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In empirical financial analyses, is there a difference when examining stock price changes and stock price returns? Would a model with a response variable price changes tell a different story than price returns? Thank you in advance.

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Given a time series $\{y_t\}=(y_1,\dots,y_t)$, you can obtain both price changes $d_t:=y_{t}-y_{t-1}$ and price returns $r_t:=\frac{y_{t}-y_{t-1}}{y_{t-1}}$. For any model of $d_t$, you can write an equivalent model of $r_t$ by dividing both sides of the model's equation by $y_{t-1}$. For any model of $r_t$, you can write an equivalent model of $d_t$ by multiplying both sides by $y_{t-1}$. Therefore, there does not have to be a difference. Consequently, any difference between the models for $d_t$ and $r_t$ is your choice rather than a necessity. And if the models are telling different stories, it is by the modeller's choice, not by necessity.

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