Initial and final estimates of the Bilinear seasonal time series model

Abstract

A particular class of non-linear models which has been found to be useful in many fields is the bilinear models. A special class of it is discussed in this paper. In getting the estimates of the parameters of this model special attention was paid to the problem of having good initial estimates as it is proposed that with good initial values of the parameters the estimates obtaining by the Newton-Raphson iterative technique usually not only converge but also are good estimates. In this paper we examined the initial and final estimates of the bilinear seasonal time series model. The Box-Jenkins linear convergence process, the Newton-Raphson iterative procedure, the Fortran Progran and the MINITAB software package were all employed in achieving both the initial estimates and the final estimates of the bilinear seasonal time series model studied. The results showed considerable closeness between the initial estimates and the final estimates for both simulations (n - 100 and n - 500). This confirmed that the initial estimates are good enough. The implication of this is that in estimations of this nature efforts should be made using the right procedures to achieve good initial estimates so that the final estimates could be achieved quickly after few iterations. JONAMP Vol. 11 2007: pp. 615-620