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

1979 ◽  
Vol 7 (3) ◽  
pp. 490-506 ◽  
Author(s):  
W. Dunsmuir
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Vector Time Series ◽  
Stationary Vector

The asymptotic theory of linear time-series models

1973 ◽  
Vol 10 (01) ◽  
pp. 130-145 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Theory ◽  
Linear Time ◽  
Stationary Time Series ◽  
Linear Predictor ◽  
The Central Limit Theorem ◽  
Best Linear Predictor

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.

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