Application of State-Space Model to Exact Time Series Forecasting

摘要

The forecasting method of future values of a time series from current and past values is of considerable practical interest and in important areas of application. In addition to calculating the best forecasts, it is also necessary to specify their accuracy, so that the risks associated with decisions based upon the forecasts may be calculated. Many empirical time series behave as though they had no fixed mean. They exhibit homogeneity in the sense that apart from local level, or perhaps local level and trend, one part of the series behaves much like any other part. Models that describe such homogeneous nonstationary behavior can be obtained by supposing some suitable difference of the process to be stationary. There has been much recent interest in the representation of ARIMA models in the statespace form, for purposes of forecasting, as well as for model specification and maximum likelihood estimation of parameters. In this paper we briefly consider the state-space form of an ARIMA model in this section and discuss its uses in exact finite sample forecasting.