Multivariate Time Series Approach to Cointegration
This chapter considers the case where there are a number of non-stationary series driven by common processes. It was shown in the previous chapter that the underlying behaviour of time series may arise from a range of different time series processes. Time series models separate into autoregressive processes that have long-term dependence on past values and moving average processes that are dynamic but limited in terms of the way they project back in time. In the previous chapter the issue of non-stationarity was addressed in a way that was predominantly autoregressive. That is, stationarity testing via the comparison of a difference stationary process under the null with a stationary autoregressive process of higher order under the alternative. The technique is extended to consider the extent to which the behaviour of the discrepancy between two series is stationary or not. In the context of single equations, a Dickey-Fuller test can be used to determine whether such series are related; when they are this is called cointegration. When it comes to analyzing more than one series then the nature of the time series process driving the data becomes more complicated and the number of combinations of non-stationary series that are feasible increases.
KeywordsUnit Root Purchasing Power Parity Trace Test Vector Error Correction Model Cointegrating Vector
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