A Numerical Comparison of the Modified Method of Moments and Maximum Likelihood for the Estimation of Short-Range Correlations

This paper focuses on the inference of the correlation parameters from data that have either spatial or temporal short-range dependence. A comparative study of two inference methods is presented: the established method of maximum likelihood estimation (MLE) and the recently proposed modified method of moments (MMoM). For reasons of computational efficiency the comparisons are based on simulations of correlated data arranged on uniform open chains. Four commonly used correlation models, i.e., the Gaussian, the exponential, the spherical, and the WhittleMatérn are investigated. As the domain size increases, the MLE estimates exhibit slightly lower bias and dispersion than the MLE estimates for the Gaussian and the Whittle-Matérn models. Both methods produce comparable results in the case of the spherical model. In the exponential case, the MMoM estimates are slightly more accurate, while the dispersion is comparable. Issues related to finite sample size and sampling resolution are investigated for the three-parameter Whittle-Matérn model. In all cases, the CPU time required by the MMoM is much lower than that of the MLE. In addition, the MLE slows down significantly for large samples, while the MMoM computational time is practically insensitive to the domain size. Hence, the MMoM is useful for the analysis of large data sets. Alternatively, it can be used to obtain initial estimates for the ML estimation.