Abstract
There are no definitive solutions available for the order estimation of the auto-regressive process. First, the performance of the three criteria, namely FPE, AIC and MDL is illustrated. Next, it is indicated that there are possibilities of their performance being improved. The algorithmtri proposed here utilizes three minimum values of any of the conventional loss functions in the FPE, AIC and MDL methods. It also uses three statistics derived from these three minimum values. The estimated order is a rounded weighted average of these six statistics. The algorithm is found to do better in a qualified sense of yielding peakier distribution of the estimated orders when tested for 1000 synthetic models of orders 3, 5 and 7 each. The conclusion drawn is that there are open possibilities of improving upon the conventional order estimators for auto-regressive processes. This means that till axiologically sounder estimators are available one should be ready to use heuristic estimators proposed here.
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References
Akaike H 1969 Power spectrum estimation through autoregressive model fitting.Ann. Inst. Stat. Math. 21: 407–409
Akaike H 1970 Statistical predictor identification.Ann. Inst. Stat. Math. 22: 203–217
Akaike H 1973 Maximum likelihood identification of Gaussian autoregressive moving average models.Biometrika 60: 255–265
Akaike H 1974 A new look at statistical model identification.IEEE. Trans. Autom. Control 19: 716–723
Alexander S T 1986Adaptive signal processing, theory and applications (New York: Springer Verlag) pp. 34–45, 99–110
Anderson C A 1963 Simplicity in structural geology. InThe fabric of geology (ed.) C C Albritton. Jr (Stanford: Freeman, Cooper) pp. 175–183
Barnett V, Lewis T 1978Outliers in statistical data (Chichester: John Wiley) pp. 25–48
Bernal J D 1969Science in history, The emergence of science (Harmondsworth: Pelican) 1: 301
Box G E, Jenkins G M 1976Time series analysis: forecasting and control (San Francisco: Holder Day) p. 575
Broersen M T, Wensink H E 1993 On finite sample theory for autoregressive model order selection.IEEE Trans. Signal Process. 41: 194–204
Constable S C, Parker R L, Constable C G 1987 Occam’s inversion, a practical algorithm for generating smooth models for electromagnetic sounding data.Geophysics 52: 289
Diaconis P, Efron B 1983 Computer intensive methods in statistics.Sci. Am. 248: 116
Hoel P G 1966Introduction to mathematical statistics (New York: John Wiley) p. 44
Judge G G, Bock M E 1978The statistical implications of pretest and Stein-rule estimators in econometrics (Amsterdam: North Holland) p. 340
Kay S M, Marple S L Jr 1981 Spectrum analysis — a modern perspective.Proc. IEEE 69: 1380–1419
Makhoul J 1975 Linear prediction: A tutorial review.Proc. IEEE 63: 561–580
Moharir P S 1985 Predictive deconvolution. Parts 1 & 2.J. Inst. Electron. Telecommun. Eng. 31: 111–121, 157–168
Moharir P S 1988 Central tendency and dispersion: a broader lookProc. 6th Indian Geol. IGC, Roorkee, pp. 217–219
Moharir P S 1991 Non-optimality and positive Occamic gradient.Inst. Eng. India J. 71: 116–121
Moharir P S 1993 Induced Condorcet paradox. InSignal processing and communications (eds) T V Sreenivas, K V S Hari (New Delhi: Tata McGraw-Hill) 129–134
Proakis J G, Manolakis D G 1989Introduction to digital signal processing (London: Maxwell Macmillan) 203–205
Rissanen J 1983 A universal prior for the integers and estimation by minimum description length.Ann. Stat. 11: 417: 431
Shibata R 1976 Selection of order of an autoregressive model by Akaike’s information criterion.Biometrika 73: 117–126
Vinod H D, Ullah 1981Recent advances in regression methods (New York: Marcel Dekker)
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Sudarshan Rao, N., Moharir, P.S. Estimation of the order of an auto-regressive model. Sadhana 20, 749–758 (1995). https://doi.org/10.1007/BF02744408
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DOI: https://doi.org/10.1007/BF02744408