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Abstract:
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We approach variable selection in high-dimensional Vector Autoregression (VAR) via adopting a forecast error fitting criterion based upon a few key series of principal interest, and dropping ancillary variables that do not Granger-cause these principal variables. It is not feasible to fit a high-dimensional VAR model unless most of the coefficients are zero; when the zeroes are aligned in the same column of the coefficient matrices, the corresponding variable can be omitted. So we impose substantial sparsity restrictions in the autoregressive coefficients by sequentially allocating columns of zeroes, and for each such configuration utilize Wald tests to validate variable deletion. The method is used in cases where hundreds of time series are jointly analyzed.
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