摘要: An efficient procedure for computing autocovariance sequences of multiple autoregressive moving-average processes is proposed. While the computational complexity existing algorithms proportional to p/sup 3/, where p denotes degree polynomial, proposed has a O(p/sup 2/). The resulting scheme leads substantial savings, especially when dealing with polynomials high and therefore facilitates estimation exact maximum-likelihood methods. >
sci-hub.se 参考文章(14)
Ian McLeod, Derivation of the Theoretical Autocovariance Function of Autoregressive–Moving Average Time Series Journal of The Royal Statistical Society Series C-applied Statistics. ,vol. 24, pp. 255- 256 ,(1975) , 10.2307/2346573
J.-P. Dugre, A. Beex, L. Scharf, Generating covariance sequences and the calculation of quantization and rounding error variances in digital filters IEEE Transactions on Acoustics, Speech, and Signal Processing. ,vol. 28, pp. 102- 104 ,(1980) , 10.1109/TASSP.1980.1163365
Stefan Mittnik, Non-recursive methods for computing the coefficients of the autoregressive and the moving-average representation of mixed ARMA processes Economics Letters. ,vol. 23, pp. 279- 284 ,(1987) , 10.1016/0165-1765(87)90165-0
Stefan Mittnik, Derivation of the theoretical autocovariance and autocorrelation function of autoregessive moving average processes Communications in Statistics-theory and Methods. ,vol. 17, pp. 3825- 3831 ,(1988) , 10.1080/03610928808829837
Hirotugu Akaike, Block Toeplitz Matrix Inversion Siam Journal on Applied Mathematics. ,vol. 24, pp. 234- 241 ,(1973) , 10.1137/0124024
G. Merchant, T. Parks, Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations IEEE Transactions on Acoustics, Speech, and Signal Processing. ,vol. 30, pp. 40- 44 ,(1982) , 10.1109/TASSP.1982.1163845
Craig F. Ansley, Computation of the theoretical autocovariance function for a vector arma process Journal of Statistical Computation and Simulation. ,vol. 12, pp. 15- 24 ,(1980) , 10.1080/00949658008810423
Robert Kohn, Craig Ansley, A note on obtaining the theoretical autocovariances of an ARMA process Journal of Statistical Computation and Simulation. ,vol. 15, pp. 273- 283 ,(1982) , 10.1080/00949658208810594
D. F. NICHOLLS, A. D. HALL, THE EXACT LIKELIHOOD FUNCTION OF MULTIVARIATE AUTOREGRESSIVE-MOVING AVERAGE MODELS Biometrika. ,vol. 66, pp. 259- 264 ,(1979) , 10.1093/BIOMET/66.2.259
A.D. Hall, D.F. Nicholls, The evaluation of exact maximum likelihood estimates for varma models Journal of Statistical Computation and Simulation. ,vol. 10, pp. 251- 262 ,(1980) , 10.1080/00949658008810373