Maximum Likelihood Drift Estimation for Gaussian Process with Stationary Increments

Maximum Likelihood Drift Estimation for Multiscale Diffusions

We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of fast/slow problems for which a closed coarse-grained equation for the slow variables can be rigorously derived, which we refer to as averaging and homogenizatio...

Fast Spatial Gaussian Process Maximum Likelihood Estimation via Skeletonization Factorizations

Maximum likelihood estimation for parameter-fitting given observations from a Gaussian process in space is a computationally-demanding task that restricts the use of such methods to moderately-sized datasets. We present a framework for unstructured observations in two spatial dimensions that allows for evaluation of the log-likelihood and its gradient (i.e., the score equations) in Õpn3{2q time...

Representations of Gaussian processes with stationary increments

Nonparametric Quasi-maximum Likelihood Estimation for Gaussian Locally Stationary Processes1 by Rainer Dahlhaus

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are conside...

Asymptotic Theory for Maximum Likelihood Estimation of the Memory Parameter in Stationary Gaussian Processes

Consistency, asymptotic normality and e¢ ciency of the maximum likelihood estimator for stationary Gaussian time series, were shown to hold in the short memory case by Hannan (1973) and in the long memory case by Dahlhaus (1989). In this paper, we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility. In the process of proving the mai...