Nonparametric estimates for conditional quantiles of time series

Jürgen Franke, Peter Mwita and Weining Wang

AStA Advances in Statistical Analysis, 2015, vol. 99, issue 1, 107-130

Abstract: We consider the problem of estimating the conditional quantile of a time series $$\{ Y_t\}$$ { Y t } at time $$t$$ t given covariates $$\varvec{X}_{t}$$ X t , where $$\varvec{X}_{t}$$ X t can be either exogenous variables or lagged variables of $${ Y_t}$$ Y t . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function, and we prove its asymptotic normality and uniform strong consistency. The performance of the estimate for light and heavy-tailed distributions of the innovations is evaluated by a simulation study. Finally, the technique is applied to estimate VaR of stocks in DAX, and its performance is compared with the existing standard methods using backtesting. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Kernel estimate; Quantile autoregression; Uniform consistency; Value at Risk (VaR) (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:alstar:v:99:y:2015:i:1:p:107-130

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DOI: 10.1007/s10182-014-0234-4

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