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My professor gave me some data to study basic econometrics and I'm trying to develop the best model possible to fit financial returns of a company based on two different stock indexes (one from the local exchange and the other one is SP500), and USD exchange rates to my currency.

My data is monthly from 1995 to 2019.

I just kind of did the most basic thing fitting the stock returns using OLS and those three independent variables [all of them as log(1+variable) since they are percentual returns {not sure if this is the correct approach}].

Then I used chow breakpoint test and found 3 significant breakpoints in the model under 5% p-value. The first breakpoint was in 1999/01

Since I didn't know what else to do, I just discarded the data before the first breakpoint and ran the regression again. Now there are no breakpoints (didn't test every month but tested all the relevant ones based on qualitative data from our local economy).

Problem is that now my model has a 22% adjusted R^2, whereas if I used the same model but keeping the entire data (and therefore 3 significant breakpoints), adjusted R^2 is 36%.

Is there a better way to adjust these breakpoints without discarding data? Is a model useless if it has a very significant breakpoint in it? Is it useless if it has a R^2 of 22%?

None of the two options has heteroskedasticity and I corrected the significant autocorrelation up to 12 lags (testing using Breusch-Godfrey).

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I don't think you necessarily have to discard the entire time series from 1995 to 1999 prior to the first break point. There are several ways to handle break points, some simple, some more complicated. An easy way is to include a binomial dummy variable (0, 1) with a value of 1 for all the periods prior to the first break point. You could use another similar dummy variable to capture the time period from the 1st to the 2nd breakpoint. In essence, it will change your intercept and reflect that over those respective periods stock returns were at a different mean expected level than outside of those periods. You could also include interaction variables that will affect the slope or regression coefficients of your independent variable during the 1995 to 1999 period, and other similar periods between break points.

You could also explore polynomial regressions that can "turn" and better fit the shift in trend associated with the mentioned breakpoint.

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  • $\begingroup$ Thank you. Should this dummy variable interact with all of the independent variables? As a product? Y = X*Dummy + Intercept? Should it also interact with the dependent variable? Does it also have to be included in the model by itself or just the interactions? Sorry for so many questions... $\endgroup$ – Delta Jul 3 at 20:25
  • $\begingroup$ Those are good clarifications. First, add just the dummy in your model, and see how your model improves. The model may be ok after that first step. If necessary, move on to the next step that we both describe. I call it "interaction variables", you call it a dummy "that interact with the independent variables". That is the same thing. You don't need to create interaction variables for all Xs. You could do it with just the main X variable to begin with. But, never create such a variable with the Y dependent variable on the right side of your regression. That won't work. $\endgroup$ – Sympa Jul 4 at 15:31

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