Vadim Teverovsky

ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY

Various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones t...

Stock Market Prices and Long-Range Dependence

Abstract. 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, Los 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.

Is Network Traffic Self-Similar or Multifractal?

This paper addresses the question of whether self-similar processes are sufficient to model packet network traffic, or whether a broader class of multifractal processes is needed. By using the absolute moments of aggregate traffic measurements, we conclude that measured local-area network (LAN) and wide-area network (WAN) traffic traces, with the sample means subtracted, are well modeled by random processes that are either exactly or asymptotically self-similar.

Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator

In this paper we examine the effects of certain types of non- stationarity on the detection of long-range dependence and on the estimation of the Hurst parameter H, when using a variance-type estimator. The resulting estimate of H can be misleading when the series has either a jump in the mean or a slow trend. In such a case, plotting the logarithm of the variance versus the logarithm of the level of aggregation gives a curve which is quite different from a straight line. A method for distinguishing between the effects of long-range dependence and these types of non-stationarity is developed.

Estimating long-range dependence in the presence of periodicity: An empirical study

Recent results in applied statistics have shown that the presence of periodicity in a time series may have an influence on the estimation of the long memory (long-range dependence) parameter H. In particular, some estimators falsely detect the presence of long-range dependence when periodicity is present. In this paper, we apply various estimation procedures to synthetic periodic time series in order to verify the performance of each estimation method and to determine which estimators should be used when periodicity may be present.

Robustness of whittle-type estimators for time series with long-range dependence

We study the robustness of the “standard Whittle ”, “local Whittle” and “aggregated Whittle” estimators by using a large number of simulated Gaussian time series with long-range dependence. We also consider what happens when the Gaussian innovations are replaced by infinite variance symmetric stable ones. The standard Whittle estimator is a parametric estimator, the local Whittle estimator is a semi-parametric one recently developed by Robinson (1995) and the aggregated Whittle estimator smoothes out the high frequencies. The goal is to estimate H, the intensity of long-range dependence. We investigate the standard deviation and bias of these estimators in order to determine when they are reliable. These estimators are then applied to real-life Ethernet data

Semi-parametric graphical estimation techniques for long-memory data

This paper reviews several periodogram-based methods for estimating the long-memory parameter H in time series and suggests a way to robustify them. The high frequencies tend to bias the estimates. Using only low frequencies eliminates the bias but increases the variance. We hence suggest plotting the estimates of H as a function of a parameter which balances bias versus variance and, if the plot flattens in a central region, to use the flat part for estimating H. We apply this technique to the periodogram regression method, the Whittle approximation to maximum likelihood and to the local Whittle method. We investigate its effectiveness on several simulated fractional ARIMA series and also apply it to estimate the long-memory parameter H in computer network traffic.