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Rates of convergence for time series regression

Published online by Cambridge University Press:  01 July 2016

E. J. Hannan
E. J. Hannan*
Affiliation:
The Australian National University, Canberra
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Extract

Consider, initially, a time series regression model of the simplest kind, namely Assume that x(t) is second-order stationary with zero mean and absolutely continuous spectrum with density f(ω) so that The y(t) are taken to be part of a sequence generated entirely independently of x(t) and will be treated as constants. Let βN be the least squares estimate of β and Call the numerator and denominator of b(N), respectively, c(N), d(N). We shall use K for a positive finite constant, not always the same one. We have the following result, which is Menchoff's inequality [3].

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 740 - 743
Copyright
Copyright © Applied Probability Trust 1978 

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References

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