volume-returns cross correlation interpretation

Question

I want to find the relationship between volume and price returns in the S&P500. My first thought was to run a cross correlation in order to find who leads and who lags in the relation. It´s my first time running cross correlations so I have three basic questions:

1) Using volume as X and returns as Y in a CCF I obtain the following results using SPSS.

• Lag -2 : 0.103
• Lag -1 : -0.131
• Lag 0 : -0.113
• Lag 1 : -0.022

• Lag 2 : -0.008

  Under these results, who lead and who lags? If I obtained higher values in the negative lags is correct to assume that volume (x) leads returns (y)?

2) Should I consider not the trading volume, but rather the volume growth rate? (the difference in logarithm between two consecutive values of trading volume)

3) Any idea for testing the significance level and p-value for each lag?

Thanks!

Answer 1

The direction of the relationship cannot be determined from just this information (a set of correlation coefficients). You need to estimate a model of volume based on lagged volume and lagged returns, checking if the lagged return terms are significant. Then as a second step you estimate a model of returns that includes past returns and past volumes and see if the volume terms are statistically significant. This is the procedure known as Granger causality testing.

It will show whether past information about volume is helpful in predicting returns and vice versa. Having done this exercise many years ago I found that returns have an influence on volume, but not vice versa.