%0 Journal Article
%T On the Estimation and Performance of One-dimensional Autoregressive Integrated Moving Average Bilinear Time Series Models
%A J.F. Ojo
%J Asian Journal of Mathematics & Statistics
%D 2010
%I Asian Network for Scientific Information
%X In this study, full and subset one-dimensional autoregressive integrated moving average bilinear models which are capable of achieving stationarity for all non linear series are proposed and were compared to determine which of them perform better. The parameters of the proposed models were estimated using Newton-Raphson iterative method and an algorithm is proposed to eliminate redundant parameters from the full models to have subset models. Akaike Information Criterion (AIC) was used to determine the order of the model. To determine the best model, the residual variance attached to the proposed full and subset models were studied. In the fitted models different sample sizes were used and the statistical properties of the derived estimates are investigated. It was found that the residual variance attached to the full bilinear model was smaller than the subset model and this was so because of the introduction of the d factor in our new models which has made us to capture trend and seasonality in the data, which in turn helps arrive at stationarity easily for any time series data set and at the same time made the full model a better model.
%K residual variance
%K newton-raphson
%K Parameters
%K algorithm and stationarity
%U http://docsdrive.com/pdfs/ansinet/ajms/2010/225-236.pdf