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

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

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Persistence in memory Nonlinear transformations Random walks Thick tails Stable distributions;

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References

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  1. Svensson, L.E.O., 1990. "The Term Structure of Interest Rate Differentials in a Target Zone: Theory and Swedish Data," Papers 466, Stockholm - International Economic Studies.
  2. Paul R. Krugman, 1988. "Target Zones and Exchange Rate Dynamics," NBER Working Papers 2481, National Bureau of Economic Research, Inc.
  3. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  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. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  6. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
  7. Dufour, Jean-Marie & Kurz-Kim, Jeong-Ryeol, 2003. "Exact tests and confidence sets for the tail coefficient of a-stable distributions," Discussion Paper Series 1: Economic Studies 2003,16, Deutsche Bundesbank, Research Centre.
  8. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  9. 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.
  10. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
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Citations

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Cited by:
  1. Han, Heejoon & Park, Joon Y., 2006. "Time series properties of ARCH processes with persistent covariates," MPRA Paper 5199, University Library of Munich, Germany.
  2. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
  3. Chang, Yoosoon & Miller, J. Isaac & Park, Joon Y., 2005. "Extracting a Common Stochastic Trend: Theories with Some Applications," Working Papers 2005-06, Rice University, Department of Economics.
  4. Park, Joon & Chung, Heetaik, 2005. "Nonstationary Nonlinear Heteroskedasticity in Regression," Working Papers 2004-02, Rice University, Department of Economics.
  5. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.
  6. Ioannis Kasparis & Peter C.B. Phillips & Tassos Magdalinos, 2012. "Non-linearity Induced Weak Instrumentation," University of Cyprus Working Papers in Economics 02-2012, University of Cyprus Department of Economics.

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