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Abstract:
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In this talk, we introduce a novel parametric infinite-order vector autoregressive model. As a variant of the vector autoregressive moving average (ARMA) model, it not only inherits desirable properties such as parsimony and rich temporal dependence structures, but avoids two well-known drawbacks of the former: (i) non-identifiability and (ii) computational intractability even for moderate-dimensional data. Moreover, its parameter estimation is scalable with respect to the complexity of temporal dependence, namely the number of decay patterns constituting the autoregressive structure; hence it is called the scalable ARMA (SARMA) model. In the high-dimensional setup, we further impose a low-Tucker-rank assumption on the coefficient tensor of the proposed model. The resulting model has the form of a regression with embedded dynamic factors and hence can be especially suited for financial and economic data. Non-asymptotic theory, algorithm, and numerical examples will be discussed.
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