Estimation for ARMA Models

The determination of an appropriate ARMA(p, q) model to represent an observed stationary time series involves a number of inter-related problems. These include the choice of p and q (order selection), and estimation of the remaining parameters, i.e. the mean, the coefficients {φ _i , θ _j : i = 1,..., p; j = 1,..., q} and the white noise variance σ2, for given values of p and q. Goodness of fit of the model must also be checked and the estimation procedure repeated with different values of p and q. Final selection of the most appropriate model depends on a variety of goodness of fit tests, although it can be systematized to a large degree by use of criteria such as the AICC statistic discussed in Chapter 9.