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Maximum Likelihood Estimation of a Poissonian Count Rate Function for the Followers of a Twitter Account Making Directional Forecasts of the Stock Market

We derive expressions of use in the maximum likelihood estimation of a parameterized growth rate where the quantity growing is a Poissonian count rate parameterized in such a manner as to make it suitable to measure the number of Twitter accounts following an account that makes directional forecasts of the stock market. We use these expressions to estimate the model for data collected for a forecasting system publicised during the Spring of 2009. We find a positive correlation between success and an increase in the number of followers, and use the maximum likelihood ratio test to reject the null hypothesis (of no correlation) with a confidence of better than 95%.