Forecasting Stationary Processes

Abstract

An important goal of time series analysis is forecasting. In the following we will consider the problem of forecasting X _T+h , h > 0, given {X _T , …, X ₁} where {X _t } is a stationary stochastic process with known mean μ and known autocovariance function γ(h). In practical applications μ and γ are unknown so that we must replace these entities by their estimates. These estimates can be obtained directly from the data as explained in Sect. 4.2 or indirectly by first estimating an appropriate ARMA model (see Chap. 5) and then inferring the corresponding autocovariance function using one of the methods explained in Sect. 2.4 Thus the forecasting problem is inherently linked to the problem of identifying an appropriate ARMA model from the data (see Deistler and Neusser 2012).