Detecting trends in twitter time series

Detecting underlying trends in time series is important in many settings, such as market analysis (stocks, social media coverage) and system monitoring (production facilities, networks). Although many properties of the trends are common across different domains, others are domain-specific. In particular, modelling human activities such as their behaviour on social media, often leads to sharply defined events separated by periods without events. This paper is motivated by time series representing the number of tweets per day addressed to a specific Twitter user. Such time series are characterized by the combination of (1) an underlying trend, (2) concentrated bursts of activity that can be arbitrarily large, often attributable to an event, e.g., a tweet that goes viral or a real-world event, and (3) random fluctuations/noise. We present a new probabilistic model that accurately models such time series in terms of peaks on top of a piece-wise exponential trend. Fitting this model can be done by solving an efficient convex optimization problem. As an empirical validation of the approach, we illustrate how this model performs on a set of Twitter time series, each one addressing a particular music artist, which we manually annotated with events as a reference.