This article proposes the asymmetric linear double autoregression, which jointly models conditional mean and heteroscedasticity characterized by effects. A sufficient condition is established for existence of a strictly stationary solution. With quasi-maximum likelihood estimation (QMLE) procedure introduced, Bayesian information criterion (BIC) its modified version are proposed model selection...

Parametric copulae are shown to be an attractive device for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed estimators are established, leading to a general framework for inference and model specificat...

The problem of tting continuous time autoregressions linear and non linear to closely and regularly spaced data is considered For the linear case Jones and Bergstrom used state space representations to compute exact maximum likelihood estimators and Phillips did so by tting an appropriate discrete time ARMA process to the data In this paper we use exact conditional maximum likelihood estimators...

We congratulate Koenker and Xiao on their interesting and important contribution to the quantile autoregression (QAR). The paper provides a comprehensive overview on the QAR model, from probabilistic aspects, to model identification, statistical inferences, and empirical applications. The attempt to integrate the quantile regression and the QAR process is intriguing. It demonstrates surprisingl...

We develop a new quantile autoregression neural network (QARNN) model based on an artificial neural network architecture. The proposed QARNN model is flexible and can be used to explore potential nonlinear relationships among quantiles in time series data. By optimizing an approximate error function and standard gradient based optimization algorithms, QARNN outputs conditional quantile function...