Improved Estimation of the Memory Parameter

Reschenhofer, Erhard; Mangat, Manveer Kaur; Stark, Tom

doi:10.4236/tel.2020.101004

TEL

2020

DOI: 10.4236/tel.2020.101004

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Improved Estimation of the Memory Parameter

Erhard Reschenhofer¹,

Manveer Kaur Mangat²,

Tom Stark³

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-Four… Show more

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Cited by 3 publications

References 60 publications

(47 reference statements)

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Fast computation and practical use of amplitudes at non-Fourier frequencies

Reschenhofer

Mangat

2021

Comput Stat

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In this paper, it is shown that the performance of various frequency-domain estimators of the memory parameter can be boosted by the inclusion of non-Fourier frequencies in addition to the regular Fourier frequencies. A fast two-stage algorithm for the efficient computation of the amplitudes at these additional frequencies is presented. In the first stage, the naïve sine and cosine transforms are computed with a modified version of the Fast Fourier Transform. In the second stage, these transforms are amended by taking the violation of the standard orthogonality conditions into account. A considerable number of auxiliary quantities, which are required in the second stage, do not depend on the data and therefore only need to be computed once. The superior performance (in terms of root-mean-square error) of the estimators based also on non-Fourier frequencies is demonstrated by extensive simulations. Finally, the empirical results obtained by applying these estimators to financial high-frequency data show that significant long-range dependence is present only in the absolute intraday returns but not in the signed intraday returns.

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Fast computation and practical use of amplitudes at non-Fourier frequencies

Reschenhofer

Mangat

2021

Comput Stat

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Frequency-Domain Evidence for Climate Change

Mangat

Reschenhofer

2020

Econometrics

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The goal of this paper is to search for conclusive evidence against the stationarity of the global air surface temperature, which is one of the most important indicators of climate change. For this purpose, possible long-range dependencies are investigated in the frequency-domain. Since conventional tests of hypotheses about the memory parameter, which measures the degree of long-range dependence, are typically based on asymptotic arguments and are therefore of limited practical value in case of small or medium sample sizes, we employ a new small-sample test as well as a related estimator for the memory parameter. To safeguard against false positive findings, simulation studies are carried out to examine the suitability of the employed methods and hemispheric datasets are used to check the robustness of the empirical findings against low-frequency natural variability caused by oceanic cycles. Overall, our frequency-domain analysis provides strong evidence of non-stationarity, which is consistent with previous results obtained in the time domain with models allowing for stochastic or deterministic trends.

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

Reschenhofer¹,

Mangat²

2020

Econometrics

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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.

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Improved Estimation of the Memory Parameter

Cited by 3 publications

References 60 publications

Fast computation and practical use of amplitudes at non-Fourier frequencies

Fast computation and practical use of amplitudes at non-Fourier frequencies

Frequency-Domain Evidence for Climate Change

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

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