Estimation of ARMA Models

Abstract

The specification and estimation of an ARMA(p,q) model for a given realization involves several intermingled steps. First one must determine the orders p and q. Given the orders one can then estimate the parameters ϕ _j , $\theta _{j}$ and $\sigma ^{2}$. Finally, the model has to pass several robustness checks in order to be accepted as a valid model. These checks may involve tests of parameter constancy, forecasting performance or tests for the inclusion of additional exogenous variables. This is usually an iterative process in which several models are examined. It is rarely the case that one model imposes itself. All too often, one is confronted in the modeling process with several trade-offs, like simple versus complex models or data fit versus forecasting performance. Finding the right balance among the different dimensions therefore requires some judgement based on experience.