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

2026-06-10

AI Summary

This study addresses the high computational cost associated with parameter estimation in fractional Gaussian processes by proposing an efficient composite likelihood–based estimation method. By deriving analytical expressions for the Fisher and Godambe information of fractional Brownian motion and fractional Gaussian noise, the authors design a sequential strategy to select optimal subsets of observations that maximize Godambe information. This approach substantially reduces computational burden while enhancing estimation accuracy. Simulation studies demonstrate superior performance compared to conventional moment-based methods and maximum likelihood estimation. The efficacy of the proposed method is further corroborated through empirical analyses of stock index volatility and wind speed time series.

Abstract

The composite likelihood method reduces the computational cost of parameter estimation in time series by considering several subsets of observations instead of all observations at once. The asymptotic properties of this method are related to the Godambe information, an extension of the Fisher information that accounts for the dependence between subsets of observations. We aim to apply this method to linear Gaussian models, in particular fractional Brownian motion and fractional Gaussian noise. We derive theoretical expressions for their Fisher information and their Godambe information and deduce a subset selection design that sequentially maximizes the Godambe information. The size of the subsets then allows us to control the trade-off between estimation accuracy and computational cost. Through simulations, we compare this method with the method of moments and maximum likelihood estimation, and we apply it to real data, namely volatility series of a stock index and a wind speed time series.

Problem

• composite likelihood
• fractional Gaussian processes
• parameter estimation
• computational cost
• Godambe information

Innovation

• composite likelihood
• fractional Gaussian processes
• Godambe information
• subset selection
• sequential optimization