Politická ekonomie X:X | DOI: 10.18267/j.polek.1526

Enhancing the HAR model: PCA and scaled PCA methods on heterogeneous realized volatilities

Huachen Zhang, Huifang Liu, Han Yan, Shenglin Ma
Huachen Zhang, School of Finance, Capital University of Economics and Business, Beijing, China
Huifang Liu, School of Economics and Management, Shandong Youth University of Political Science, Jinan, Shandong, China
Han Yan, School of Business, Nankai University, Tianjin, China
Shenglin Ma (corresponding author), School of Economics and Management, North University of China, Taiyuan, China

This study extends the heterogeneous autoregressive (HAR) model by employing the principal component analysis (PCA) and scaled PCA (sPCA) methods on lagged heterogeneous realized volatilities to construct the HAR-PCA and HAR-sPCA models using high-frequency data from 20 stock indices. The in-sample fitting and out-of-sample forecasting performances consistently show that the HAR-PCA and HAR-sPCA models have superior performance. The findings suggest that the heterogeneous principal components of lagged volatilities alleviate the subjectivity associated with the selection of the heterogeneous lag terms. This emphasizes the importance of optimizing the long-period lags under the HAR framework to better capture the heterogeneity of investors.

Keywords: Volatility, heterogenous autoregressive model, principal component analysis, scaled principal component analysis, heterogeneous market hypothesis

Received: February 8, 2025; Revised: August 14, 2025; Accepted: August 18, 2025; Prepublished online: April 28, 2026 

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