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Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory


  • Miller, J. Isaac
  • Park, Joon Y.


We consider nonlinear functions of random walks driven by thick-tailed innovations. Nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of autocorrelation patterns consistent with the observed persistence in memory of many economic and financial time series. Depending upon the type of transformation considered and whether it is observed with noise, the autocorrelations are given by unity, random constants, or hyperbolically decaying deterministic functions, possibly with some independent noise, and thus may decay slowly or even not at all. Along with other sample characteristics, such patterns suggest that these three ingredients may generate the ubiquitous evidence for long memory.

Suggested Citation

  • Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
  • Handle: RePEc:eee:econom:v:155:y:2010:i:1:p:83-89

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    References listed on IDEAS

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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. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.
    9. 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


    Persistence in memory Nonlinear transformations Random walks Thick tails Stable distributions;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions


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