Application of the theory of KM2O-Langevin equations to the non-linear prediction problem for the one-dimensional strictly stationary time series

Yasunori OKABE; Takashi OOTSUKA

doi:10.2969/jmsj/04720349

Application of the theory of KM₂O-Langevin equations to the non-linear prediction problem for the one-dimensional strictly stationary time series

Yasunori OKABE, Takashi OOTSUKA

著者情報

ジャーナルフリー

1995 年 47 巻 2 号 p. 349-367

DOI https://doi.org/10.2969/jmsj/04720349

詳細

Published: 1995 Received: 1993/02/05 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Application of the theory of KM₂O-Langevin equations to the nonlinear prediction problem for the one-dimensional strictly stationary time series
Right : Application of the theory of KM₂O-Langevin equations to the non-linear prediction problem for the one-dimensional strictly stationary time series

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Kiyoshi Ito on his seventy-seven birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. Durbin, The fitting of time series models, Rev. Int. Stat., 28 (1960), 233-244.
2) N. Levinson, The Wiener RMS error criterion in filter design and prediction, J. Math. Phys., 25 (1947), 261-278.
3) P. Masani, The prediction theory of multivariate stochastic processes, III, Unbounded spectral densities, Acta Math., 104 (1960), 141-162.
4) P. Masani and N. Wiener, Non-linear prediction, Probability and Statistics, The Harald Cramér Volume, (ed. U. Grenander), John Wiley, 1959, pp. 190-212.
5) Y. Okabe, On a stochastic difference equation for the multi-dimensional weakly stationary process with discrete time, Prospect of Algebraic Analysis, (ed. M. Kashiwara and T. Kawai), Academic Press, Tokyo, 1988, pp. 601-645.
6) Y. Okabe, Langevin equation and causal analysis, Sûgaku, 43 (1991), 322-346 (in Japanese).
7) Y. Okabe, Application of the theory of KM₂O-Langevin equations to the linear prediction problem for the multi-dimensional weakly stationary time series, J. Math. Soc. Japan, 45 (1993), 277-294.
8) Y. Okabe and A. Inoue, The theory of KM₂O-Langevin equations and its applications to data analysis (II): Causal analysis (I), Nagoya Math. J., 134 (1994), 1-28.
9) Y. Okabe and Y. Nakano, The theory of KM₂O-Langevin equations and its applications to data analysis (I): Stationay analysis, Hokkaido Math. J., 20 (1991), 45-90.
10) Y. Okabe and O. Ootsuka, The theory of KM₂O-Langevin equations and its applications to data analysis (III): Prediction analysis, in preparation.
11) P. Whittle, On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix, Biomerika, 50 (1963), 129-134.
12) N. Wiener, Collected Works, Vol. 3, The MIT Press, 1981.
13) N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes, I, The regularity condition, Acta Math., 98 (1957), 111-150.
14) N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes, II, The linear predictor, Acta Math., 99 (1958), 93-137.
15) R. A. Wiggins and E. A. Robinson, Recursive solution to the multichannel fitting problem, J. Geophys. Res., 70 (1965), 1885-1891.

Right : [1] J. Durbin, The fitting of time series models, Rev. Int. Stat., 28 (1960), 233-244.
[2] N. Levinson, The Wiener RMS error criterion in filter design and prediction, J. Math. Phys., 25 (1947), 261-278.
[3] P. Masani, The prediction theory of multivariate stochastic processes, III, Unbounded spectral densities, Acta Math., 104 (1960), 141-162.
[4] P. Masani and N. Wiener, Non-linear prediction, Probability and Statistics, The Harald Cramér Volume, (ed. U. Grenander), John Wiley, 1959, pp. 190-212.
[5] Y. Okabe, On a stochastic difference equation for the multi-dimensional weakly stationary process with discrete time, Prospect of Algebraic Analysis, (ed. M. Kashiwara and T. Kawai), Academic Press, Tokyo, 1988, pp. 601-645.
[6] Y. Okabe, Langevin equation and causal analysis, Sûgaku, 43 (1991), 322-346 (in Japanese).
[7] Y. Okabe, Application of the theory of KM₂O-Langevin equations to the linear prediction problem for the multi-dimensional weakly stationary time series, J. Math. Soc. Japan, 45 (1993), 277-294.
[8] Y. Okabe and A. Inoue, The theory of KM₂O-Langevin equations and its applications to data analysis (II): Causal analysis (I), Nagoya Math. J., 134 (1994), 1-28.
[9] Y. Okabe and Y. Nakano, The theory of KM₂O-Langevin equations and its applications to data analysis (I): Stationay analysis, Hokkaido Math. J., 20 (1991), 45-90.
[10] Y. Okabe and O. Ootsuka, The theory of KM₂O-Langevin equations and its applications to data analysis (III): Prediction analysis, in preparation.
[11] P. Whittle, On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix, Biomerika, 50 (1963), 129-134.
[12] N. Wiener, Collected Works, Vol. 3, The MIT Press, 1981.
[13] N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes, I, The regularity condition, Acta Math., 98 (1957), 111-150.
[14] N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes, II, The linear predictor, Acta Math., 99 (1958), 93-137.
[15] R. A. Wiggins and E. A. Robinson, Recursive solution to the multichannel fitting problem, J. Geophys. Res., 70 (1965), 1885-1891.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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