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

Philip Hans Franses

Journal of Econometric Methods2025https://doi.org/10.1515/jem-2024-0025article
AJG 1ABDC B
Weight
0.37

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.

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https://doi.org/https://doi.org/10.1515/jem-2024-0025

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@article{philip2025,
  title        = {{The Story of a Model: The First-Order Diagonal Bilinear Autoregression}},
  author       = {Philip Hans Franses},
  journal      = {Journal of Econometric Methods},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1515/jem-2024-0025},
}

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Evidence weight

0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.