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Identification of stable elementary bilinear time-series model

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper presents new approach to estimation of the coefficients of an elementary bilinear time series model (EB). Until now, a lot of authors have considered different identifiability conditions for EB models which implicated different identifiability ranges for the model coefficient. However, all of these ranges have a common feature namely they are significantly narrower than the stability range of the EB model. This paper proposes a simple but efficient solution which makes an estimation of the EB model coefficient possible within its entire stability range.
Słowa kluczowe
Rocznik
Strony
577--595
Opis fizyczny
Bibliogr. 40 poz., rys., wykr., wzory
Twórcy
autor
  • Division of Industrial Informatics, Silesian University of Technology, Krasinskiego 8, 40-019 Katowice, Poland
Bibliografia
  • [1] A. Bibi: A note of the stability and causality of general time-dependent bilinear models. Statistics and Probability Letters, 73 (2005).
  • [2] A. Bibi and A. Oyet: Estimation of some bilinear time series models with time varying coefficients. Stochastic Analysis and Applications, 22 (2005).
  • [3] E. Bielinska: Identification of a mixed linear-bilinear diagonal time series model. Systems Science, 31 (2005).
  • [4] E. Bielinska: Bilinear time series in signal analysis. Zeszyty Naukowe Politechniki Slźskiej (in Polish), 2007.
  • [5] E. Bielinska: Bilinear time series models in signal analysis. In Zeszyty Naukowe Politechniki Slaskiej (in Polish), 2007.
  • [6] Isc E. Bielinska: Bilinear time series in signal analysis. In New Approaches in Automation and Robotics. I-Tech Education and Publishing, 2008.
  • [7] E. Bielinska and B. Zielinski: Bilinear models in adaptive control. Int. J. of Adaptive Control and Signal Processing, 14 2000
  • [8] K. Bouzachane, M. Harti and Y. Benghebrit: First-order superdiagonal bilinear time series for tracking software reliability. http://interstat.statjournals.net/YEAR/2006/articles/0602002.pdf,(2006).
  • [9] K. Bouzaachane, M. Harti and Y. Benghebrit: Parameter estimation for pure diagonal bilinear time series: An algorithm for maximum likelihood procedure. http://interstat.statjournals.net/YEAR/2006/articles/0602002.pdf,(2007).
  • [10] G. Box and G. Jenkins: Time Series Analysis: forecasting and control. Holdenday Inc, 1976.
  • [11] A. Brunner and G. Hess: Potential problems in estimating bilinear time-series models. J. of Economic Dynamics and Control, 19 (1995), 663-681.
  • [12] K. Chellapilla and S. Rao: Optimization of bilinear time series models using fast evolutionary programming. IEEE Signal Processing Letters, 5 (1998), 39-42.
  • [13] J. Gooijger and R. Heuts: Higher order moments of bilinear time series processes with symmetrically distributed errors. In Proc. of the Second Int. Tempere Conf. in Statistics, (1987), 467-478.
  • [14] C. Granger and A. Andersen: An introduction to bilinear time series models. Vandenhoeck and Ruprecht, 1978.
  • [15] C. Granger and A. Andersen: On the invertibility of time series models. Stochastic Processes and their Applications, 8 (1978), 87-92.
  • [16] D. Graupe: Identification and adaptive filtering. Robert E. Krieger Publishing Company, 1994.
  • [17] D. Guegan and D. T. Pham: A note on the estimation of the parameters of the diagonal bilinear model by method of least squares. Scandinavian J. of Statistics, 16 (1989), 129-136.
  • [18] O. Hili: Hellinger distance estimation of general bilinear time series models. Statistical Methodology, 5 (2008), 119-128.
  • [19] D. Hristova: Maximum likelihood estimation of a unit root bilinear model with application to prices. Studies in Nonlinear Dynamics and Econometrics, 9 (2005), 56-70.
  • [20] S. Iwaueze and J. Ohakwe: Penalties for misclassification of first order bilinear and linear moving average time series processes. Interstat J. of Statistics, (2009).
  • [21] W. Kim, L. Billard and I. Baswa: Estimation for first-order diagonal bilinear time series model. J. of Time Series Analysis, 11 (1990), 215-229.
  • [22] G. Kirchgässner and J. Wolters: Introduction to Modern Time Series Analysis. Springer Berlin Heidelberg, 2007.
  • [23] D. Kristensen: On stationarity and ergodicity of the bilinear model with applications to garch models. J. of Time Series Analysis, 30 (2005), 125-144.
  • [24] L. Malinski: The evaluation of saturation level for smse cost function in identification of elementary bilinear time-series model. In Proc. of the 17th Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2012).
  • [25] L. Malinski and E. Bielinska: Statistical analysis of minimum prediction error variance in the identification of a simple bilinear time-series model. In Advances in System Science. Academic Publishing House EXIT, 2010.
  • [26] L. Malinski and J. Figwer: On stationarity of bilinear time-series. In Proc. to 16th Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2013).
  • [27] C. Martins: A note on the autocorrelations related to bilinear model with nonindependent shocks. Statistics and Probability Letters, 36 (1997), 245-250.
  • [28] C. Martins: A note on third-order moment structure of a bilinear model with non-independent shocks. Portugaliae Mathematica, 56 (1999), 115-125.
  • [29] J. Mathews and J. Lee: Techniques for bilinear time series analysis. In 27-th Asilomar Conf. on Systems and Computers, (1993), 1016-1020.
  • [30] J. Mathews and T. Moon: Parameter estimation for a bilinear time series model. In Int. Conf. on Acoustics, Speech and Signal Processing, (1991), 3513-3516.
  • [31] R. Mohler and Z. Tang: On bilinear time-series modelling and estimation. In Proc. of the 27th Conf. on Decision and Control, Austin, Texas, (1988), 953-954.
  • [32] T. D. Pham: Bilinear markovian representation and bilinear modelss. Stochastic Processes and Their Applications, 20 (1985), 295-306.
  • [33] T. D. Pham: The mixing property of bilinear and generalised random coefficient autoregressive models. Stochastic Processes and Their Applications, 23 (1986), 291-300.
  • [34] M. Priestley: Nonlinear and Non-stationary Time Series Analysis. Academic Press Ltd., 1988.
  • [35] T. Subba Rao: On the theory of bilinear time series models. J. of the Royal Statistical Society B, 44 (1981), 244-255.
  • [36] M. Small: pplied Nonlinear Time Series Analysis. World Scientific Publishing Co. Pte. Ltd., 2005.
  • [37] C. Therrien: Discrete random signals and statistical signal processing. Prentice Hall International Editions, 1992.
  • [38] H. Tong: Non-linear time series. Clarendon Press, 1993.
  • [39] H. Wang: Parameter estimation and subset detection for separable lower triangular bilinear models. J. of Time Series Analysis, 26 (2004), 743-757.
  • [40] B. Wu and S. Hung: A fuzzy identification procedure for nonlinear time-series: With example on arch and bilinear models. Fuzzy Sets and Systems, 108 (1999), 275-287.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-de442e07-1e8e-47a2-b9bd-ce6adb825646
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