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1 ARMA Estimation on Process of ARMA Time Series Model

2 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.,

3 ARMA VBA Trend :T,Cyclic fluctuation :C,Seasonal variation :S Irregular motion :I Business fluctuation 1 Blackman-Tukey FFT

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

5 ARMA Jacobian Matrix

6 Sanno University Bulletin Vol.26 No. 2 February Hessian

7 ARMA termination criterion

8 Sanno University Bulletin Vol.26 No. 2 February

9 ARMA

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

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

12 Sanno University Bulletin Vol.26 No. 2 February Business Statistics 83

13 ARMA 3 1Blackman-Tukey

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

15 ARMA Blackman-Tukey 86

16 Sanno University Bulletin Vol.26 No. 2 February SARIMA A C 4 W 5 6 R JR A

17

Sanno University Bulletin Vol. No. February Casino Legalization and Its Influence to Local Japanese City Economies Nobukazu Shirai Satoshi Saito If ga

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