Mean and Autocovariance Function Estimation Near the Boundary of Stationarity
We analyze the applicability of standard normal asymptotic theory for linear process models near the boundary of stationarity. The concept of stationarity is reﬁned, allowing for sample size dependence in the array and paying special attention to the rate at which the boundary unit root case is approached using a localizing coeﬀicient around unity. The primary focus of the present paper is on estimation of the mean, autocovariance and autocorrelation functions within the broad region of stationarity that includes near boundary cases which vary with the sample size. The rate of consistency and the validity of the normal asymptotic approximation for the corresponding estimators is determined both by the sample size n and a parameter measuring the proximity of the model to the unit root boundary. An asymptotic result on the estimation of the localizing coeﬀicient is also presented. To assist in the development of the limit theory in the present case, a suitable asymptotic theory for the behavior of quadratic forms in the vicinity of the boundary of stationarity is provided.
Giraitis, Liudas and Phillips, Peter C.B., "Mean and Autocovariance Function Estimation Near the Boundary of Stationarity" (2009). Cowles Foundation Discussion Papers. 2007.