Correlation Network Evolution Using Mean Reversion Autoregression

In this paper, we present a new method for modeling time-evolving correlation networks, using a Mean Reversion Autoregressive Model, and apply this to stock market data. The work is motivated by the assumption that the price and return of a stock eventually regresses back towards their mean or average. This allows us to model the stock correlation time-series as an autoregressive process with a mean reversion term. Traditionally, the mean is computed as the arithmetic average of the stock correlations. However, this approach does not generalize the data well. In our analysis we utilize a recently developed generative probabilistic model for network structure to summarize the underlying structure of the time-varying networks. In this way we obtain a more meaningful mean reversion term. We show experimentally that the dynamic network model can be used to recover detailed statistical properties of the original network data. More importantly, it also suggests that the model is effective in analyzing the predictability of stock correlation networks.