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APPARENT LONG MEMORY IN TIME SERIES AS AN ARTIFACT OF A TIME-VARYING MEAN: CONSIDERING ALTERNATIVES TO THE FRACTIONALLY INTEGRATED MODEL

Published online by Cambridge University Press:  05 May 2010

Richard A. Ashley  and
Douglas M. Patterson
Richard A. Ashley*
Affiliation:
Virginia Tech
Douglas M. Patterson
Affiliation:
Virginia Tech
*
Address correspondence to: Richard A. Ashley, Economics Department (0316), Virginia Tech, Blacksburg, VA 24061, USA; e-mail: ashleyr@vt.edu.
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Abstract

Structural breaks and switching processes are known to induce apparent long memory in a time series. Here we show that any significant time variation in the mean renders the sample correlogram (and related spectral estimates) inconsistent. In particular, smooth time variation in the mean—i.e., even a weak trend, either stochastic or deterministic—induces apparent long memory. This apparent long memory can be eliminated by either high-pass filtering or by detrending. Here we demonstrate the effectiveness in this regard of nonlinear detrending via penalized-spline nonparametric regression. A time-varying mean can be of economic interest in its own right. This suggests that isolating out and separately examining both a local mean (i.e., a nonlinear trend or the realization of a stochastic trend) and deviations from it is preferable as a modeling strategy to simply estimating a fractionally integrated model. We illustrate the superiority of this strategy using stock return volatility data.

Keywords

Long MemoryFractional IntegrationDetrendingStock ReturnsVolatility
Type
Articles
Information
Macroeconomic Dynamics , Volume 14 , Supplement S1: Nonlinear Time Series , May 2010 , pp. 59 - 87
Copyright
Copyright © Cambridge University Press 2010

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