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Long Memory in Nonlinear Processes

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Author Info
Rohit Deo (IOMS)
Meng-Chen Hsieh (IOMS)
Clifford M. Hurvich (IOMS)
Philippe Soulier (MODAL'X)

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Abstract

It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line relationship. This necessitates a class of models for describing such behavior. A popular class of such models is the autoregressive fractionally integrated moving average (ARFIMA) which is a linear process. However, there is also a need for nonlinear long memory models. For example, series of returns on financial assets typically tend to show zero correlation, whereas their squares or absolute values exhibit long memory. Furthermore, the search for a realistic mechanism for generating long memory has led to the development of other nonlinear long memory models. In this chapter, we will present several nonlinear long memory models, and discuss the properties of the models, as well as associated parametric andsemiparametric estimators.

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File URL: http://arxiv.org/abs/0706.1836
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Publisher Info
Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0706.1836.

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Date of creation: Jun 2007
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Publication status: Published in D\'ependence in probability and statistics, Springer (Ed.) (2006) 221--244
Handle: RePEc:arx:papers:0706.1836

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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. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January. [Downloadable!] (restricted)
  2. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March. [Downloadable!] (restricted)
    Other versions:
  3. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, 07. [Downloadable!] (restricted)
    Other versions:
  4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  5. Rohit Deo & Clifford Hurvich & Yi Lu, 2005. "Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment," Econometrics 0501002, EconWPA. [Downloadable!]
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  6. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August. [Downloadable!]
  7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July. [Downloadable!] (restricted)
  8. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348. [Downloadable!] (restricted)
  9. Clifford M. Hurvich & Bonnie K. Ray, 2003. "The Local Whittle Estimator of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 1(3), pages 445-470.
  10. Rohit Deo & Clifford Hurvich & Philippe Soulier & Yi Wang, 2005. "Propagation of Memory Parameter from Durations to Counts," Econometrics 0511010, EconWPA. [Downloadable!]
  11. Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August. [Downloadable!] (restricted)
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  12. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February. [Downloadable!]
  13. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
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  1. Kuswanto, Heri & Sibbertsen, Philipp, 2008. "A Study on "Spurious Long Memory in Nonlinear Time Series Models"," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover dp-410, Universität Hannover, Wirtschaftswissenschaftliche Fakultät. [Downloadable!]
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