The Story of a Model: The First-Order Diagonal Bilinear Autoregression

Abstract This paper deals with a detailed analysis of the first-order diagonal bilinear time series model, first proposed in Granger and Andersen (1978. An Introduction to Bilinear Time Series Models. Göttingen: Vandenhoeck & Ruprecht). This model allows for sequences of “outliers” in the data. We show that the model has a variety of features that we can observe in practice, while we also document that the bilinear features show up in just a limited number of observations. When the moment restrictions are close, parameter estimation becomes difficult. When the parameters are further away from the moment restrictions, parameter estimation is easy. Yet, in those latter cases, approximative linear models appear to generate equally accurate fit and forecasts. In sum, in cases of proper inference on a bilinear model, the model is barely relevant for forecasting.