Measuring and Forecasting Stock Market Volatilities with High-Frequency Data

This paper investigates the efficacy of various heterogeneous autoregressive models (HAR) in forecasting volatility across the U.S. financial markets. We address potential data measurement errors and leverage a comprehensive dataset of 22 years of tick-by-tick data encompassing three major stock indices: the S&P500, the Dow Jones Industrial Average (DJI), and the Nasdaq. Our analysis reveals several key findings: (1) Long-term (monthly) realized volatility (RV) has a stronger influence on future volatility compared to short-term (daily and weekly) RV. This aligns with the Heterogeneous Market Hypothesis, suggesting all market participants prioritize long-term volatility due to its impact on market direction. (2) Daily jumps have a short-term negative impact on future volatility, while aggregated monthly jumps have a positive effect due to their influence on market direction. The transient nature of jumps implies that the persistence of volatility stems from its continuous component. (3) The leverage effect is present and persists for up to 1 week. Models incorporating this effect demonstrate significantly better performance. (4) Across all models, forecast accuracy peaks at the 1-week horizon. More general models offer superior predictive power for short-term forecasts. For longer horizons, while there is no statistically significant difference among models, the loss function shows a slight improvement for more general models. (5) All models are able to confirm the theoretical link between expected return and volatility by identifying a positive correlation between return and risk in the data.