Do We Search on What We Tweet or Tweet on What We Search?

We investigate the properties of Twitter and search using a vector auto-regressive model. The VAR has two advantages. First it allows us to jointly decompose the time series into a stationary trend and random shocks. We investigate the relation between the shocks to gain further insights into the correlation between the shocks. Second, using the VAR model we perform a Granger causality test to see whether one variable Granger causes the other. An important implication of Granger causality is that the lagged versions of one variables can help predict the other variable. We tested our models on daily Twitter and search data. We found that Twitter and search can simultaneously Granger cause each other, Twitter Granger causes search, and neither search nor Twitter Granger causes the other. When Granger causality holds, the VAR model reduces the standard deviation of the out-of-sample prediction error by over 37% when compared to the best univariate model.