ABSTRACT

In this chapter, we discuss techniques for forecasting the future behavior of a time series, given present and past values. ARMA and ARUMA models are popular tools for obtaining such forecasts. Forecasts found using ARMA and ARUMA models differ from forecasts based on curve fitting in a fundamental way. Given a realization, such as the sunspot data in Figure 1.23a, one might forecast into the future based on a mathematical curve fit to the data, that is, based on the underlying assumption that future behavior follows some deterministic path with only random fluctuations. However, for data, such as the sunspot data, it is unlikely that the use of such a deterministic function for forecasting is a reasonable approach. On the other hand, the ARMA and ARUMA forecasting techniques to be discussed in this chapter are based on the assumption that the transition to the future is guided by its correlation to the past. When there is no physical model for connecting the past with the future, the correlation-based approach seems reasonable.