Extracting Garch Effects from Asset Returns Using Robust NMF

Identification of assets on the stock market that exhibit co-movement is a critical task for generating an efficiently diversified portfolio. We present a new application of non-negative matrix factorization to factor analysis of financial time series. We consider a conditionally heteroscedastic latent factor model, where each series is parameterized by a univariate ARCH model. Volatility clustering characteristics, e.g. GARCH effects, of the constituent assets of the Dow Jones Industrial Average are lever-aged to cluster assets based on the commonality of their volatility clusters. We present a new non-negative matrix factorization algorithm which is robust in the presence of noise, Robust NMF. We use a mixed low-rank over-complete dictionary learning approach to separate out the background Gaussian noise, emphasize the GARCH effects and achieve clearer asset groupings.