Abstract
We consider in a first part the problem of the identification of the order of a bilinear model. We investigate different methods based on the use of recurrence’s function on the higher order moments. We establish the recurrent relations on the third order moment for a general superdiagonal model BL(p, q, P, Q), and for this model we obtain the asymptotic distribution of Glasbey’s statistic which permits to have a consistency method to identify the parameters p and max(q, Q). In a second part we examine the problem of the prediction for non-linear models and we give for the AR (p) with ARCH (p) noise model and for the diagonal Bilinear model the analytic expression of the function of prediction.
Joint work with PHAM T.D. LMC, Universite Grenoble 1 BP53x–38041 Grenoble France.
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© 1993 Springer-Verlag New York, Inc.
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Guegan, D. (1993). On the Identification and Prediction of Nonlinear Models. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_11
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DOI: https://doi.org/10.1007/978-1-4613-9296-5_11
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