QUESTION: How should I analyze the statistical significance of the difference between two buy-and-hold strategies (or the relative performance) when the samples are not independent?
Background:
I want to compare the performance of two stock classes from a certain company (e.g. Class A shares and Class B shares) after a stock-split. I want to analyze how this stock-split affects the return of Class B shares relative to Class A shares.
I want to analyze the performance difference over a long time span, hence an event-study is inappropriate. Therefore, I want to use a buy-and-hold strategy. Simple analyzing the statistical differences by conducting a t-test or F-test is not appropriate as both samples are not independent. Hence, I want to analyze the difference in prices between the buy-and-hold strategy holding Class A shares (P1) and the buy-and-hold strategy holding Class B (P2) shares, i.e.:
c = P1 - P2, where c is a constant (e.g. 1)
However, as both shares increase in value over the years the variance increases and I'm left with heteroskedasticity. Thus, analyzing whether the constant is statistically significant also does not make sense. Can someone tell me how I should analyze the statistical significance of the difference between two buy and hold strategies (or the relative performance)? For example, how can I tell whether P2 is higher than P1 and statistically significant?
P.S I do not want to analyze returns as the returns only differ on the days surrounding the stock-split, hence the differences in returns are negligible over longer time periods. On the other hand, differences in prices can vary significantly (my hypothesis) as differences in returns accumulate.