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Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity

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  • Cathy Chen
  • Richard Gerlach

Abstract

Compared to the conditional mean or median, conditional quantiles provide a more comprehensive picture of a variable in various scenarios. A semi-parametric quantile estimation method for a double threshold auto-regression with exogenous regressors and heteroskedasticity is considered, allowing representation of both asymmetry and volatility clustering. As such, GARCH dynamics with nonlinearity are added to a nonlinear time series regression model. An adaptive Bayesian Markov chain Monte Carlo scheme, exploiting the link between the quantile loss function and the asymmetric-Laplace distribution, is employed for estimation and inference, simultaneously estimating and accounting for nonlinear heteroskedasticity plus unknown threshold limits and delay lags. A simulation study illustrates sampling properties of the method. Two data sets are considered in the empirical applications: modelling daily maximum temperatures in Melbourne, Australia; and exploring dynamic linkages between financial markets in the US and Hong Kong. Copyright Springer-Verlag 2013

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  • Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:3:p:1103-1131
    DOI: 10.1007/s00180-012-0346-9
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    Cited by:

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    2. Cathy W. S. Chen & Muyi Li & Nga T. H. Nguyen & Songsak Sriboonchitta, 2017. "On Asymmetric Market Model with Heteroskedasticity and Quantile Regression," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 155-174, January.
    3. Cathy W. S. Chen & Mike K. P. So & Thomas C. Chiang, 2016. "Evidence of Stock Returns and Abnormal Trading Volume: A Threshold Quantile Regression Approach," The Japanese Economic Review, Springer, vol. 67(1), pages 96-124, March.
    4. Wang, Kai Y.K. & Chen, Cathy W.S. & So, Mike K.P., 2023. "Quantile three-factor model with heteroskedasticity, skewness, and leptokurtosis," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    5. Vahid Nassiri & Ignace Loris, 2014. "An efficient algorithm for structured sparse quantile regression," Computational Statistics, Springer, vol. 29(5), pages 1321-1343, October.
    6. Cathy Chen & Simon Lin & Philip Yu, 2012. "Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 19-48, June.

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