This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This restriction includes topic models, a popular method for...

Many economic and financial time series exhibit time-varying volatility. GARCH models are tools for forecasting and analyzing the dynamics of this volatility. The co-movements in financial markets and financial assets around the globe have recently become the main area of interest of financial...