A survey of the most frequently used criteria for determination of the order of autoregressive models is presented. Algorithms based on extremal filtration, linear forecasting, as well as addition of a reference component to the signal are proposed. It is demonstrated that neural networks may be used to solve the problem.
Similar content being viewed by others
References
S. L. Marple, Jr., Digital Spectral Analysis and Applications [Russian translation], Mir, Moscow (1990).
S. M. Key and S. L. Marple, Jr., “Modern methods of spectral analysis. A survey,” TIIER, No. 11, 5–51 (1981).
B. V. Tsypin et al., “Application of methods of digital spectral estimation in the measurement of the parameters of a signal,” Izmer. Tekhn., No. 10, 26–30 (2010); Measur. Techn., 53, No. 10, 1118–1124 (2010).
M. G. Myasnikova and V. V. Kozlov, “Methods of determining the order of an autoregressive model,” in: Modern Problems of Estimation in Engineering Applications: Proc. 1st Int. Sci.-Tech. Conf., Yaroslavl (2005), pp. 354–364.
R. J. Hyndman, Empirical Information Criteria for Time Series Forecasting Model Selection: Working Paper, B. Billah, R. J. Hyndman, and A. B. Koehler (eds.), Dept. Econometrics and Business Statistics, Monash University, Australia (2003).
R. Schibata, “Selection of the order of an autoregressive model by Akaike’s information criterion,” Biometrika, No. 63, 147–164 (1976).
G. Schwarz, “Estimating the dimension of a model,” Annals Stat., 6, No. 2, 461–464 (1978).
M. P. Stroganov, N. V. Myasnikova, and M. P. Beresten, “Approximation of multi-extremal functions and its applications in technical systems,” in: Problems of Automation and Control in Technical Systems: Proc. Int. Sci.-Tech. Conf., Izd. Penza State University, Penza (2009), pp. 387–390.
N. E. Huang et al., “The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis,” Proc. Royal Soc. London, 454, pp. 903–995 (1998).
M. G. Myasnikova, “Implementation of Prony’s methods on neutral networks,” in: Problems of Automation and Control in Technical Systems: Interuniv. Coll. Sci. Works, Izd. Penza State University, Penza (2005), Iss. 24, pp. 151–158.
V. V. Kozlov, “Use of artificial neural networks for determination of the order of an autoregressive model,” Information Instruments: Proc. Penza State University, Penza (2008), Iss. 33, pp. 33–45.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izmeritel’naya Tekhnika No. 4 pp. 38–41 2011.
Rights and permissions
About this article
Cite this article
Dmitrienko, A.G., Myasnikova, M.G. & Tsypin, B.V. Estimating the order of autoregressive models in approximation of signals. Meas Tech 54, 416–421 (2011). https://doi.org/10.1007/s11018-011-9741-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11018-011-9741-9