A simplified approach to inverting the autocovariance matrix of a general ARMA(p, q) process

Statistics and Probability Letters

Volumn 78, Issue 1, 2008, Pages 36-41

  Lin, Tsung I ^a   Ho, Hsiu J ^a  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

Author keywords

Autocorrelation function; Autoregressive; Gaussian process; Inverse matrix; Moving average; Time dependence

Indexed keywords

EID: 36148933007     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2007.05.002     Document Type: Article

References (15)

1. Anderson O.D. An improved approach to inverting the autocovariance matrix of a general mixed autoregressive moving average time process. Austral. J. Statist. 18 (1976) 73-75
2. Anderson O.D. On the inverse of the autocovariance matrices for general autoregressive moving average (p, q) processes. Metron 35 (1977) 243-254
3. Anderson T.W. An Introduction to Multivariate Statistical Analysis. third ed. (2003), Wiely, New York
4. Box G.E.P., Jenkins G.M., and Reinsel G.C. Time Series Analysis Forecasting and Control. third ed. (1994), Prentice-Hall, Englewood Cliffs, NJ
5. Galbraith R.F., and Galbraith J.I. On the inverse of some patterned matrices arising in the theory of stationary time series. J. Appl. Probab. 11 (1974) 63-71
6. Golub G.H., and Van Loan C.F. Matrix Computations. second ed. (1989), Johns Hopkins University Press, Baltimore, MD
7. Haddas J.N. On the closed form of the covariance matrix and its inverse of the causal ARMA process. J. Time Ser. Anal. 25 (2004) 443-448
8. Lee J.C., Lin T.I., Lee K.J., and Hsu Y.L. Bayesian analysis of Box-Cox transformed linear mixed models with ARMA(p, q) dependence. J. Statist. Plann. Inference 133 (2005) 435-451
9. Lin T.I., and Lee J.C. On modelling data from degradation sample paths over time. Aust. N.Z. J. Statist. 45 (2003) 257-270
10. Rochon J. ARMA covariance structures with time heteroscedasticity for repeated measures experiments. J. Amer. Statist. Assoc. 87 (1992) 777-784
11. Siddiqui M.M. On the inversion of the sample covariance matrix in a stationary autoregressive process. Ann. Math. Statist. 29 (1958) 585-588
12. Tsay R.S. Regression models with time series errors. J. Amer. Statist. Assoc. 79 (1984) 118-124
13. Van Der Leeuw J. The covariance matrix of ARMA errors in closed form. J. Econometrics 63 (1994) 397-405
14. Victoria Z.W. Some exact formulae for autoregressive moving average processes. Econom. Theory 4 (1988) 384-402
15. Wise J. The autocorrelation function and the spectral density function. Biometrika 42 (1955) 151-159