Analysis of Financial Data

Chapter 10. Regression with time series variables

In regression analysis, researchers are typically interested in measuring the effect of an explanatory variable or variables on a dependent variable. As mentioned in Chapter 8, this goal is complicated when the researcher uses time series data since an explanatory variable may influence a dependent variable with a time lag. This often necessitates the inclusion of lags of the explanatory variable in the regression. Furthermore, as discussed in Chapter 9, the dependent variable may be correlated with lags of itself, suggesting that lags of the dependent variable should also be included in the regression.

As we shall see, there are also several theories in finance which imply such a regression model. This is not a book which derives financial theories to motivate our regression models. However, to give you a flavor of the kind of things financial researchers do with time series data, it is useful briefly to mention a few classic articles in finance and the time series data sets they use. An influential paper by Campbell and Ahmer called "What moves the stock and bond markets? A variance decomposition for long-term asset returns"^[56] used American data on excess stock returns, various interest rates, the yield spread (defined using the difference between long- and short-term interest rates) and the dividend-price ratio. Another influential paper by Lettau and Ludvigson called "Consumption, aggregate wealth and expected stock returns" ...