Nonstationarity, Unit Root and Structural Break

Abstract

The presence of unit roots in macroeconomic time series has received a major area of theoretical and applied research since the early 1980s. This chapter presents some issues regarding unit root tests and explores some of the implications for macroeconomic theory and policy by illustrating the evidence on the presence of unit roots in GDP series for India. Univariate model is used to examine the trend behaviour of the series. The popular trend model used in estimating growth rate suggests that the change of a series is the average change and is called the deterministic trend. If, on the other hand, a time series variable is generated through the random walk model, its change is purely stochastic and it exhibits stochastic trend. A series containing unit root is generated through the accumulation of shocks exhibiting stochastic trend. The TSP (nonstationary without unit root) and DSP (nonstationary with unit root) are indeed different and have different implications. It is important to check whether a time series can be better described as a TSP or a DSP. This could be done by testing for the presence of a unit root in the autoregressive representation of the series. Unit root tests are biased towards non-rejection of the unit root null when there are structural breaks in the series. This chapter takes care of structural break in carrying out unit root test. Seasonality brings many difficulties to model specification, estimation and inference. We have discussed the popular way to deseasonalisation of time series data. Identification of trend and cycle of a macroeconomic variable is often an important empirical issue in macroeconomic analysis. HP filter is a popular method of decomposition of a time series.