed a known value. The test is robust to trends which are piecewise polynomials. We study the empirical size and power by means of simulations and find that they are good and do not depend on specific choices of wavelet functions and models for the wavelet coefficients. The test is applied to annual minima of the Nile River and confirms the presence of long-range dependence in this time series.

Testing for long-range dependence in stock market returns: a further evidence from MENA emerging stock markets

The financial rates of return from Middle East and North African markets are found to be nonnormal, nonstationary and long-range dependent, i.e. they have long memory. The degree of long-term dependence is measured by Hurst exponents using local Whittle method which is a semi-parametric method that presents robustness to data seasonality and short-range dependence. Our long-term results are consistent with similar empirical findings from American, European and Asian financial markets. Therefore, the article extends the domain of the empirical investigation of the dynamics characteristics of the global financial markets and disproves the hypothesis of perfectly efficient financial markets.

Testing for long range dependence in banking equity indices

This paper presents empirical evidence of long range dependence in returns and volatility for banking indices for 41 different countries. We employ the Rescaled Hurst analysis and develop a formal statistical procedure to test for long range dependence. This procedure allows to rank these countries by relative inefficiency, which can provide guidance for investors and portfolio managers.

Note on bandwidth selection in testing for long range dependence

Many tests for I(0) versus I( d) processes are standardized by long-run variance estimators, which are estimated by nonparametric methods that entail a choice of bandwidth. Data-dependent bandwidth choices using plug-in methods have been suggested and used in many applications. In a recent paper, Teverovsky et al. [Journal of Statistical Planning and Inference 80 (1999) 211] conducted a Monte Carlo study on the modified rescaled range (R/S) test and found that the test “has a strong bias towards accepting the null hypothesis”. In this note, we show that the Monte Carlo finding of unusually low power and the empirical finding of short-memory in stock returns indexes are related to the data-dependent bandwidth choice. Simply using the data-dependent bandwidth choice is inappropriate.

A critical look at Lo's modified R/S statistic

Abstract We report on an empirical investigation of the modified rescaled adjusted range or R/S statistic that was proposed by Lo, 1991 . Econometrica 59, 1279–1313, as a test for long-range dependence with good robustness properties under ‘extra’ short-range dependence. In contrast to the classical R/S statistic that uses the standard deviation S to normalize the rescaled range R, Lo's modified R/S-statistic Vq is normalized by a modified standard deviation Sq which takes into account the covariances of the first q lags, so as to discount the influence of the short-range dependence structure that might be present in the data. Depending on the value of the resulting test-statistic Vq, the null hypothesis of no long-range dependence is either rejected or accepted. By performing Monte-Carlo simulations with ‘truly’ long-range- and short-range dependent time series, we study the behavior of Vq, as a function of q, and uncover a number of serious drawbacks to using Lo's method in practice. For example, we show that as the truncation lag q increases, the test statistic Vq has a strong bias toward accepting the null hypothesis (i.e., no long-range dependence), even in ideal situations of ‘purely’ long-range dependent data.

Stock market prices and long-range dependence

Using the CRSP (Center for Research in Security Prices) daily stock return data, we revisit the question of whether or not actual stock market prices exhibit long-range dependence. Our study is based on an empirical investigation reported in Teverovsky, Taqqu and Willinger [33] of the modified rescaled adjusted range or R/S statistic that was proposed by Lo [17] as a test for long-range dependence with good robustness properties under “extra” short-range dependence. Our main conclusion is that because the modified R/S statistic shows a strong preference for accepting the null hypothesis of no long-range dependence, irrespective of whether long-range dependence is present in the data or not, Lo's acceptance of the hypothesis for the CRSP data (i.e., no long-range dependence in stock market prices) is less conclusive than is usually regarded in the econometrics literature. In fact, upon further analysis of the data, we find empirical evidence of long-range dependence in stock price returns, but because the corresponding degree of long-range dependence (measured via the Hurst parameter H) is typically very low (i.e., H-values around 0.60), the evidence is not absolutely conclusive.