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

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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.

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Bibliographic Info

Paper provided by Department of Economics, University of Missouri in its series Working Papers with number 0801.

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Length: 43 pgs.
Date of creation: 15 Jan 2008
Date of revision:
Handle: RePEc:umc:wpaper:0801

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Keywords: persistency in memory; nonlinear transformations; random walks; thick tails; stable distributions; wholesale electricity prices; target zone exchange rates;

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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. 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.
  3. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
  4. 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.
  5. 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.
  6. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
  7. 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.
  8. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
  9. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  10. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
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Cited by:
  1. Ioannis Kasparis & Peter C.B. Phillips & Tassos Magdalinos, 2012. "Non-linearity Induced Weak Instrumentation," Cowles Foundation Discussion Papers 1872, Cowles Foundation for Research in Economics, Yale University.
  2. Han, Heejoon & Park, Joon Y., 2006. "Time series properties of ARCH processes with persistent covariates," MPRA Paper 5199, University Library of Munich, Germany.
  3. Joon Y. Park & Heetaik Chung, 2004. "Nonstationary Nonlinear Heteroskedasticity in Regression," Econometric Society 2004 Far Eastern Meetings 508, Econometric Society.
  4. Guillaume Chevillon & Sophocles Mavroeidis, 2013. "Learning generates Long Memory," Post-Print hal-00661012, HAL.
  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. 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.

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