A0590
Title: Bayesian analysis of long memory and roughness in financial volatility
Authors: Toshiaki Watanabe - Hitotsubashi University (Japan) [presenting]
Jouchi Nakajima - Hitotsubashi University (Japan)
Abstract: Realized volatility (RV) calculated using intraday returns has recently been used as an accurate estimator of financial volatility. Some researchers have documented that the log-RV may follow a long-memory process, which is represented by a fractional Brownian motion with the Hurst exponent greater than 0.5 or a fractionally integrated process with a positive difference parameter. Recent studies show that the log difference in RV may be rough, which is represented by a fractional Brownian motion with the Hurst exponent less than 0.5 or a fractionally integrated process with a negative difference parameter. A discrete-time model that is consistent with these two phenomena is presented, and a Bayesian method is developed for the analysis of this model using Markov chain Monte Carlo. Empirical analysis using the RV of the Nikkei 225 stock index reveals that the long-term memory model has the best in-sample fit, and the model that takes into account both long-term memory and roughness has the highest volatility prediction accuracy, surpassing the heterogeneous autoregressive (HAR) model, which is known to have high volatility prediction accuracy.
