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Title: Tensor autoregression in economics and finance Authors:  Giuseppe Brandi - LUISS University (Italy) [presenting]
Abstract: The increase of data dimensionality poses a problem in its analysis. Standard methods try to reduce the multidimensional data in vectors or matrices and do analysis on this simpler objects. However, this approach has two main drawbacks. The first one in related to the fact that vectorize a multidimensional dataset destroys the interconnections between dimensions and secondly, it generates an exponentially increase of the parameters to be estimated. Take a dataset \textbf{A} consisting of three dimensions and that such dimensions are $30, 30, 50$. The vectorized form of statistical analysis would need to estimate $30 \times 30 \times 50 = 45000$ parameters. A common way to reduce the problem is to use PCA methods, but as it is known, PCA factors are then difficult to interpret. A way to overcome this problem is to rely on tensor analysis. Treating the dataset \textbf{A} as a tensor and fitting a model on it, requires to estimate ``just'' $30+30+50=110$ parameters. We employ a Tensor Autoregression model on multidimensional economic data trying to show the superiority of such method to the classical VAR.