• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.53-64
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• 2022

High dimensional time series is gaining considerable attention in recent years. The sparse vector heterogeneous autoregressive (VHAR) model proposed by Baek and Park (2020) uses adaptive lasso and debiasing procedure in estimation, and showed superb forecasting performance in realized volatilities. This paper extends the sparse VHAR model by considering non-convex penalties such as SCAD and MCP for possible bias reduction from their penalty design. Finite sample performances of three estimation methods are compared through Monte Carlo simulation. Our study shows first that taking into cross-sectional correlations reduces bias. Second, nonconvex penalties performs better when the sample size is small. On the other hand, the adaptive lasso with debiasing performs well as sample size increases. Also, empirical analysis based on 20 multinational realized volatilities is provided.

• The Korean Journal of Applied Statistics
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• v.36 no.6
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• pp.529-545
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• 2023

This paper introduces the Banded-VHAR model suitable for high-dimensional long-memory time series with band structure. The Banded-VHAR model has nonignorable correlations only with adjacent dimensions due to data features, for example, geographical information. Row-wise estimation method is adapted for fast computation. Also, two estimation methods, namely BIC and ratio methods, are proposed to estimate the width of band. We demonstrate asymptotic consistency of our proposed estimation methods through simulation study. Real data applications to pm2.5 and apartment trading volume substantiate that our Banded-VHAR model outperforms traditional sparse VHAR model in forecasting and easy to interpret model coefficients.