Univariate time-series models are a class of specifications where one attempts to model and to predict financial variables using only information contained in their own past values and current and possibly past values of an error term. This practice can be contrasted with structural models, which are multivariate in nature and attempt to explain changes in a variable by reference to the movements in the current or past values of other (explanatory) variables. Time-series models are usually a-theoretical, implying that their construction and use is not based upon any underlying theoretical model of the behaviour of a variable. Instead, time-series models are an attempt to capture empirically relevant features of the observed data that may have arisen from a variety of different (but unspecified) structural models.

An important class of time-series models is the family of AutoRegressive Moving Average (ARMA) models, usually associated with Box and Jenkins (1976). Time-series models may be useful when a structural model is inappropriate. For example, suppose that there is some variable yt whose movements a researcher wishes to explain. It may be that the variables thought to drive movements of yt are not observable or not measurable, or that these forcing variables are measured at a lower frequency of observation than yt. Additionally, as will be examined later in this chapter, structural models are often not useful for out-of-sample forecasting. These observations motivate the consideration of pure time-series models, which are the focus of this chapter.