The exact likelihood function for a mixed autoregressive-moving average process

Biometrika ◽  
1974 ◽  
Vol 61 (3) ◽  
pp. 423-426 ◽  
Author(s):  
PAUL NEWBOLD
Keyword(s):  
Likelihood Function ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Autoregressive Moving Average Process

On the inverses of some patterned matrices arising in the theory of stationary time series

1974 ◽  
Vol 11 (01) ◽  
pp. 63-71 ◽  
Author(s):  
R. F. Galbraith ◽  
J. I. Galbraith
Keyword(s):  
Moving Average ◽  
Autoregressive Process ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
First Order ◽  
Explicit Formulae ◽  
Patterned Matrices ◽  
Autoregressive Moving Average Process

Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ≧ p), and for the first order mixed autoregressive moving average process.

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