ABSTRACT
From the study of unit roots in Chapter 2 we have learned the distinctive characteristics of stationary and non-stationary time series. Nevertheless, although one of the main concerns in Chapter 2 was whether a time series has a unit root or not, there was no further examination regarding different properties of nonstationary time series – whether they are pure random walks or possess serial correlation. Furthermore, what is the serial correlation structure of a time series, if it is not a pure random walk? There are generally two categories of non-pure random walk time series. If the time series can be viewed as a combination of a pure random walk process and a stationary process with serial correlation, the long-run effect would be smaller than that of a pure random walk, and the time series would contain unit roots due to its non-stationary component. If there is no stationary component in the time series which is not a pure random walk either, then the first difference of the time series is a stationary process with serial correlation, and the long-run effect would be larger than that of a pure random walk. There would be, to a certain degree, a mean-reverting tendency in the former category due to its stationary component; and there would be a compounding effect in the latter. The interest in this chapter is then centred on the characteristics and behaviour of time series associated with their correlation structure, and the relative contribution and importance of the two components: the trend which is a pure random walk, and the cycle (after taking the first difference in the latter category) which is a stationary process involving serial correlation in the long run. How persistent a time series is depends on the relative contribution of these two components.
