Structural Breaks in AR Models

Abstract

Threshold autoregressions are a way of characterising structural changes associated with the degree of persistence of shocks in particular regimes. If the regime indicator is taken to be some function of yt itself the process is said to be ‘self-exciting’ leading to the acronym SETAR for self-exciting threshold autoregression. Another form of structural change is when there are distinct break points, leading to different regimes, at particular points of time. For example in the simplest case, regime 1 operates up to time T1 and regime 2 operates thereafter, where the regimes are distinguished in some way, for example by the degree of persistence in the autoregression (but other characteristics of the process such as the variance could change). The particular nature of the effect of the structural change could also vary from transient to permanent. There may be multiple change (or break) points, which may occur with certainty (probability of break = 1) or uncertainty (probability of break greater than 0 but less than 1) and the actual or potential breakpoints may or may not be known to the researcher. Transition may be abrupt, suddenly from one regime to another, or smooth, taking place gradually over several periods.