Estimation of non-stationary spectra by simulated annealing. (English) Zbl 0875.62431
Summary: The simulated annealing method has been applied to the estimation of non-stationary spectra. In the estimation, the simulated annealing method is used to minimize the mean square percentage error which is a nonlinear function with many local minima. The estimation based on simulated annealing has the advantage of being more reliable in finding the global minimum. Moreover, the method of simulated annealing requires much less prior knowledge on the non-stationary spectrum. Some concerns about the application of simulated annealing to the estimation of non-stationary spectra are also discussed in this paper.
MSC:
| 62M15 | Inference from stochastic processes and spectral analysis |
References:
| [1] | Bowden J., Review of Economic Study 41 pp 173– (1974) · Zbl 0276.90006 · doi:10.2307/2296711 |
| [2] | Hajek B., Mathematics of Operations Research 13 (2) pp 311– (1988) · Zbl 0652.65050 · doi:10.1287/moor.13.2.311 |
| [3] | Hammond K., Journal of Royal Statistical Society 35 (2) pp 167– (1973) |
| [4] | Hasofer M., Journal of Advanced Applied Probability 10 (2) pp 711– (1978) · Zbl 0402.60038 · doi:10.2307/1426649 |
| [5] | Kirkpatrick S., Science 220 (2) pp 671– (1983) · Zbl 1225.90162 · doi:10.1126/science.220.4598.671 |
| [6] | Johnson M. E., Simulated Annealing (SA) and Optimization: Modern Algorithms with VLSI, Optimal Design, and Missile Defense Applications (1988) |
| [7] | Metropolis N., Journal of Chemical Physics 21 pp 1087– (1953) · doi:10.1063/1.1699114 |
| [8] | Page H., Journal of Applied Physics 23 pp 103– (1952) · Zbl 0047.37702 · doi:10.1063/1.1701949 |
| [9] | Press W., Numerical Recipes in C (1988) · Zbl 0661.65001 |
| [10] | Priestley M. B., Journal of Royal Statistical Society, Series B 27 pp 204– (1965) |
| [11] | Priestley M. B., Spectral Analysis and Time Series (1981) · Zbl 0537.62075 |
| [12] | Rao G., Management Sciences 17 pp 208– (1970) · Zbl 0204.51901 · doi:10.1287/mnsc.17.3.208 |
| [13] | Tjtheim D., Journal of Advanced Applied Probability 8 pp 820– (1976) · Zbl 0359.60012 · doi:10.2307/1425936 |
| [14] | Van Laarhoven P. J. M., Simulated Annealing:Theory and Applications (1987) · doi:10.1007/978-94-015-7744-1 |
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