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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

Suggested Citation

  • Joon Y. Park & J. Isaac Miller, 2004. "Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory," Econometric Society 2004 North American Summer Meetings 597, Econometric Society.
  • Handle: RePEc:ecm:nasm04:597
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    References listed on IDEAS

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    1. Max Stevenson, 2001. "Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market," Research Paper Series 63, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March.
    3. Chang, Yoosoon & Isaac Miller, J. & Park, Joon Y., 2009. "Extracting a common stochastic trend: Theory with some applications," Journal of Econometrics, Elsevier, vol. 150(2), pages 231-247, June.
    4. 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.
    5. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
    6. 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.
    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. 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.
    9. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
    10. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    11. 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. Chevillon, Guillaume & Hecq , Alain & Laurent, S├ębastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    2. Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
    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. Chung, Heetaik & Park, Joon Y., 2007. "Nonstationary nonlinear heteroskedasticity in regression," Journal of Econometrics, Elsevier, vol. 137(1), pages 230-259, March.
    5. Han, Heejoon & Park, Joon Y., 2008. "Time series properties of ARCH processes with persistent covariates," Journal of Econometrics, Elsevier, vol. 146(2), pages 275-292, October.
    6. Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
    7. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    8. repec:eee:econom:v:204:y:2018:i:1:p:54-65 is not listed on IDEAS
    9. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.
    10. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.

    More about this item

    Keywords

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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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