This paper establishes error orders for integral limit approximations to traces of powers (to the pth order) of products of Toeplitz matrices. Such products arise frequently in the analysis of stationary time series and in the development of asymptotic expansions. The elements of the matrices...

A scalar pth-order autoregression (AR(p)) is considered with heteroskedasticity of the unknown form delivered by a transition function of time. A limit theory is developed and three heteroskedasticity-robust test statistics are proposed for inference, one of which is based on the nonparametric...

First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient rho = rho_n is an element of [0, 1) provided (1 - rho_n)n goes to infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho...

type="main" xml:id="jtsa12083-abs-0001"A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random-walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential...