Parameter stability over time

#1
Hi guys,

I am taking this introductory methods to statistics in a finance program and I need to do the following. Compare S&P500 vs TSX and analyse is the parameters change over time.

So let's say a model like this :

y = a0 + b1*x1 would be our base model.

Now, we were suggested to try this check if our parameters were time varying

y = a0 + b1*x1 + b2*x2 up to b12*x12 for all twelve months of the year. Were x1 is in fact x1*Indicator(data point is in month 1)

And to test wheter b1 = b2 = b3 = b4 = ... = b12.

I've researched many places, but were never able to find such a test. I've also looked into Chow's test or AQ tests, but these seem to only apply for two periods.

Has anyone had to deal with such a problem before ? If someone could point me in the right direction - suggest an alternative method or a test ?

Thank you!!