Estimation of T- period’s ahead extreme quantile autoregression function

Abstract

This paper considers the estimation of extreme quantile autoregression function by using a parametric model. We combine direct estimation of quantiles in the middle region with that of extreme parts using the model and results from extreme value theory (EVT). The volatility used to scale the residuals is estimated indirectly, without estimating conditional mean, using the conditional quantile (CQ) range. The estimators are found to be consistent. A small simulation study carried out shows that the estimator of the volatility function converges to the true function over a range of distributional errors. Finally, the T-periods ahead extreme quantile autoregression function is given.