Matrix-valued heterogeneous autoregressive modeling†
Eehyun Park1 · Changryong Baek2
12Department of Statistics, Sungkyunkwan University
Correspondence to: † This work was supported by the Basic Science Research Program from the National Research Foundation of Korea (NRF-2022R1F1A1066209).
1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea.
2 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail: crbaek@skku.edu
1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea.
2 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail: crbaek@skku.edu
Received October 8, 2024; Revised November 19, 2024; Accepted November 26, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- In this paper, we introduce the matrix-valued heterogeneous autoregressive (MHAR) model, which extends the matrix-valued autoregressive (MAR) model to handle long-memory processes within the heterogeneous autoregressive (HAR) framework. The MHAR model maintains the matrix structure of time series without requiring vectorization and addresses the issues of dimensionality in high-dimensional settings and the interpretation of relationships between different time series. The MHAR model is estimated using the Kronecker projection (PROJ) method and the iterative least squares (ILS) method. Our simulation study demonstrates that both estimators are consistent, with the ILS method performing particularly well when initialized with the PROJ estimator. We apply the MHAR model to daily PM10 and PM2.5 mean concentration data from five cities in South Korea to evaluate its forecasting performance in long-memory processes.
- Keywords : bilinear form, HAR, iterative least square, Kronecker product, MAR, MHAR
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