| Sumario: | This article proposes a generalized conditional autoregressive expectile model, including autoregressive components in assessing tail risk, which can be treated as an infinite version of the conditional autoregressive expectile model proposed by Kuan, Yeh, and Hsu (2009) and can be implemented as a vehicle for estimating the CAViaR model proposed in Engle and Manganelli (2004) and studied by Xiao and Koenker (2009). Due to the unobservable latent components in the proposed model, the quasi-maximum likelihood estimation method is suggested and a HAC covariance matrix estimator is proposed. Furthermore, a dynamic expectile test is proposed for both in-sample model adequacy evaluation and out-of-sample forecasting for comparison purposes. Finally, Monte Carlo simulations and a real example are conducted to illustrate that the proposed methodology is practically useful. Our empirical study demonstrates that the tail risk characterized by the proposed model achieves a better performance in the period of the Covid-19 epidemic.
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