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On the Theory of Bilinear Time Series Models
Abstract
SUMMARY: The theory of bilinear time series models is considered in this paper. The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained. The conditions for the invertibility of the model are also included. The estimation of the parameters of the scalar bilinear time series model is considered. The bilinear models are fitted to sunspot numbers and also to a P-wave of a nuclear explosion. The forecasting of sunspot numbers is also considered.
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Cites
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Threshold Autoregression, Limit Cycles and Cyclical Data
Tong, H., & Lim, K. S. (1980) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1980.tb01126.x · Cited by 1,309
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Nonlinear problems in random theory
(1959) · Journal of the Franklin Institute · doi:10.1016/0016-0032(59)90191-7 · Cited by 982
Natural Bilinear Control Processes
Mohler, R. R. (1970) · IEEE Transactions on Systems Science and Cybernetics · doi:10.1109/tssc.1970.300341 · Cited by 403
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Recurrent neural networks and robust time series prediction
Connor, J. T., Martin, R. D., & Atlas, L. E. (1994) · IEEE Transactions on Neural Networks · doi:10.1109/72.279188 · Cited by 1,316
Threshold Autoregression, Limit Cycles and Cyclical Data
Tong, H., & Lim, K. S. (1980) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1980.tb01126.x · Cited by 1,309
Modelling Nonlinear Economic Time Series
Teräsvirta, T., Tjøstheim, D., & Granger, C. W. J. (2010) · doi:10.1093/acprof:oso/9780199587148.001.0001 · Cited by 352
Prognosis of machine health condition using neuro-fuzzy systems
Wang, W. Q., Golnaraghi, M. F., & Ismail, F. (2004) · Mechanical Systems and Signal Processing · doi:10.1016/s0888-3270(03)00079-7 · Cited by 329
Evidence of Nonlinearity in Daily Stock Returns
Hinich, M. J., & Patterson, D. M. (1985) · Journal of Business & Economic Statistics · doi:10.1080/07350015.1985.10509428 · Cited by 288
Metadata
- Authors
- Rao, T. S.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1981-01-01
- Volume
- 43
- Issue
- 2
- Pages
- 244-255
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2408011753
- Cited by
- 256
- References
- 17
- FWCI
- 13.48
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
