A new algorithm for recursive estimation of parameters in controlled ARMA processes. (English) Zbl 0559.93076
A new algorithm for recursive estimation of parameters in controlled ARMA processes is presented. Following J. Durbin’s [Bull. Int. Stat. Inst. 38, 273-282 (1961; Zbl 0104.378)] two-stage least squares algorithm, this is actually a recursive multi-step method in which least squares are used in each step. It is shown that the estimate is p- consistent and p-efficient, i.e. the properties of consistency and efficiency are approached arbitrarily closely as p tends to infinity.
Reviewer: I.Valuşescu
MSC:
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 93E10 | Estimation and detection in stochastic control theory |
| 62L12 | Sequential estimation |
Citations:
Zbl 0104.378References:
| [1] | (Hammond, P. H., Adaptive Control (1966), Plenum Press: Plenum Press New York) · Zbl 0156.40801 |
| [2] | Åström, K. J.; Mayne, D. Q., A new algorithm for recursive estimation of controlled ARMA processes, (Proc. 6th IFAC Symposium on Identification and Systems Parameters Estimation. Proc. 6th IFAC Symposium on Identification and Systems Parameters Estimation, Arlington, Virginia, USA (1982)), 122-126 · Zbl 0559.93076 |
| [3] | Clarke, D. W., Generalized least-squares estimation of the parameters of a dynamic model, paper 3.17, (Proc. IFAC Symposium on Identification in Automatic Control Systems. Proc. IFAC Symposium on Identification in Automatic Control Systems, Prague, Czechoslovakia (1967)) |
| [4] | Davis, K. H., M.Sc. Thesis (1978), Imperial College: Imperial College London, U.K |
| [5] | Durbin, J., The fitting of time-series models, Revue Inst. Int. de Stat., 28, 233-243 (1961) · Zbl 0101.35604 |
| [6] | Ljung, L., Analysis of recursive stochastic algorithms, IEEE Trans., AC-22, 551-575 (1977) · Zbl 0362.93031 |
| [7] | Mayne, D. Q.; Firoozan, F., An efficient multi-stage, linear identification method for ARMA processes, (Proc. JACC (1977)), 435-438 · Zbl 0488.93055 |
| [8] | Mayne, D. Q.; Firoozan, F., Linear estimation of ARMA systems, (Proc. IFAC 7th World Congress. Proc. IFAC 7th World Congress, Helsinki (1978)) · Zbl 0459.93049 |
| [9] | Mayne, D. Q.; Firoozan, F., Linear identification of ARMA processes, Automatica, 18, 461-466 (1982) · Zbl 0488.93055 |
| [10] | Panuska, V., An adaptive recursive least-squares identification algorithm, (Proc. JACC (1968)) · Zbl 0428.93067 |
| [11] | Söderström, T.; Ljung, L.; Gustavson, I., A comparative study of recursive identification methods, (Report 7427 (1974), Department of Automatic Control, Lund Institute of Technology: Department of Automatic Control, Lund Institute of Technology Lund, Sweden) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
