Analysis of the behaviour of the quarterly inflation in Colombia under changes of regime: evidence through Hamilton's "switching" model

We study the evolution of quarterly inflation in Colombia between 1954 and 1966, using Hamilton's (1998) methodology. We introduce some concepts related to this method, which adds regime changes into traditional time series ARIMA models. Generally, this method allows the estimation of ARIMA models with variable parameters and variances. In this case, such changes in the inflation model are assumed to be associated with different regimes in which inflation varies in its level or in its variability. This modeling allows for the assesment of the regimes over time (for instance, two regimes: high inflation and low inflation) according to their average duration time and their associated probabilities, that is, the likelihoo of being in a particular regime at a given point in time.  The computed transition probabilities let us conclude, for example, that being in a moderate quarterly inflation regime, the probability of staying in it is very high (0.94), while changing to a high inflation regime has a probability of 0.05, which is five times higher that the one computed for the transition from moderate to low (0.01). Aditionally, the maximum probability of staying in a single reime is obtained in the moderate-inflation-and-variability regime.