This part consists of five chapters that consider various extensions of the basic models discussed in part II.

Chapter 8 discusses the Bayesian approach to unit roots and cointegration. In chapters 4 and 7 we mentioned the problems created by uncertain unit roots. The Bayesian approach where the posterior probabilities of a unit root and stationarity are taken into account, is a natural solution to this problem. The chapter discusses the different priors and their merits and defects in the analysis of unit roots and cointegration. It also discusses the Bayesian model selection approach.

Chapter 9 is on fractional unit roots and fractional cointegration. These models are alternative ways of modeling persistence in economic time series. The chapter discusses different estimation methods and the empirical relevance of fractional integration.

Chapter 10 is on the bootstrap approach. Almost all the literature on unit roots and cointegration is asymptotic. However, it has also been found that the estimators suggested are biased, and the tests exhibit substantial size distortions. The bootstrap method helps in correcting these two problems. This chapter discusses the different methods of bootstrap data generation and bootstrap-based tests.

Chapter 11 is on cointegrated system with I(2) variables. It has been observed that some variables like prices are more appropriately characterized as I(2) processes rather than I(1) processes. This chapter discusses problems of analysis with I(2) variables and mixtures of I(1) and I(2) variables.