English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The classical vector autoregressive model is a fundamental tool formultivariate time series analysis. However, it involves too many parameterswhen the number of time series and lag order are even moderately large. Thispaper proposes to rearrange the transition matrices of the model into a tensorform such that the parameter space can be restricted along three directionssimultaneously via tensor decomposition. In contrast, the reduced-rankregression method can restrict the parameter space in only one direction.Besides achieving substantial dimension reduction, the proposed model isinterpretable from the factor modeling perspective. Moreover, to handlehigh-dimensional time series, this paper considers imposing sparsity on factormatrices to improve the model interpretability and estimation efficiency, whichleads to a sparsity-inducing estimator. For the low-dimensional case, we deriveasymptotic properties of the proposed least squares estimator and introduce analternating least squares algorithm. For the high-dimensional case, weestablish non-asymptotic properties of the sparsity-inducing estimator andpropose an ADMM algorithm for regularized estimation. Simulation experimentsand a real data example demonstrate the advantages of the proposed approachover various existing methods.

High-dimensional vector autoregressive time series modeling via tensor decomposition