On the estimation of time-series quantiles using smoothed order statistics

The paper describes how smoothed order statistics can be used to estimate time-series quantiles in a stationary and non-stationary context. The approach proposed, termed a Smoothed Order Statistics quantile estimation (SOS) does not rely on assumptions about the distribution of the fitting errors of a time-series model. The approach is based on a recursive estimation mechanism and the order statistics obtained from a time-varying window-sample of the observations of a time-series. An illustrative example of the application of the model is presented along with experimental results based on its application to a sample of simulated and real time-series; a comparison is provided with three alternative quantile estimation procedures. The results show that the SOS quantiles compare favorably overall and are robust to changes in a time-series generating process.