The Mixture Transition Distribution approach to networks: Evidence from stock markets

Networks can be built by using correlations between time series. The approach based on correlations has many advantages which are essentially related to its simplicity. Nevertheless, it is well known that time series may show strong dependence even if they are uncorrelated. In this paper, we will advance a multivariate Markov chain model based on the Mixture Transition Distribution (MTD) model to build networks between time series. The multivariate MTD is able to consider the dependence between time series and, at the same time, reduce the number of parameters to be estimated compared to the classical multivariate Markov chain. We show, by a numerical example, that the multivariate MTD outperforms the classical correlation approach. Moreover, using the same model, we build the network of the 30 constituents of the Dow Jones index showing the usefulness of the methodology in real problems in financial markets.