×

Estimation and setting starting values in ARMA algorithms. (English) Zbl 0768.93078

Summary: For the given observations set of the ARMA (autoregressive moving average) process, the likelihood function depends, not only on model parameters, but on the starting values of the input and output. Therefore, it is called the conditional likelihood function. The unconditional likelihood function can be obtained in two ways. The first is to set the starting values to zero, as is often done, and the second is to set them to the properly estimated values. The difference between these two types of likelihood functions is significant when the given data sequence is short, and any of the zeros of the moving average part is close to the boundary of the unit circle.
In this paper the direct method of starting value estimation and its application to two off-line ARMA estimation algorithms, the maximum likelihood (ML) algorithm and the iterative inverse filtering (ITIF) algorithm, is proposed. Experimental results prove both increased efficiency and stability of these algorithms.
The importance of setting the starting values properly is also significant when the recursive algorithm, with previously estimated parameters, has to be restarted. The advantage of the proposed reinitialization method is shown on the recursive lattice algorithm working in the block mode.

MSC:

93E03 Stochastic systems in control theory (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] U. Appel and A. V. Brandt, Adaptive sequential segmentation of piecewise stationary time series,Inform. Sci., Vol. 29, No. 1, 1983, pp. 27–56. · Zbl 0584.62155 · doi:10.1016/0020-0255(83)90008-7
[2] G. P. Box and G. M. Jenkins,Time Series Analysis Forecasting and Control, Holden-Day, San Francisco, CA, 1970. · Zbl 0249.62009
[3] B. Friedlander, Lattice filters for adaptive processing,Proc. IEEE, Vol. 70, No. 8, Aug. 1982, pp. 892–1017.
[4] B. P. Furht, Maximum likelihood identification of Åström model by quasilinearization,Proc. 3rd IFAC Symp. on Identification of System Parameter Estimates, The Hague, 12–15 June 1973, Pt. 2, pp. 737–740.
[5] I. Konvalinka, Generation of pseudorandom signals with prescribable amplitude spectrum,Proc. XXIInd ETAN Conf., Struga, Yugoslavia, June 1983, pp. IV.215–IV.218.
[6] I. Konvalinka and M. R. Mataušek, Simultaneous estimation of poles and zeros in speech analysis and ITIF–iterative inverse filtering algorithm,IEEE Trans. Acoust. Speech Signal Process., Vol. 27, Oct. 1979, pp. 485–491. · doi:10.1109/TASSP.1979.1163276
[7] L. Ljung,Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1983. · Zbl 0548.93075
[8] M. M. Milosavljević. The modified generalized likelihood ratio algorithm (MGLR) for automatic detection of abrupt changes in stationarity of signals,Proc. XXIInd Annual Conf. on Systems, Princeton, NJ, 1988.
[9] Z. Šarić and S. Turajlić, Reinitialization of the recursive estimation ARMA model,Proc. Vth European Signal Processing Conf., Barcelona, 18–21 September 1990, pp. 205–208.
[10] S. R. Turajlić and V. Čurčić, Setting free parameters in the initialization of adaptive lattice algorithms,Proc. XXXIInd ETAN Conf., Sarajevo, June 1988.
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.