The Annals of Statistics

A Central Limit Theorem for Parameter Estimation in Stationary Vector Time Series and its Application to Models for a Signal Observed with Noise

W. Dunsmuir

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Abstract

A general finite parameter model for stationary ergodic nondeterministic vector time series is considered. A central limit theorem for parameter estimates, obtained by maximising frequency domain approximations to the Gaussian likelihood, is established. The treatment given extends the central limit theorem of Dunsmuir and Hannan in that the innovations covariance matrix and the linear transfer function need not be separately parameterised. Models for a stationary vector signal observed with stationary vector noise are discussed in relation to the central limit theorem and the conditions imposed for this result are related to this model. Finally, the special case of a scalar autoregressive signal observed with noise is discussed. It is shown that this model may be reparameterised so that the central limit theorem of Dunsmuir and Hannan may be applied.

Article information

Source
Ann. Statist., Volume 7, Number 3 (1979), 490-506.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344671

Digital Object Identifier
doi:10.1214/aos/1176344671

Mathematical Reviews number (MathSciNet)
MR527485

Zentralblatt MATH identifier
0406.62068

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G10: Stationary processes

Keywords
Linear processes ARMA models central limit theorems martingales prediction theory signal with noise Fourier methods

Citation

Dunsmuir, W. A Central Limit Theorem for Parameter Estimation in Stationary Vector Time Series and its Application to Models for a Signal Observed with Noise. Ann. Statist. 7 (1979), no. 3, 490--506. doi:10.1214/aos/1176344671. https://projecteuclid.org/euclid.aos/1176344671


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