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Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory

  • Miller, J. Isaac
  • Park, Joon Y.

We consider nonlinear functions of random walks driven by thick-tailed innovations. Nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of autocorrelation patterns consistent with the observed persistence in memory of many economic and financial time series. Depending upon the type of transformation considered and whether it is observed with noise, the autocorrelations are given by unity, random constants, or hyperbolically decaying deterministic functions, possibly with some independent noise, and thus may decay slowly or even not at all. Along with other sample characteristics, such patterns suggest that these three ingredients may generate the ubiquitous evidence for long memory.

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File URL: http://www.sciencedirect.com/science/article/B6VC0-4X9NV9T-3/2/abeb77843a14454ca1d4ce804cf2a348
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 155 (2010)
Issue (Month): 1 (March)
Pages: 83-89

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Handle: RePEc:eee:econom:v:155:y:2010:i:1:p:83-89
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  2. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  3. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  4. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
  5. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
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