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.

翻译：复合似然方法通过考虑观测的子集而非全体观测，降低了时间序列参数估计的计算成本。该方法的渐近性质与Godambe信息相关，后者是Fisher信息的扩展形式，可反映观测子集间的依赖关系。我们旨在将此方法应用于线性高斯模型，特别是分数布朗运动和分数高斯噪声。我们推导了其Fisher信息与Godambe信息的理论表达式，并据此设计了一种序贯最大化Godambe信息的子集选择方案。通过调整子集规模，可以控制估计精度与计算成本之间的权衡。通过模拟实验，我们将该方法与矩估计法和极大似然估计法进行比较，并应用于实际数据，即股票指数的波动率序列和风速时间序列。