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In this paper, quantile regression methods are suggested for a class of smooth coefficient time series models. We employ a local linear fitting scheme to estimate the smooth coefficients in the quantile framework. The programming involved in the local linear quantile estimation is relatively simple and it can be modified with few efforts from the existing programs for the linear quantile model. We derive the local Bahadur representation of the local linear estimator for α-mixing time series and establish the asymptotic normality of the resulting estimator. Also, a bandwidth selector based on the nonparametric version of the Akaike information criterion is proposed, together with a consistent estimate of the asymptotic covariance matrix. The asymptotic behaviors of the estimator at the boundaries are examined. A comparison of the local linear quantile estimator with the local constant estimator is presented. A simulation study is carried out to illustrate the performance of the estimates. An empirical application of the model to the exchange rate time series data and the well-known Boston house price data further demonstrates the potential of the proposed modeling procedures.

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