This PhD thesis consists of three related chapters; each contributes to the study of inflation dynamics by examining different issues that have previously been raised in the relevant literature. In particular, the first chapter is concerned with the nature of different changes that have taken place in the conditional mean and variance of inflation. To shed light on this question, an iterative structural break testing methodology is developed which allows the possibility of distinct changes in the conditional mean and variance components by iterating tests between them, with outliers also identified in relation to regimes. This methodology is applied to models that link domestic and foreign inflation, and uncovers a positive and strengthening contemporaneous relationship between domestic and foreign inflation, adding to the literature that provides evidence of increasing globalization of inflation. The second chapter sheds further light on the nature of the globalization of inflation by separating core, energy and food components of aggregate inflation, analyzing changes in the international links in these separate components. Comparison with the aggregate inflation reveals that the overall globalization is driven largely by the mean levels of core inflation being very similar across countries, especially from the early 1990s. Further, an increased synchronization of short-run movements in non-core (energy and food) components contribute to the overall globalization effect, but such short-run synchronization is less evident in core inflation. The first and second chapters show that structural breaks either in the conditional mean or variance parameters of inflation are a common feature. Therefore, the third chapter focuses on the problem of forecasting in the presence of structural breaks. Specifically, chapter 3 proposes a forecast method which allows for break date uncertainty by employing a confidence interval estimate of the break date. A Monte Carlo simulation study and an empirical application to inflation time series demonstrate the usefulness of this approach. This chapter also proposes an algorithm that re-orders time series data based on the similarity of regimes. It is shown that such re-ordering can improve forecast accuracy when estimation exploits the additional information provided by the re-ordered series. These improvements are significant when there are multiple breaks which have the form of reverting coefficients.