Interval forecasting

Abstract

In this paper we explore techniques for obtaining interval forecasts based on estimated time-series models for processes which may exhibit autoregressive conditional heteroskedasticity (ARCH). To deal with the available variety of possible interval forecasts, we propose a method for combining these forecasts based on quantile regression techniques. Our approach is practical rather than theoretical, with attention focused directly on obtaining interval forecasts for two U.S. time series: a measure of unemployment and a Treasury bill rate. We evaluate the performance of our procedures using a variety of diagnostics. We find interval estimates which perform reasonably well, judged by both in-sample and out-of-sample criteria. Our experience suggests that a certain amount of care is required in order to obtain useful forecasts.