Paper: arXiv 2503.00851

Authors: Xiangdong Liu, Sicheng Fu, Shaopeng Hong

Abstract

Volatility forecasting in financial markets is a topic that has received more attention from scholars. In this paper, we propose a new volatility forecasting model that combines the heterogeneous autoregressive (HAR) model with a family of path-dependent volatility models (HAR-PD). The model utilizes the long- and short-term memory properties of price data to capture volatility features and trend features. By integrating the features of path-dependent volatility into the HAR model family framework, we develop a new set of volatility forecasting models. And, we propose a HAR-REQ model based on the empirical quartile as a threshold, which exhibits stronger forecasting ability compared to the HAR-REX model. Subsequently, the predictive performance of the HAR-PD model family is evaluated by statistical tests using data from the Chinese stock market and compared with the basic HAR model family. The empirical results show that the HAR-PD model family has higher forecasting accuracy compared to the underlying HAR model family. In addition, robustness tests confirm the significant predictive power of the HAR-PD model family.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative extension to the HAR framework by incorporating path-dependent volatility (PDV) features and empirical quantile thresholds (HAR-REQ). It performs rigorous statistical testing (MCS, out-of-sample R-squared, robustness checks) using Chinese stock market data to demonstrate superior forecasting performance.

Research Flowchart

  flowchart TD
    A[Goal: Improve Stock Market Volatility Forecasting Accuracy] --> B[Data: Chinese Stock Market Price Data]
    B --> C[Feature Extraction: Capture Long/Short-Term Memory & Path-Dependent Trends]
    C --> D[Model Development: Integrate Path Dependency into HAR Family HAR-PD & HAR-REQ]
    D --> E[Statistical Testing & Comparative Evaluation vs. Base HAR Models]
    E --> F[Outcomes: HAR-PD Family Achieves Higher Accuracy & Robust Predictive Power]

Cited References (86)

  1. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation (1982)
  2. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation (1982)
  3. Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models (2018)
  4. Well-posedness and stability analysis of two classes of generalized stochastic volatility models (2021)
  5. Perfect hedging in rough Heston models (2018)
  6. Volatility is rough (2018)
  7. Generalized autoregressive conditional heteroskedasticity (1986)
  8. Generalized autoregressive score models with applications (2013)
and 78 more
  1. A new approach to Markov-switching GARCH models (2004)
  2. On the relation between the expected value and the volatility of the nominal excess return on stocks (1993)
  3. Conditional heteroskedasticity in asset returns: A new approach (1991)
  4. A permanent and transitory component model of stock return volatility (1993)
  5. A long memory property of stock market returns and a new model (1993)
  6. Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts (1998)
  7. Modeling and forecasting realized volatility (2003)
  8. An introduction to long-memory time series models and fractional differencing (1980)
  9. Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements (2005)
  10. Path-dependent volatility (2014)
  11. Time series analysis: forecasting and control (2015)
  12. Rough Path-Dependent Volatility Models (2022)
  13. Path dependent volatility (2008)
  14. Volatility is (mostly) path-dependent (2023)
  15. Complete models with stochastic volatility (1998)
  16. Mimicking the one-dimensional marginal distributions of processes having an It ^o differential (1986)
  17. From implied to spot volatilities (2010)
  18. Implied volatility surface: Construction methodologies and characteristics (2011) — link
  19. Continuous-time VIX dynamics: On the role of stochastic volatility of volatility (2013)
  20. A jump diffusion model for VIX volatility options and futures (2010)
  21. Pricing with a smile (1994)
  22. A Simple Approximate Long-Memory Model of Realized Volatility (2009)
  23. Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling (2012)
  24. Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility (2015)
  25. Measuring downside risk-realised semivariance (2008)
  26. Moderate and extreme volatility: Do the magnitude of returns matter for forecasting? (2019)
  27. Jumps in financial markets: A new nonparametric test and jump dynamics (2008)
  28. Answering the skeptics: Yes, standard volatility models do provide accurate forecasts (1998)
  29. Option pricing when underlying stock returns are discontinuous (1976)
  30. Another look at measures of forecast accuracy (2006)
  31. Long-range forecasting, 2nd (2010)
  32. Realized power variation and stochastic volatility models (2003)
  33. Power and bipower variation with stochastic volatility and jumps (2004)
  34. HAR volatility modelling with heterogeneous leverage and jumps (2009)
  35. Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility (2007)
  36. Estimating the degree of activity of jumps in high frequency data (2009)
  37. The relative contribution of jumps to total price variance (2005)
  38. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  39. The pricing of options and corporate liabilities (1973)
  40. A forecast comparison of volatility models: does anything beat a GARCH(1,1)? (2005)
  41. Comparing predictive accuracy (2002)
  42. A reality check for data snooping (2000)
  43. A test for superior predictive ability (2005)
  44. The model confidence set (2011)
  45. Volatility processes and volatility forecast with long memory (2003)
  46. Predicting excess stock returns out of sample: Can anything beat the historical average? (2008)
  47. Do jumps matter for volatility forecasting? Evidence from energy markets (2016)
  48. Approximately normal tests for equal predictive accuracy in nested models (2007)
  49. Investigating Approaches to Modeling Rough Path-Dependent Volatility: Insights and Implications (2023)
  50. A tale of two time scales: Determining integrated volatility with noisy high-frequency data (2005)
  51. How often to sample a continuous-time process in the presence of market microstructure noise (2005)
  52. The volatility of realized volatility (2008)
  53. Regression shrinkage and selection via the lasso (1996)
  54. Neural network approach in forecasting realized variance using high-frequency data (2018)
  55. Multimodel inference: understanding AIC and BIC in model selection (2004)
  56. Deepvol: Volatility forecasting from high-frequency data with dilated causal convolutions (2024)
  57. Forecasting the volatility of crude oil futures using HAR -type models with structural breaks (2016)
  58. Realized volatility forecast with the Bayesian random compressed multivariate HAR model (2020)
  59. A nonparametric GARCH model of crude oil price return volatility (2012)
  60. Volatility forecasting of crude oil futures market: Which structural change-based HAR models have better performance? (2023)
  61. Forecasting volatility of the US oil market (2014)
  62. Out-of-sample volatility prediction: Rolling window, expanding window, or both? (2024)
  63. Well-posedness and stability analysis of two classes of generalized stochastic volatility models (2021)
  64. Forecasting crude oil market volatility: A Markov switching multifractal volatility approach (2016)
  65. Modeling and forecasting multifractal volatility established upon the heterogeneous market hypothesis (2018)
  66. Realized volatility forecast of stock index under structural breaks (2015)
  67. Modeling the volatility of realized volatility to improve volatility forecasts in electricity markets (2018)
  68. Forecasting realised volatility: Does the LASSO approach outperform HAR ? (2021)
  69. Lassoing the HAR model: A model selection perspective on realized volatility dynamics (2016)
  70. Trading volume and realized volatility forecasting: Evidence from the China stock market (2023)
  71. Do natural disasters and geopolitical risks matter for cross-border country exchange-traded fund returns? (2020)
  72. How do market volatility and risk aversion sentiment inter-influence over time? Evidence from Chinese SSE 50 ETF options (2024)
  73. Heterogeneity effect of positive and negative jumps on the realized volatility: Evidence from China (2024)
  74. A model for stock returns and volatility (2014)
  75. Forecasting realized volatility: HAR against Principal Components Combining, neural networks and GARCH (2017)
  76. Modeling stock market volatility using new HAR -type models (2019)
  77. A model confidence set approach to the combination of multivariate volatility forecasts (2020)
  78. Choosing the best volatility models: the model confidence set approach (2003)

0 of 86 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.