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How They Interact to Generate Persistency in Memory

  • Miller, J. Isaac

    (Rice U)

  • Park, Joon Y.

In this paper, we consider nonlinear transformations of random walks driven by thick-tailed innovations with infinite 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 autocorrelation patterns, along with other sample characteristics of the transformed time series, suggest the possibility that these three ingredients are involved in the data generating processes for many actual economic and financial time series data. We also discuss nonlinear regression asymptotics when the regressor is observable and an alternative regression technique when it is unobservable. 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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File URL: http://www.ruf.rice.edu/~econ/papers/2005papers/park01.pdf
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Paper provided by Rice University, Department of Economics in its series Working Papers with number 2005-01.

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Date of creation: Jan 2005
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Handle: RePEc:ecl:riceco:2005-01
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  1. 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.
  2. de Jong, F, 1994. "A Univariate Analysis of EMS Exchange Rates Using a Target Zone Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(1), pages 31-45, Jan.-Marc.
  3. 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.
  4. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  5. Peter C.B. Phillips, 1989. "Time Series Regression with a Unit Root and Infinite Variance Errors," Cowles Foundation Discussion Papers 897R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  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. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
  8. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(03), pages 354-362, December.
  9. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
  10. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  11. 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.
  12. 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.
  13. 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.
  14. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
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