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UNDERSTANDING UNIVARIATE PROCESSES
The first class of time series models we investigate are univariate models called ARMA (autoregressive moving average) models. In the Appendix, we show how to gain significant insights into the dynamics of difference equations –the basis of time series econometrics – by simply solving them and plotting solutions over time. By stipulating a model based on our verbal theory and deriving its solution, we can note the conditions under which the processes we model return to equilibrium.
In the series of models discussed in this chapter, we turn this procedure round. We begin by studying the generic forms of patterns that could be created by particular datasets. We then analyze the data to see what dynamics are present in the data-generating process, which induce the underlying structure of the data. As a modeling process, ARMA models were perfected by Box and Jenkins (1970), who were attempting to come up with a better way than extrapolation or smoothing to predict the behavior of systems. Indeed, their method of examining the structures in a time series, filtering them from the data, and leaving a pure stochastic series improved predictive (i.e., forecasting)ability. Box-Jenkins modeling became quite popular, and as Kennedy notes,“for years the Box-Jenkins methodology was synonymous with time series analysis” (Kennedy, 2008, 297).
The intuition behind Box-Jenkins modeling is straightforward. Time series data redundent can be composed of multiple temporal processes.