Edge deletion tests and ℓ1-regularization methods in graphical modelling for multivariate time series. (2016)
AuthorsEllis, Roryshow all
In this thesis, the primary aim is to examine graphical modelling in the context of multivariate time series. This work develops on previous work, which provided two approaches, the GMTS and SIN methods, which gave results for the conditional independencies between the variables in datasets. These methods will be compared with a more recent range of methods for estimating the structure of the graphical model, called ℓ1-regularization, which focused on inducing sparsity in the model. Examining a Gaussian graphical model context, the aim becomes to estimate the covariance/precision matrix, and then produce the partial correlations between variables. This matrix then provides the significant or insignificant edges (lines) between vertices/nodes (variables) in the Conditional Independence Graph (CIG). These methods are compared using a Monte Carlo simulation study, by simulating structural vector autoregressive models (SVAR), which are a mathematical form of representing the dependencies between variables. These simulation studies suggest that the original GMTS and SIN methods produced very useful results in the classification analysis, compared to some of the four ℓ1-regularization methods used in these studies. Convergence rate analysis and more details on each of these ℓ1-regularization methods are provided in a comprehensive discussion.