Time Series Modelling and Interpretation

SUMMARY By considering the model generating the sum of two or more series, it is shown that the mixed ARMA model is the one most likely to occur. As most economic series are both aggregates and are measured with error it follows that such mixed models will often be found in practice. If such a model is found, the possibility of resolving the series into simple components is considered both theoretically and for simulated data. 1. INrRODUCTION THE recent publication of the book by Box and Jenkins has greatly increased interest by time series analysts and econometricians in more complicated, even if more parsimonious, time series models. However, the intuitive interpretation of the models that arise is not always simple and an applied research worker may well ask how such a model could have arisen in practice. In this paper, the possibility that a complicated looking model could have arisen from a simpler situation is explored and some suggestions made about the possible interpreta- tion of some models that appear to arise in practice. The only series to be considered are those with zero means and generated by models with time-invariant parameters. Thus, possibly after an appropriate linear transformation, the series will be taken to be second-order stationary. Let Xi be such a series, so that EX =O, all t.