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 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.
|Date of creation:||Jan 2009|
|Date of revision:|
|Publication status:||Published in Journal of Econometrics (August 2012), 169(2): 166-178|
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- Liudas Giraitis & Peter C.B. Phillips, 2004.
"Uniform Limit Theory for Stationary Autoregression,"
Cowles Foundation Discussion Papers
1475, Cowles Foundation for Research in Economics, Yale University.
- Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, 01.
- L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
- Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
- Phillips, Peter C.B. & Magdalinos, Tassos, 2007.
"Limit theory for moderate deviations from a unit root,"
Journal of Econometrics,
Elsevier, vol. 136(1), pages 115-130, January.
- Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
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