TITLE:
Improved Estimation of the Memory Parameter
AUTHORS:
Erhard Reschenhofer, Manveer K. Mangat, Thomas Stark
KEYWORDS:
Long-Range Dependence, Log Periodogram Regression, Kolmogorov-Smirnov Test
JOURNAL NAME:
Theoretical Economics Letters,
Vol.10 No.1,
January
19,
2020
ABSTRACT: In this paper, it is proposed to estimate the memory
parameter of a potentially long-range dependent time series by applying
goodness-of-fit tests to the cumulative normalized periodogram in the
neighborhood of frequency zero. The results of an extensive simulation study
show that this new estimator performs well compared to conventional
frequency-domain estimators which are based on the Whittle likelihood or are
obtained from the popular log periodogram estimator by trimming, smoothing, and
utilizing non-Fourier frequencies, respectively. In an empirical investigation
of log absolute daily index returns, we find evidence of long-range dependence
with values of the memory parameter in the range between 0.2 and 0.3 both in
developed and developing stock markets. There are no indications of long-range
dependence in the case of the original index returns.