This paper examines the Gaussian maximum likelihood estimator (GMLE) in the context of a general form of spatial autoregressive and moving average (ARMA) processes with finite second moment. The ARMA processes are supposed to be causal and invertible under the half-plane unilateral order, but...

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with...

This note can be considered as a continuation of a nice paper from Francq and Zakoian (2012) concerning with strict stationarity testing and estimation of GARCH models. We compute the asymptotic variances of the quasi-maximum likelihood estimators for stationary GARCH models.