Regularized Partially Functional Autoregressive Model

43 Pages Posted: 15 Nov 2019 Last revised: 23 Nov 2021

See all articles by Xiaofei Xu

Xiaofei Xu

National University of Singapore; Waseda University

Ying Chen

National University of Singapore

Ge Zhang

Institute of Data Science, National University of Singapore

Thorsten Koch

Technische Universitat Berlin - Software and Algorithms for Discrete Optimization

Date Written: June 7, 2020

Abstract

In many business and economics studies, researchers have sought to measure the dynamic dependence of curves with high-dimensional mixed-type predictors. We propose a partially functional autoregressive model (pFAR) where the serial dependence of curves is controlled by coefficient operators that are defined on a two-dimensional surface, and the individual and group effects of mixed-type predictors are estimated with a two-layer regularization. We develop an efficient estimation with the proven asymptotic properties of consistency and sparsity. We show how to choose the sieve and tuning parameters in regularization based on a forward-looking criterion. In addition to the asymptotic properties, numerical validation suggests that the dependence structure is accurately detected. The implementation of the pFAR within a real-world analysis of dependence in German daily natural gas flow curves, with seven lagged curves and 85 scalar predictors, produces superior forecast accuracy and an insightful understanding of the dynamics of natural gas supply and demand for the municipal, industry, and border nodes, respectively.

Keywords: Functional Data, High Dimensionality, Mixed-Type Covariates, Two-Layer Sparsity, Energy Forecasting

JEL Classification: C18, C22, C23, C53

Suggested Citation

Xu, Xiaofei and Chen, Ying and Zhang, Ge and Koch, Thorsten, Regularized Partially Functional Autoregressive Model (June 7, 2020). Available at SSRN: https://ssrn.com/abstract=3482262 or http://dx.doi.org/10.2139/ssrn.3482262

Xiaofei Xu

National University of Singapore ( email )

Department of Mathematics
Singapore, 117543
Singapore
82265175 (Phone)

HOME PAGE: http://https://www.linkedin.com/in/xiaofei-xu/

Waseda University ( email )

1-104 Totsukamachi, Shinjuku-ku
tokyo, 169-8050
Japan

Ying Chen (Contact Author)

National University of Singapore ( email )

Department of Mathematics, Faculty of Science
Block S17, Level 4, 10 Lower Kent Ridge Road
Singapore, Singapore 119076
Singapore

Ge Zhang

Institute of Data Science, National University of Singapore ( email )

3 Research Link, #04-06
Singapore, 117602
Singapore
97277036 (Phone)

Thorsten Koch

Technische Universitat Berlin - Software and Algorithms for Discrete Optimization ( email )

Berlin
Germany

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