Forecasting in One-Dimensional and Generalized Integrated Autoregressive Moving Average Bilinear Time Series Models

Abstract

In this paper, forecast of one-dimensional integrated autoregressive moving average bilinear time series model is compared with forecast of generalized integrated autoregressive moving average bilinear time series model. We described methods for estimation of these models and the forecast. It is also pointed out that for this class of non-linear time series models; it is possible to obtain optimal forecast. The estimation technique is illustrated with respect to a time series, and the optimal forecast of these time series are calculated. A comparison of these forecasts is made using the two models under study. The mean square error for forecast in one-dimensional integrated autoregressive moving average bilinear model is smaller than the mean square error for forecast in generalized integrated autoregressive moving average bilinear model. Though the two models are adequate for forecast when compared with the real series but forecast with one-dimensional integrated autoregressive moving average bilinear model is more adequate.