A1467
Title: Heterogeneous autoregressive models driven by Gaussian processes with the generalized Cauchy covariance function
Authors: Tsunehiro Ishihara - Takasaki City University of Economics (Japan) [presenting]
Toshihiro Hirano - Kanto Gakuin University (Japan)
Abstract: Recent studies on volatility have highlighted the importance of path roughness measured by the fractal dimension $D$ or the Hurst index $H$ in modeling the dynamics of asset return volatility. Most existing approaches rely on fractional Brownian motion (fBM), which imposes $H+D=2$. This constraint conflates long memory in levels with roughness in increments, preventing separate identification of the two properties. A Gaussian process approach with generalized Cauchy (GC) covariance functions has been recently proposed. The GC covariance function allows $D$ and $H$ to vary independently. Heterogeneous autoregressive (HAR) models for log realized volatility driven by Gaussian process innovations with GC covariance functions are proposed to estimate roughness, persistence, and heterogeneity separately. The proposed method is compared with several models, including AR(1), HAR, and HAR with jump components under three innovation specifications: i.i.d. Gaussian, fractional Gaussian noise (fGN), and the GC process. Bayesian estimation is conducted via MCMC with an adaptive Metropolis algorithm that reduces the number of matrix manipulations. Rolling-window forecasting performance is evaluated using MSE and QLIKE robust loss functions. In an application to daily realized volatility of the TOPIX index, prediction results and posterior quantities of $D+H$ are reported.
