Reducing the Bias of the Smoothed Log Periodogram Regression for Financial High-Frequency Data

Erhard Reschenhofer,Manveer K Mangat

doi:10.3390/econometrics8040040

Abstract

For typical sample sizes occurring in economic and financial applications, the squared bias of estimators for the memory parameter is small relative to the variance. Smoothing is therefore a suitable way to improve the performance in terms of the mean squared error. However, in an analysis of financial high-frequency data, where the estimates are obtained separately for each day and then combined by averaging, the variance decreases with the sample size but the bias remains fixed. This paper proposes a method of smoothing that does not entail an increase in the bias. This method is based on the simultaneous examination of different partitions of the data. An extensive simulation study is carried out to compare it with conventional estimation methods. In this study, the new method outperforms its unsmoothed competitors with respect to the variance and its smoothed competitors with respect to the bias. Using the results of the simulation study for the proper interpretation of the empirical results obtained from a financial high-frequency dataset, we conclude that significant long-range dependencies are present only in the intraday volatility but not in the intraday returns. Finally, the robustness of these findings against daily and weekly periodic patterns is established.

Highlights

After Mandelbrot (1971) had discussed the possibility that the strength of the statistical dependence of stock prices decreases very slowly, several researchers investigated this issue empirically
Qn, which is defined as the range of all partial sums of a time series of length n from its mean divided by its standard deviation
We employ the estimators discussed in the previous sections for the search of possible long-range dependencies in intraday returns and absolute intraday returns

Summary

Introduction

After Mandelbrot (1971) had discussed the possibility that the strength of the statistical dependence of stock prices decreases very slowly, several researchers investigated this issue empirically. Greene and Fielitz (1977) found indications of long-range dependence when they applied a technique called range over standard deviation (R/S) analysis (Hurst 1951; Mandelbrot and Wallis 1969; Mandelbrot 1972, 1975) to daily stock return series. This technique is based on the R/S statistic. Lo (1991) pointed out that the results obtained with this technique may be misleading because of the sensitivity of Qn to short-range dependence (see Davis and Harte 1987; Hauser and Reschenhofer 1995) and proposed, a

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