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Abstract:
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In this paper, we consider the estimation of structured multivariate VAR modeling. The big challenge is that as either the dimension of VAR process grows or the number of VAR variables grows, that the number of parameters grows extremely fast so that conventional lasso method would fail to estimate both the dependent effects among variables and the correlations within each VAR process are difficult to be measured. We proposed a new model for illustrating the dependencies within each variable and cross-influence among these VAR variables precisely, we proposed a procedure for estimating the correlation among variables and within each VAR process alternatively by using ADMM, we also proved the asymptotic properties like restricted strong bi-convexity and deviation bounds. We applied our model to analyze the climate defined variable database. Numerical studies and real data analysis demonstrate that both theory and algorithm work efficiently and outperform the conventional lasso estimation.
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