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

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  • Joon Y. Park
  • J. Isaac Miller

Abstract

In this paper, we consider nonlinear transformations of random walks driven by thick-tailed innovations with undefined means or variances. In particular, we show how nonlinearity, nonstationarity, and thick tails interact to generate persistency in memory, and we clearly demonstrate that this triad may generate a broad spectrum of persistency patterns. Time series generated by nonlinear transformations of random walks with thick-tailed innovations have asymptotic autocorrelations that decay very slowly as the number of lags increases or do not even decay at all and remain constant at all lags. Depending upon the type of transformation considered and how the model error is specified, they are given by random constants, deterministic functions which decay slowly at polynomial rates, or mixtures of the two. These patterns in autocorrelations, along with other sample characteristics of the transformed time series, make it very plausible that this triad is involved in the data generating processes for many actual economic and financial time series data. We use our model to analyze two empirical applications: exchange rates governed by a target zone and electricity price spikes driven by capacity shortfalls

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 597.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:597

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

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References

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  1. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
  2. 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.
  3. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
  4. 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.
  5. Lars E.O. Svensson, 1991. "The Term Structure of Interest Rate Differentials in a Target Zone: Theory and Swedish Data," NBER Working Papers 3374, National Bureau of Economic Research, Inc.
  6. 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.
  7. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
  8. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
  9. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  10. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
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Citations

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Cited by:
  1. 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.
  2. J. Isaac Miller & Yoosoon Chang & Joon Y. Park, 2005. "Extracting a Common Stochastic Trend:Theories with Some Applications," Working Papers 0507, Department of Economics, University of Missouri, revised 18 Aug 2005.
  3. Chung, Heetaik & Park, Joon Y., 2007. "Nonstationary nonlinear heteroskedasticity in regression," Journal of Econometrics, Elsevier, vol. 137(1), pages 230-259, March.
  4. Han, Heejoon & Park, Joon Y., 2006. "Time series properties of ARCH processes with persistent covariates," MPRA Paper 5199, University Library of Munich, Germany.
  5. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
  6. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.

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