Suppose there are two time series that I want to analyze and compare. However, many, or most, of the data are zeroes for some reason. For example, consider a pair of intraday trading returns time series. In most days, the trading strategies don't trade at all, so most of the returns are zeroes.
How can I understand their correlation? I suppose I can just keep all the zeroes, and use the raw data to calculate the correlation. Any other thoughts?
If I want to identify the time period when the returns are different substantially, I must think about the zeroes carefully. For example, time period A gives 0.2% in each of 20 days out of 100 days, but time period B gives 0.1% in 40 days out of 100 days. How do I compare and determine them?