Best way to calculate correlation of stock price movements I'm looking at correlations between stock price movements.
Most recommendations are to use Pearson correlation which, iiuc, requires normality, but then they proceed to use to actual prices for the period in question and calculate differences wrt the average price.
I can though imagine scenarios where the average price is perhaps not a good measure of the price over the period.  Does this not make the actual price compared to the average a questionable metric to use, and perhaps not normal?
If so, would not the percentage price movement [1] each day (or other period) be a more accurate input to calculate correlation?
[1] Or maybe the log?  I see this being referred to as more normal, though I admit I really don't understand the reasons.

It's well known that prices are not normally distributed.  Thus, I would first transform prices into either "simple returns" defined as $r_t = (P_t - P_{t-1})/P_{t-1}$ or "log-returns", defined as $r_t = \log(P_t) - \log(P_{t-1})$, where $t$ is the time of the price, like day, week, month, minute, etc.
Then run correlation between the different assets.
Correlation is used very often in quantitative finance, as is covariance -- as long as the denominating currency is the same for all the assets.  Correlation and auto-correlation change with time as well, and this refers to the stationarity vs non-stationarity of a times-series.  There are also seasonality issues, among other characteristics which are addressed.
