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ARMA Estimation on Process of ARMA Time Series Model

Sanno University Bulletin Vol.26 No. 2 February 2006 ARMA Estimation on Process of ARMA Time Series Model Many papers and books have been published on the subject of achieving the steadystate of the SARIMA time series model, which contains seasonal factors and its estimation. However, these papers or books do not always provide optimum methods for doing this. Therefore, many users depend on commercially available software. This paper studies the estimation of the steady-state time series model. Time series models are non-linear in nature. Maximum likelihood estimation or the least squares method is generally used for estimation. The least squares method is used for estimation in this research, and the Gauss-Newton method is used to find the solutions of the normal equations. Favorable results are acquired., 2005 10 3 73

ARMA VBA Trend :T,Cyclic fluctuation :C,Seasonal variation :S Irregular motion :I 1212 11 12 6 11 Business fluctuation 1 Blackman-Tukey FFT 1 12 74

Sanno University Bulletin Vol.26 No. 2 February 2006 cut-off 0 0 Akaike s Information Criterion 3 1 3 1 3 2 75

ARMA 3 3 3 4 3 5 Jacobian Matrix 3 6 3 4 76

Sanno University Bulletin Vol.26 No. 2 February 2006 3 7 2 3 8 3 92 3 9 3 10 Hessian 3 10 3 8 3 11 3 12 3 13 77

ARMA 3 142 21 3 14 3 15 3 133 11 3 15 termination criterion 3 16 3 17 3 18 78

Sanno University Bulletin Vol.26 No. 2 February 2006 3 19 3 20 3 21 0 79

ARMA 3 22 3 23 3 233 243 25 3 16 3 24 80

Sanno University Bulletin Vol.26 No. 2 February 2006 3 25 [step01] [step02] [step03] [step04] 81

ARMA [step05] Jacobian Matrix [ step06] Hessian [step07] [step08] step09, step04 [step09] 82

Sanno University Bulletin Vol.26 No. 2 February 2006 1947 11970 12 111 2 1971 Business Statistics 83

ARMA 3 1Blackman-Tukey 4 57 6 5 84

Sanno University Bulletin Vol.26 No. 2 February 2006 6 AIC 7 85

ARMA 1 11 2 3 Blackman-Tukey 86

Sanno University Bulletin Vol.26 No. 2 February 2006 1 SARIMA 72004 2 3 A C 4 W 5 6 R JR A 7 8 9 10 11 12 13 87