Algebra of Integrated Time Series: Evidence from Unit Root Analysis

2015 ◽  
Author(s):  
Hari S. Luitel ◽  
Gerry J. Mahar
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Root Analysis ◽  
Integrated Time Series

scholarly journals HOW TO ESTIMATE AUTOREGRESSIVE ROOTS NEAR UNITY

2001 ◽  
Vol 17 (1) ◽  
pp. 29-69 ◽  
Author(s):  
Peter C.B. Phillips ◽  
Hyungsik Roger Moon ◽  
Zhijie Xiao
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Time Series Data ◽  
Diffusion Processes ◽  
Rates Of Convergence ◽  
Series Data ◽  
New Class ◽  
Power Rate ◽  
Integrated Time Series ◽  
Conventional Unit

A new model of near integration is formulated in which the local to unity parameter is identifiable and consistently estimable with time series data. The properties of the model are investigated, new functional laws for near integrated time series are obtained that lead to mixed diffusion processes, and consistent estimators of the localizing parameter are constructed. The model provides a more complete interface between I(0) and I(1) models than the traditional local to unity model and leads to autoregressive coefficient estimates with rates of convergence that vary continuously between the O(√n) rate of stationary autoregression, the O(n) rate of unit root regression, and the power rate of explosive autoregression. Models with deterministic trends are also considered, least squares trend regression is shown to be efficient, and consistent estimates of the localizing parameter are obtained for this case also. Conventional unit root tests are shown to be consistent against local alternatives in the new class.

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