Canonical correlation analysis of time series and the use of an information criterion

Mathematics in Science and Engineering

Volumn 126, Issue C, 1976, Pages 27-96

  Akaike, Hirotugu ^a  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956828132     PISSN: 00765392     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0076-5392(08)60869-3     Document Type: Article

References (35)

1. Blackmann, R.B., Tukey, J.W., The Measurement of Power Spectra, 2nd ed., 1959, Dover, New York.
2. Jenkins, G.M., Watts, D.G., Spectral Analysis and Its Applications, 1968, Holden-Day, San Francisco.
3. Akaike, H., “On the Use of an Index of Bias in the Estimation of Power Spectra,”. Ann. Inst. Statist. Math. 20 (1968), 55–69.
4. Yule, G.U., “On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers,”. Phil. Trans. A226 (1927), 267–298.
5. Akaike, H., “Fitting Autoregressive Models for Prediction,”. Ann. Inst. Statist. Math. 21 (1969), 243–247.
6. Akaike, H., “Statistical Predictor Identification,”. Ann. Inst. Statist. Math. 22 (1970), 203–217.
7. Akaike, H., “On a Semiautomatic Power Spectrum Estimation Procedure,” in Proc. 3rd Hawaii Int. Conf. System Sciences, 1970, pp. 974–977.
8. Gersch, W., Sharpe, D.R., “Estimation of Power Spectra with Finite-Order Autoregressive Models,”. IEEE Trans. Automat. Contr. AC-18 (1973), 367–379.
9. Jones, R.H., “Identification and Autoregressive Spectrum Estimation,”. IEEE Trans. Automat. Contr. AC-19 (1974), 894–898.
10. Akaike, H., “Autoregressive Model Fitting for Control,”. Ann. Inst. Statist. Math. 23 (1971), 163–180.
11. Otomo, T., Nakagawa, T., Akaike, H., “Statistical Approach to Computer Control of Cement Rotary Kilns,”. Automatica 8 (1972), 35–48.
12. Akaike, H., Nakagawa, T., Statistical Analysis and Control of Dynamic Systems, 1972, Saiensu-sha, Tokyo (In Japanese, with a list of a computer program package TIMSAC for time series analysis and control written in a Fortran IV type language and with English comments.).
13. Akaike, H., “Information Theory and an Extension of the Maximum Likelihood Principle,” in 2nd International Symposium on Information Theory, B. N. Petrov and F. Csaki, eds., Akademiai Kiado, Budapest, 1973, pp. 267–281.
14. Akaike, H., “A New Look at the Statistical Model Identification,”. IEEE Trans. Automat. Contr. AC-19 (1974), 716–723.
15. Box, G.E.P., Jenkins, G.M., Time Series Analysis, Forecasting and Control, 1970, Holden-Day, California.
16. Akaike, H., “Stochastic Theory of Minimal Realization,”. IEEE Trans. Automat. Contr. AC-19 (1974), 667–674.
17. Akaike, H., “Markovian Representation of Stochastic Processes and its Application to the Analysis of Autoregressive Moving Average Processes,”. Ann. Inst. Statist. Math. 26 (1974), 363–387.
18. Kullback, S., Information Theory and Statistics, 1959, Wiley, New York.
19. Boltzmann, L., “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht,”. Wiener Berichte 76 (1877), 373–435.
20. Chernoff, H., “Large Sample Theory - Parametric Case,”. Ann. Math. Stat. 27 (1956), 1–22.
21. Rao, C.R., “Efficient Estimates and Optimum Inference Procedure in Large Sample,”. J. Roy. Statist. Soc., B. 24 (1962), 46–72.
22. Åström, K.J., Eykhoff, P.E., “System Identification - A Survey,”. Automatica 7 (1971), 123–162.
23. Anderson, T.W., Introduction to Multivariate Statistical Analysis, 1958, Wiley, New York.
24. Goloub, G.H., “Matrix Decompositions and Statistical Calculations,”. Milton, R.C., Nelder, J.A., (eds.) Statistical Computation, 1969, Academic Press, New York, 365–397.
25. Ho, B.L., Kalman, R.E., “Effective Construction of Linear State-Variable Models from Input/Output Functions,”. Regelungestechnik 14 (1966), 545–548.
26. Akaike, H., “Markovian Representation of Stochastic Processes by Canonical Variables,”. SIAM J. Control 13 (1975), 162–173.
27. Åström, K.J., Källström, C.G., “Application of System Identification Techniques to the Determination of Ship Dynamics,”. Eykhoff, P., (eds.) Identification and System Parameter Estimation, 1973, North-Holland Publishing Co., Amsterdam, 415–424.
28. Whittle, P., “On the Fitting of Multivariate Autoregressions, and the Approximate Factorization of a Spectral Density Matrix,”. Biometrika 50 (1963), 129–134.
29. Akaike, H., “Block Toeplitz Matrix Inversion,”. SIAM J. Appl. Math. 24 (1973), 234–241.
30. Gupta, N.K., Mehra, R.K., “Computational Aspects of Maximum Likelihood Estimation and Reduction in Sensitivity Function Calculation,”. IEEE Trans. Automat. Contr. AC-19 (1974), 774–783.
31. Mehra, R. K., “Maximum Likelihood Identification of Aircraft Parameters,” in 1970 Joint Automatic Control Conf., Preprints, Atlanta, Georgia, June 1970.
32. Mehra, R.K., “Identification of Stochastic Linear Dynamic Systems,”. AIAA Journal 9 (1971), 28–31.
33. Akaike, H., “Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models,”. Biometrika 60 (1973), 255–265.
34. Akaike, H., E. Arahata and T. Ozaki, “TIMSAC-74 - A Time Series Analysis and Control Program Package - (1),”Computer Science Monographs, No. 5, The Institute of Statistical Mathematics, Tokyo, March 1975.
35. Fisher, R. A., “Uncertain Inference,” Proceedings of the American Academy of Arts and Sciences, 71, 1936, pp. 245–258.