Long memory estimation in a non-Gaussian bivariate process

Abstract The asymptotic theory for the memory-parameter estimator constructed from the log-regression with wavelets is incomplete for 1/$f$ processes that are not necessarily Gaussian or linear. Having a complete version of this theory is necessary because of the importance of non-Gaussian and non-linear long-memory models in describing financial time series. To bridge this gap, we prove that, under some mild assumptions, a newly designed memory estimator, named LRMW in this paper, is asymptotically consistent. The performances of LRMW in three simulated long-memory processes indicate the efficiency of this new estimator.

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Inducing normality from non-Gaussian long memory time series and its application to stock return data

Applied Stochastic Models in Business and Industry ◽

10.1002/asmb.784 ◽

2009 ◽

Vol 26 (4) ◽

pp. 374-388

Author(s):

Kyungduk Ko

Keyword(s):

Time Series ◽

Long Memory ◽

Stock Return ◽

Memory Time ◽

Non Gaussian ◽

Return Data

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REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES

Econometric Theory ◽

10.1017/s0266466609990260 ◽

2009 ◽

Vol 25 (6) ◽

pp. 1589-1624 ◽

Cited By ~ 4

Author(s):

James Davidson ◽

Nigar Hashimzade

Keyword(s):

Long Memory ◽

Moving Average ◽

Full Range ◽

Sample Covariance ◽

Fractional Integrator ◽

The Mean ◽

Non Gaussian ◽

The Time Domain ◽

The Relationship ◽

Harmonic Representation

This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process—possibly itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analyzed in a previous paper (Davidson and Hashimzade, 2008), and the construction derived from moving average representations in the time domain. Depending on the values of the long memory parameters and choice of normalization, the limiting integral is shown to be expressible as the sum of a constant and two Itô-type integrals with respect to distinct Brownian motions. In certain cases the latter terms are of small order relative to the former. The mean is shown to match that of the harmonic representation, where the latter is defined, and satisfies the required integration by parts rule. The advantages of our approach over the harmonic analysis include the facts that our formulas are valid for the full range of the long memory parameters and that they extend to non-Gaussian processes.

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The effect of round-off error on long memory processes

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2013-0011 ◽

2014 ◽

Vol 18 (4) ◽

Cited By ~ 1

Author(s):

Gabriele La Spada ◽

Fabrizio Lillo

Keyword(s):

Long Memory ◽

Hurst Exponent ◽

Asymptotic Properties ◽

Regularity Conditions ◽

Fluctuation Analysis ◽

Memory Process ◽

Asymptotically Normal ◽

Long Memory Process ◽

Long Memory Processes ◽

Non Gaussian

AbstractWe study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the detrended fluctuation analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both estimators are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic (i.e., non-Gaussian) long memory process and we apply the result to discretized processes.

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