Non-stationary Time Series: Differencing and ARIMA Modelling

Abstract

The class of ARMA models developed in the previous chapter relies on the assumption that the underlying process is weakly stationary, thus implying that the mean, variance and autocovariances of the process are invariant under time shifts. As we have seen, this restricts the mean and variance to be constant and requires the autocovariances to depend only on the time lag. Many economic and financial time series, however, are certainly not stationary and, in particular, have a tendency to exhibit time-changing means and/or variances.