Approximate confidence sets for a stationary AR( p) process

Approximate confidence intervals are derived for the autoregressive parameters of a stationary, Gaussian auto-regressive process of arbitrary order and shown to be asymptotically correct to order o ( 1 / n ) , where n is the sample size. Simulation studies are included for small and moderate sample...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2006-08, Vol.136 (8), p.2719-2745
Main Authors: Weng, Ruby C., Woodroofe, Michael
Format: Article
Language:English
Subjects:
Asymptotic confidence levels
Asymptotic expansions
Exact sciences and technology
General topics
Mathematics
Nonparametric inference
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stationary autoregressive process
Statistics
Stochastic processes
Very weak expansions
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Summary:Approximate confidence intervals are derived for the autoregressive parameters of a stationary, Gaussian auto-regressive process of arbitrary order and shown to be asymptotically correct to order o ( 1 / n ) , where n is the sample size. Simulation studies are included for small and moderate sample sizes for the case of two auto-regressive parameters, and these indicate excellent approximation for sample sizes as small as n = 10 , 20 . The convergence is in the very weak sense, and the derivation differs from most existing work through its direct focus on Studentized estimation error and its use of Stein's identity.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2004.11.007