# How to deal with zeroes in returns?

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?

• Usually the choice of when not to trade is also part of a strategy, so zeros are also meaningful imho and should not be discounted for. Or is the choice of whether to trade or not exhogenous? I would also suggest looking at the literature on performance attribution to better frame your problem. Jul 9, 2013 at 9:38
• Would you rate the output of a regression or correlation study between time series A(0.5%, NA, NA, -0.3%, NA, 0.1%, NA, 1%, NA, NA) and time series B(1%, 0.5%, NA, -1.2%, NA, NA, 0.5%, 0.4%, -0.2%, -0.1%) more highly than the outcome if you aggregated into weekly bins (NA = no trading that day, numerically = 0%)? I highly doubt it. You basically assume a perfect correlation between TS A and TS B on days where both strategies did not generate any returns, which completely falsifies your statistical results. Thats all I like to add to this topic. Jul 10, 2013 at 0:39