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Asymptotics of Quantiles and Rank Scores in Nonlinear Time Series

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  • Kanchan Mukherjee

Abstract

This paper extends the concept of regression and autoregression quantiles and rank scores to a very general nonlinear time series model. The asymptotic linearizations of these nonlinear quantiles are then used to obtain the limiting distributions of a class of L‐estimators of the parameters. In particular, the limiting distributions of the least absolute deviation estimator and trimmed estimators are obtained. These estimators turn out to be asymptotically more efficient than the widely used conditional least squares estimator for heavy‐tailed error distributions. The results are applicable to linear and nonlinear regression and autoregressive models including self‐exciting threshold autoregressive models with known threshold.

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  • Kanchan Mukherjee, 1999. "Asymptotics of Quantiles and Rank Scores in Nonlinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(2), pages 173-192, March.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:2:p:173-192
    DOI: 10.1111/1467-9892.00132
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    Cited by:

    1. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    2. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
    3. Fabrizio Cipollini & Giampiero M. Gallo & Alessandro Palandri, 2023. "Modeling and evaluating conditional quantile dynamics in VaR forecasts," Papers 2305.20067, arXiv.org.
    4. repec:hal:journl:peer-00732534 is not listed on IDEAS

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