Paper: arXiv 2403.12653

Authors: Mikkel Bennedsen, Kim Christensen, Peter Christensen

Abstract

We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a pair of models that have been proposed to describe the random log-spot variance of financial asset returns. A simulation study shows that it delivers good performance in these settings and improves upon a method-of-moments estimation. In an empirical investigation, we inspect the dynamic of an intraday measure of the spot log-realized variance computed with high-frequency data from the cryptocurrency market. The evidence supports a mechanism, where the short- and long-term correlation structure of stochastic volatility are decoupled in order to capture its properties at different time scales. This is further backed by an analysis of the associated spot log-trading volume.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a rigorous parametric continuous-time composite likelihood framework with fully derived asymptotic theory. It applies this advanced mathematical machinery to high-frequency cryptocurrency volatility data, effectively demonstrating that short- and long-term correlation structures in volatility are decoupled.

Research Flowchart

  flowchart TD
    A["Research Question: Roughness vs. Long Memory<br/>in Financial Volatility"] --> B["Develop Composite Likelihood Estimation<br/>for Continuous-Time Gaussian Processes"]
    B --> C["Data Inputs: High-Frequency Crypto Data<br/>(Log-Realized Variance & Log-Trading Volume)"]
    C --> D["Simulation Study & Empirical Analysis<br/>(Benchmarked vs. Method-of-Moments)"]
    D --> E["Findings: Decoupled Short- & Long-Term<br/>Correlation Structure Across Time Scales"]