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

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Author Info
Joon Y. Park
J. Isaac Miller

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

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
    Other versions:
  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. [Downloadable!]
    Other versions:
  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. [Downloadable!] (restricted)
    Other versions:
  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. Svensson, Lars E. O., 1991. "The term structure of interest rate differentials in a target zone : Theory and Swedish data," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 87-116, August. [Downloadable!] (restricted)
    Other versions:
  6. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. J. Isaac Miller, 2006. "Testing for Purchasing Power Parity Under a Target Zone Exchange Rate Regime," Working Papers 0604, Department of Economics, University of Missouri, revised 19 Nov 2007. [Downloadable!]
  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. [Downloadable!]
  3. J. Isaac Miller, 2008. "Testing the Bounds: Empirical Behavior of Target Zone Fundamentals," Working Papers 0803, Department of Economics, University of Missouri. [Downloadable!]
  4. Han, Heejoon & Park, Joon Y., 2006. "Time series properties of ARCH processes with persistent covariates," MPRA Paper 5199, University Library of Munich, Germany. [Downloadable!]
  5. J. Isaac Miller, 2006. "A Random Coefficients Autoregressive Model with Exogenously-Driven Stochastic Unit Roots," Working Papers 0609, Department of Economics, University of Missouri, revised 11 Aug 2006. [Downloadable!]
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