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Abstract:
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Vector autoregressive models have had a considerable impact in macroeconomics and the world of finance, as it provides an appealing way of modelling spatio-temporal relationships between a number of univariate time series. However, VAR models tend to suffer from having a relatively large number of parameters,especially when available data are scarce. They are also believed to be driven by heavy tailed noise in many situations. To overcome the problem of high dimensions, we assume the underlying model is sparse and propose to estimate the parameters consistency using the well known lasso technique. To guard against heavy tailed noise, we propose the Huber loss function. We examine how the temporal dependencies and the tail conditions,affect the lasso estimator, and give theoretical guarantees for its convergence.
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