Chapter 9. Univariate time series analysis
In the previous chapter we discussed regression models with lagged explanatory variables. Remember that they assume that the dependent variable, Yt, depends on an explanatory variable, Xt, and lags of the explanatory variable, Xt−1, ..., Xt–q. Such models are a useful first step in understanding important concepts in time series analysis.
In many cases, distributed lag models can be used without any problems; however, they can be misleading in cases where either: (1) the dependent variable Yt depends on lags of the dependent variable as well, possibly, as Xt, Xt−1, ..., Xt–q; or (2) the variables are nonstationary.
Accordingly, in this chapter and the next, we develop tools for dealing with both issues and define what we mean by "nonstationary". To simplify the analysis, in this chapter we ignore X, and focus solely on Y. In statistical jargon, we will concentrate on univariate time series methods. As the name suggests, these relate to one variable or, in the jargon of statistics, one series (e.g. Y = a stock price index). As we shall see, the properties of individual series are often important in their own right (e.g. as relating to market efficiency). Furthermore, it is often important to understand the properties of each individual series before proceeding to regression modeling involving several series.
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