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The effect of memory on functional large deviations of infinite moving average processes

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  • Ghosh, Souvik
  • Samorodnitsky, Gennady

Abstract

The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change dramatically. We study this phenomenon in the context of functional large, moderate and huge deviation principles.

Suggested Citation

  • Ghosh, Souvik & Samorodnitsky, Gennady, 2009. "The effect of memory on functional large deviations of infinite moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 534-561, February.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:534-561
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    References listed on IDEAS

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    1. Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
    2. Dong, Zhi-shan & Xi-li, Tan & Yang, Xiao-yun, 2005. "Moderate deviation principles for moving average processes of real stationary sequences," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 139-150, September.
    3. Philippe Barbe & Michel Broniatowski, 1998. "Note on Functional Large Deviation Principle for Fractional ARIMA Processes," Statistical Inference for Stochastic Processes, Springer, vol. 1(1), pages 17-27, January.
    4. Jiang, Tiefeng & Wang, Xiangchen & Rao, M. Bhaskara, 1992. "Moderate deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 71-76, September.
    5. Jiang, Tiefeng & Rao, M. Bhaskara & Wang, Xiangchen, 1995. "Large deviations for moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 309-320, October.
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