I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a significant correlation.
Suppose the social media is represented by a numeric variable “sm”. All the series I'm working with are weakly stationary. The distribution of the price data is as one would expect: normal with fat tails. The basic stats of a typical set of “sm” observations, however, are:
nobs 240.000000 NAs 0.000000 Minimum 0.000000 Maximum 725.000000 1. Quartile 52.000000 3. Quartile 119.250000 Mean 99.245833 Median 82.000000 Sum 23819.000000 SE Mean 5.573789 LCL Mean 88.265806 UCL Mean 110.225861 Variance 7456.110861 Stdev 86.348775 Skewness 3.428570 Kurtosis 17.793173
For price vs. “sm” contemporaneous, lag(1), and sometimes lag(2), the correlation is positive but small, about what I would expect. Because the distribution is not normal, I'm wondering if the cross-correlation matrix (ccf() function in R) provides a reasonable assessment of cross correlation (assuming linearity). I welcome any comments regarding how to interpret these results as well as any comments on best-practices.