I'd like to calculate how much my systems are correlated to each other. Suggestions how to better do this? One method that comes to mind is to calculate the Pearson's Correlation Coefficient of daily or weekly returns. Disadvantage: if system1 is higher frequency, but also has similar trades as the system2 it will appear lowly correlated (and it is, but I'd like to also know that system2 trades are almost mimicked by system1). I'd like to also calculate the correlations of trade opening/closing times/prices, but I'm unsure how to better do this. Thank you
rank correlation does not take into account the frequency. but if you're using daily & weekly returns why wouldn't pearson work for you
Why not just count the dots? Figure out what timeframe interests you for correlation studies; in my own case, I'm interested in monthly correlation. Make a scatterplot of System A monthly returns on the horizontal axis, and system B monthly returns on the vertical axis. Now count the dots in each of the four quadrants: sysA pos, sysB pos sysA neg, sysB pos sysA neg, sysB neg sysA pos, sysB pos Quadrants 2 and 4 are "good" (returns of opposite sign), Quadrant 3 is "especially bad" (both returns negative), and Quadrant 1 is "ho hum" (both returns positive). Figure out what's important to you and make a "Important2Me Ratio", perhaps (Count(3)/Count(1+2+3+4)) or possibly (Count(2+4)/Count(1+3)). Use your imagination.
Pearson's Correl. C. should be ok for general purpose. I'd like to also calculate correlation taking into account position opening and closing time. Rank C. doesn't seems to take into account time. For example, if both systems have similar daily returns, but one trades (very short term) mostly in mornings and other in evenings then they should not be highly correlated. If one system holds it's trades just a little longer till the next day then the Pearson's correlation of daily returns could be much different, resulting in low correlation, but it should be high. Good idea, I think: calculate correlation only for trades whose opening - closing times overlap (+option: by minimum X%). If one system overlaps multiple trades then the returns should be summed for these trades (make it like 1 trade). In result would be obtained 2 columns of returns with the same length, regardless of trading frequency differences, for calculating Pearson's C. Thus would be taked into account time and returns, and calculations not restricted to fixed time (daily/weekly/monthly) intervals. Do you like it?