Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory

J. Miller and Joon Y. Park

No 801, Working Papers from Department of Economics, University of Missouri

Abstract: We consider nonlinear transformations of random walks driven by thick-tailed innovations that may have infinite means or variances. These three nonstandard characteristics: nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of asymptotic autocorrelation patterns consistent with long-memory processes. Such autocorrelations may decay very slowly as the number of lags increases or may not decay at all and remain constant at all lags. Depending upon the type of transformation considered and how the model error is speci- fied, the autocorrelation functions are given by random constants, deterministic functions that decay slowly at hyperbolic rates, or mixtures of the two. Such patterns, along with other sample characteristics of the transformed time series, such as jumps in the sample path, excessive volatility, and leptokurtosis, suggest the possibility that these three ingredients are involved in the data generating processes of many actual economic and financial time series data. In addition to time series characteristics, we explore nonlinear regression asymptotics when the regressor is observable and an alternative regression technique when it is unobservable. To illustrate, we examine two empirical applications: wholesale electricity price spikes driven by capacity shortfalls and exchange rates governed by a target zone.

Keywords: persistency in memory; nonlinear transformations; random walks; thick tails; stable distributions; wholesale electricity prices; target zone exchange rates (search for similar items in EconPapers)
JEL-codes: C16 (search for similar items in EconPapers)
Pages: 43 pgs.
Date: 2008-01-15
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (2)

Published in Journal of Econometrics 2010 (revised version)

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Related works:
Journal Article: Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory (2010)
Working Paper: Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:umc:wpaper:0801

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