38 – Multivariate Time Series, Dimension Reduction, and Miscellaneous Topics
A New Method for Interval Forecasting of Autoregressive Time Series with a Root Near 1
Staffan Fredricsson
The Scale Factor (SF) method is presented, to improve the accuracy of multiple step ahead interval forecasts for autoregressive time series with a trend and a root near unity. For this case, the inadequacy of established regression-style methods for model fitting were broadly exposed in the seminal 1982 paper by Nelson and Plosser. When the characteristic polynomial has a root near 1, bias with respect to the parameter estimates as well as the prediction interval width present great problems. The parameter estimate bias has since been addressed by several authors, and the SF method adopts a medianunbiased approach. The focus in this paper is on the prediction interval width problem. A base width is obtained using GLS and then de-biased using a multiplicative scale factor, determined using simulation and numerical optimization techniques. The substantial benefits of the SF method compared to alternatives, are first demonstrated using simulated processes and actual coverage probability accuracy. In addition, the SF method and alternatives are applied to the original Nelson-Plosser AR(p) data set, with forecasts compared to actual data through 2010.
