I'm thinking of running a time series on stock prices and the affect demographic variables may have on them. This would include testing how the size of particular age groups (i.e., 20-39, 40-64, 65+) may affect the price-to-dividend ratio (i.e., stock prices). I was hoping someone might have some advice on the steps to complete.

I'm thinking the steps should be:

- Dickey-Fuller for unit root test
- test for cointegration (e.g. Johanssen??)
- structural change (Chow test, or Gregory and Hansen?) for potential rapid increase in 40-64 age group in 1990s.

Should I be testing with anything else, e.g., Whites, Jarque-Bera, ADF, Ramsay's RESET test?

This is my first crack at econometrics and a time series, therefore naive and unknowledgable, would be delighted to hear how someone more experience would tackle this.

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#### Best Answer

Unit root test: ADF, Perron (lookup dfuller and pperron in STATA)

If your data is not stationary, you will have to take steps to make it stationary (such as for example taking first difference).

Cointegration

You can do Johanssen, but the test can be sometimes tricky, because it doesn't allow for any gaps in the data. The alternative to that is doing it by regression.

In STATA, this would be:

regress y x //regression of the variables

predict resid, residuals // creates variable resid, the residuals of the regression dfuller resid, lags(15) // ADF test to see if the residuals are stationary.

Structural change

With Chow test, you need to know what the break date is, then you test for it. If you don't know when the change is, I suggest the QLR test for coefficient stability.

Are you doing a VAR/SVAR? If so, you also need the lag selection criteria, so that you know how many past time periods affect the current period. For this, lookup the varsoc command in stata (for this, you need you series to be stationary based on the tests in step 1, because only stationary series can be transformed into a moving average processes).

After you select your lag, you can see the results of the VAR/SVAR model (command varbasic in STATA).

If you want to test Granger-causality, look up vargranger.

The remaining tests depend on the specifics of your data. You could test autocorrelation using the estat dwatson, estat bgodfrey in STATA if you need to (or even if you don't need to just to see).

Also, you should note that if you find a structural break (using Chow test or QLR), it is common to repeat the analysis on the two time periods (before the break and after the break), to identify what the effects were before and after the structural change.

I recommend you check out this link http://www.princeton.edu/~otorres/TS101.pdf.

Good luck!