Volatility puzzle: Long memory or anti-persistency

• Main Authors: SHI, Shuping, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2023
• Subjects: long memory; fractional integration; roughness; short-run dynamics; realized volatility; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2638; https://ink.library.smu.edu.sg/context/soe_research/article/3637/viewcontent/VolatilityPuzzle_sv.pdf
• Institution: Singapore Management University

The log realized volatility (RV) is often modeled as an autoregressive fractionally integrated moving average model ARFIMA(1,d,01,d,0). Two conflicting empirical results have been found in the literature. One stream shows that log RV has a long memory (i.e., the fractional parameter d > 0). The other stream suggests that the autoregressive coefficient α is near unity with antipersistent errors (i.e., d α close to 0 and d close to 0.5) from Model 2Model 2 (ARFIMA(1,d,01,d,0) with α close to unity and d close to –0.5). An intuitive explanation is given. For the 10 financial assets considered, despite that no definitive conclusions can be drawn regarding the data-generating process, we find that the frequency domain maximum likelihood (or Whittle) method can generate the most accurate out-of-sample forecasts.