The theory of difference equations underlies all of the time-series methods employed in later chapters of this text. It is fair to say that time-series econometrics is concerned with the estimation of difference equations containing stochastic components. The traditional use of time-series analysis was to forecast the time path of a variable. Uncovering the dynamic path of a series improves forecasts since the predictable components of the series can be extrapolated into the future. The growing interest in economic dynamics has given a new emphasis to time-series econometrics. Stochastic difference equations arise, quite naturally, from dynamic economic models. Appropriately estimated equations can be used for the interpretation of economic data and for hypothesis testing.

This introductory chapter has three aims:

- Explain how stochastic difference equations can be used for forecasting, and illustrate how such equations can arise from familiar economic models. The chapter is not meant to be a treatise on the theory of difference equations; only those techniques essential to the appropriate estimation of
*linear*time-series models are presented. This chapter focuses on single equation models; multivariate models are considered in Chapters 5 and 6. - Explain what it means to
*solve*a difference equation. The solution will determine whether ...

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