Assessing Tail Risk Via  a Generalized Conditional Autoregressive Expectile Model

Abstract

This paper 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 conditional autoregressive Value-at-Risk by regression quantiles 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 for estimating the relevant parameters, and a heteroskedasticity and autocorrelation consistent 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 applications to real data are conducted to illustrate that the proposed methodology is practically useful. Particularly, our empirical study demonstrates that the tail risk characterized by the proposed model achieves a better performance, especially in the period of the Covid-19 epidemic.

Keywords: Conditional autoregressive expectile model, COVID-19 pandemic, Dynamic testing, Expectile modeling, Quasi-maximum likelihood estimation, Tail risk.