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Tuesday, June 21, 2005

How's this for a cool picture

Working on a project with a graduate student concerning a time series of financial data from second quarter 1987 through third quarter 2004 (I haven't yet figured out how to get the date labels on my STATA graph). Anyway, the upshot is that the fitted residuals display a strong positive autocorrelation (rho = 0.66) but also some cyclical tendencies.

As an example of how specification errors can change everything, the red curve fits a third order time process to the fitted residuals of our original model. The green line fits a fourth order time process. To the uninitiated, the third order process will have two inflection points, unfortunately the specification starts the process with the "wrong" slope. The fourth-order process has three inflection points and starts the process with the "correct" slope.

Also, notice the dramatically different slopes at the end of the time series. I wager the fourth-order estimation might overstate the slope (for out-of-sample forecasting) whereas the third-order estimation might understate the slope.

A cool picture, nonetheless.

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