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Stock return cycles

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Hello,
I am sort of new to stata and as a student project I want to show the 4 year cycles of weekly S&P 500 index return (presidential cycles) now the model that I thought I can use is R = b + b1L.R + b2(y) + b3(D) which y is a dummy variable that takes 1 for the first half of presidency and zero for the next half, and D is a dummy for the parties. now the problem is that y is not being significant, Is my model a wrong one? or the problem is the dummy variable?

also I want to show the cycles by a graph using trigonometric functions but I do not know how should I shape my function so it will show the cycles of the returns.

Thank you
Ina

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