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A0324
Title: Tensor regression in economics and finance Authors:  Giuseppe Brandi - LUISS University (Italy) [presenting]
Abstract: Multidimensional data (tensor data) is a relevant topic in statistical and machine learning research. Examples of multidimensional data are panel data (individuals $\times$ variables $\times$ time $\times$ locations) or higher order ($>2$) multivariate portfolio moments (the coKurtosis) or 3D images (cube of pixels). Given their complexity, such data objects are usually reshaped into matrices and then analyzed. However, doing so poses other issues. First of all, it destroys the intrinsic interconnections among the datapoints in the multidimensional space and, secondly, the number of parameters to be estimated in a model increase exponentially. To alleviate these issues the data is treated as it is and a model able to deal with the multidimensionality of the dataset is developed. In particular, a parsimonious tensor regression (in which both the regressor and the response are tensors) is build such that it retains the intrinsic multidimensional structure of the dataset. Tucker decomposion is employed to achieve parsimony and an ALS algorithm is developed to estimate the model parameters. A simulation exercise is produced to validate the model and an empirical application to macroeconomic time series is carried over to compare its prediction ability with existing ones.