Testing for Long Memory and Choosing FIGARCH or HARCH Volatility Models

Summary

This article explains how to diagnose long memory in volatility and choose between two conditional variance models. It recommends applying rescaled-range Hurst analysis and the Geweke–Porter–Hudak test to absolute or squared returns, with safeguards for sample size and partition selection. A low-frequency periodogram plot provides an additional visual clue: a smooth fractional pattern supports FIGARCH, while distinct horizon peaks suggest HARCH.

The article describes implementations and examples for testing, fitting, and forecasting both models. FIGARCH represents fractional persistence and requires a truncation depth; its computation is heavier, and analytical multi-step forecasts are limited when the power parameter differs from two. HARCH combines volatility across selected horizons and is lighter to compute, but its results depend on those horizon choices. The article presents these tools as diagnostics and modeling options rather than evidence that either model improves trading performance. Estimates and visual patterns depend on the input series and sample, so model choice requires empirical assessment.

Key ideas

• Use returns-based volatility proxies, such as absolute or squared returns, when testing for persistence.
• Rescaled-range analysis estimates the Hurst exponent across logarithmically spaced window sizes and needs adequate sample length.
• The GPH test estimates fractional integration from low-frequency periodogram values, with bandwidth affecting the estimate.
• A smooth fractional spectral slope favors FIGARCH, while localized horizon peaks point toward HARCH.
• FIGARCH can be computationally heavier, whereas HARCH is sensitive to its selected horizon windows.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.