## Quantile Sieve Estimates for Time Series

• We consider the problem of estimating the conditional quantile of a time series at time $$t$$ given observations of the same and perhaps other time series available at time $$t-1$$. We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not require the specification of the innovation law. We prove consistency of those estimates and illustrate their good performance for light- and heavy-tailed distributions of the innovations with a small simulation study. As an economic application, we use the estimates for calculating the value at risk of some stock price series.

$Rev: 13581$