We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only low-level conditions are used. As the sample size increases, the spatial matrix is assumed to approach a square-integrable function on the square $(0,1)^2$. The asymptotic distribution is a ratio of...

This paper presents recent developments in model selection and model averaging for parametric and nonparametric models. While there is extensive literature on model selection under parametric settings, we present recently developed results in the context of nonparametric models. In applications,...

This paper proposes a new combined semiparametric estimator of the conditional variance that takes the product of a parametric estimator and a nonparametric estimator based on machine learning. A popular kernel-based machine learning algorithm, known as the kernel-regularized least squares...

We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the characteristic equation are well away from the unit circle, and more substantial where one or more...