Advances in Box‐Jenkins modeling: 1. Model construction

Abstract

Box‐Jenkins modeling of time series data can be improved and simplified by adhering to contemporary modeling procedures. This paper gives the theory and techniques of the application of many recent advances that have been made at the identification, estimation, and diagnostic check stages of model development. The inverse autocorrelation function and the inverse partial autocorrelation function are demonstrated to be useful identification tools for both nonseasonal and seasonal models. Parameters can be estimated more efficiently by employing the modified sum of squares technique. At the estimation stage it is also possible to obtain a maximum likelihood estimate for a Box‐Cox power transformation. The Akaike information criterion is introduced to formalize mathematically the concept of model parsimony. When checking for model adequacy, knowing the distribution of the residual autocorrelation allows for a sensitive test for residual whiteness. Diagnostic checks are given for verifying the assumption of homoscedasticity of the model residuals. In practice, heteroscedasticity and nonnormality of the residuals can often be removed by a Box‐Cox transformation.