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Abstract:
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This paper proposes a new conditional heteroscedastic model, called the linear double autoregressive (AR) model. Its conditional quantile inference tools are studied without imposing any moment condition on the process or the innovations, in contrast to the existing inference tools for conditional heteroscedastic models which all require that the innovations have a finite variance. The existence of strictly stationary solutions to the linear double AR model is discussed, and a necessary and sufficient condition is established by borrowing the linearity of the random coefficient AR model. We introduce the doubly weighted conditional quantile estimation (CQE) for the model, where the first set of weights ensures the asymptotic normality of the estimators, and the second improves its efficiency through balancing individual CQEs across multiple quantile levels. Finally, goodness-of-fit tests based on the quantile autocorrelation function are suggested for checking the adequacy of the fitted models. Simulation studies indicate that the proposed inference tools perform well in finite samples, and an empirical example is presented to illustrate the usefulness of the new model.
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