Kernel Conditional Quantile Estimation for Stationary Processes with Application to Conditional Value-at-Risk
Posted: 10 Jul 2008
Date Written: Spring 2008
The paper considers kernel estimation of conditional quantiles for both short-range and long-range-dependent processes. Under mild regularity conditions, we obtain Bahadur representations and central limit theorems for kernel quantile estimates of those processes. Our theory is applicable to many price processes of assets in finance. In particular, we present an asymptotic theory for kernel estimates of the value-at-risk (VaR) of the market value of an asset conditional on the historical information or a state process. The results are assessed based on a small simulation and are applied to AT&T monthly returns.
Keywords: asymptotic expansion, Bahadur representation, causal process, central limit theorem, kernel estimation, long-range dependence, quantile estimation, short-range dependence, value-at-risk
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