Sparse seasonal and periodic vector autoregressive modeling

Seasonal and periodic vector autoregressions are two common approaches to modeling vector time series exhibiting cyclical variations. The total number of parameters in these models increases rapidly with the dimension and order of the model, making it difficult to interpret the model and questioning the stability of the parameter estimates. To address these and other issues, two methodologies for sparse modeling are presented in this work: first, based on regularization involving adaptive lasso and, second, extending the approach of Davis, Zang and Zheng (2015) for vector autoregressions based on partial spectral coherences. The methods are shown to work well on simulated data, and to perform well on several examples of real vector time series exhibiting cyclical variations.