Testing Whether Volume or Returns Lead with Granger Causality
Summary
The document asks how to interpret cross-correlations between S&P 500 trading volume and returns across positive and negative lags, whether volume growth is preferable to raw volume, and how to assess significance. It provides example correlation values but does not explain how to calculate lag-specific p-values or choose a volume transformation.
The answer warns that a cross-correlation pattern alone does not establish which series leads or predicts the other. It recommends fitting two time-series models: one for volume using past volume and returns, and another for returns using past returns and volume. Testing the lagged terms in each direction is the Granger-causality procedure, which assesses incremental predictive information. The answer reports a past finding that returns influenced volume but volume did not influence returns; this is an anecdotal result, not evidence established by the example or a general law.
Key ideas
- Cross-correlations alone do not determine predictive direction between volume and returns.
- Granger-causality tests compare models that include each series' own lags and the other series' lags.
- Testing both model directions helps assess whether lagged volume or returns adds predictive information.
- The reported finding about returns preceding volume is anecdotal and should not be generalized.
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Full text
# volume-returns cross correlation interpretation # volume-returns cross correlation interpretation 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 by Alex C (score 2) https://quant.stackexchange.com/a/20701 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.
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