Limit Theory for Moderate Deviations from Unity
An asymptotic theory is given for autoregressive time series with a root of the form [rho]n=1+c/kn, which represents moderate deviations from unity when is a deterministic sequence increasing to infinity at a rate slower than n, so that kn=o(n) as n-->[infinity]. For c<0, the results provide a...
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2007
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| Online Access: | https://ink.library.smu.edu.sg/soe_research/282 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | An asymptotic theory is given for autoregressive time series with a root of the form [rho]n=1+c/kn, which represents moderate deviations from unity when is a deterministic sequence increasing to infinity at a rate slower than n, so that kn=o(n) as n-->[infinity]. For c<0, the results provide a rate of convergence and asymptotic normality for the first order serial correlation, partially bridging the and n convergence rates for the stationary (kn=1) and conventional local to unity (kn=n) cases. For c>0, the serial correlation coefficient is shown to have a convergence rate and a Cauchy limit distribution without assuming Gaussian errors, so an invariance principle applies when [rho]n>1. This result links moderate deviation asymptotics to earlier results on the explosive autoregression proved under Gaussian errors for kn=1, where the convergence rate of the serial correlation coefficient is (1+c)n and no invariance principle applies. |
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