ScholarWorks@성균관대학교

초록

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.

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