ABSTRACT
In a statistical model, any value to be estimated must be either a constant, or a function of constant parameters. This chapter discusses how to compute the Gaussian likelihood for three specifications. First, a time-varying parameter regression model, where the coefficients are allowed to change according to a given law of motion. Second, a periodic VARMAX (PVARMAX) model in which the parameters may change over different seasons. Third, a general dynamic model with conditionally heteroscedastic errors, where the traditional assumption of homoscedasticity is relaxed by parameterizing the conditional variance of the disturbances as a function of its own past. A periodic PVARMAX model extends the standard VARMAX framework by allowing the model parameters to change over different seasons. The PVARMAX model assumes that the observations in each of the seasons can be described using a different model. The stationarity and invertibility conditions of a periodic process often are characterized by its equivalent representation VARMA with constant parameters.
