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By D.F. Findley

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Additional resources for Applied Time Series Analysis I. Proceedings of the First Applied Time Series Symposium Held in Tulsa, Oklahoma, May 14–15, 1976

Sample text

The general Bilinear Autoregressive Moving Average model of order (p,q,Q,P), BARMA(p,q,Q,P), is of the form 33 Non-Linear Time Series Modeling where eO 1. 1) is a simplification of the general non-linear model, with the property of linearity in the X variables and the € variables separately, but not in both. At this point, it is convenient to give names to several subclasses of the general model. Firstly, if p = 0, the model is said to be homogeneous in the output, which if q = 0, one has homogeneity in the input.

And G. M. Jenkins, (1970), Time Senes AnaZysis. Foreaasting and ControZ, San Francisco: Holden Day. Brockett, R. , (1975), "Parametrically Stochastic Linear Differential Equation," Mimeo: Harvard University, Department of Control Engineering. , G. DiPillo, and G. Koch, (1974), "Bilinear Systems: An Appealing Class of 'Nearly Linear' Systems in Theory and Applications," IEEE, 4, August, 1974. Granger, C. W. J. and P. Newbold, (1976a), "Forecasting Transformed Series," J. R. Statist. Soa. B, 38. Granger, C.

Firstly, if p = 0, the model is said to be homogeneous in the output, which if q = 0, one has homogeneity in the input. The models to be considered in this paper are homogeneous in both variables. 2) Let B be the «Q + 1) x p) matrix of the S coefficients. If Sij 0 for all j < i, the model is called superdiagonal. Here, the multiplicative terms with non-zero coefficients are such that the input factor €t-i occurs after the output factor Xt " so that these two terms are independent. Cor-J respondingly, the model is subdiagonal if Sij = 0 for all j > i and is said to be diagonal if S ..

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