Sparse vector heterogeneous autoregressive model with nonconvex penalties

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.