ABSTRACT
This chapter provides theoretical fundations of stochastic procsses and optimal statistical inference. It discusses asymptotic properties of fundamental estimators for general stochastic processes. The chapter explores the asymptotics of maximum likelihood estimator for very general stochastic processes. It presents a generalized Akaike’s information criterion (AIC) for general stochastic models, which includes the original AIC as a special case. The chapter outlines the asymptotic efficiency of estimators for optimal portfolio weights. It also discusses a comprehensive study of shrinkage estimation for dependent observations. The chapter also presents the shrinkage estimation of the mean and autocovariance functions for second-order stationary processes. It analyzes the interpolation problem. The chapter shows that the pseudo interpolator is not optimal with respect to mean squared interpolation error by proposing a pseudo shrinkage interpolator motivated by James and Stein. It also provides an essentially non-Gaussian likelihood for linear processes.
