Composite likelihood inference of fractional Gaussian processes with sequentially optimal subset selection

Battle Count: 63

The paper directly applies to financial volatility modeling (S&P 500 realized volatility, VIX) using fractional Gaussian processes, which are central to rough volatility models. The composite likelihood method provides a computationally efficient alternative to MLE for estimating Hurst exponents in high-frequency financial data. The forecasting application with rolling windows and DMW/McNemar tests is directly relevant to quantitative trading. However, the method is primarily an estimation tool rather than a trading strategy, and the Gaussian assumption may limit applicability to real financial data with heavy tails and jumps.

The method requires: (1) computing theoretical covariance matrices for fBm/fGn, (2) evaluating Fisher and Godambe information via matrix operations (inversions, traces, derivatives), (3) sequential combinatorial optimization for subset selection, (4) composite likelihood maximization over sub-vectors, and (5) handling arbitrary time scales for fGn. The theoretical derivations are complex, but the final design (consecutive observations) simplifies implementation. The Trench algorithm for Toeplitz matrices adds implementation complexity. Overall, moderate-to-high complexity requiring strong numerical linear algebra skills.

The paper provides detailed theoretical derivations, algorithm descriptions, and simulation parameters (N=500, 400 trajectories, p values, H values). Data sources are identified (Oxford-Man Institute, Bloomberg, Météo-France station 7591). However, no code repository is explicitly linked, and some implementation details (e.g., exact optimization routines for sequential selection) would need to be reconstructed from the text.