ON THE THIRD‐ORDER MOMENT STRUCTURE AND BISPECTRAL ANALYSIS OF SOME BILINEAR TIME SERIES
- 1 January 1988
- journal article
- Published by Wiley in Journal of Time Series Analysis
- Vol. 9 (1) , 11-20
- https://doi.org/10.1111/j.1467-9892.1988.tb00449.x
Abstract
For the bilinear time series modelXt=βXt‐ket‐t+et, k > l, k = l andk<lformulae for the third‐order theoretical moments and an expression for the bispectral density function are obtained. These results can be used to distinguish between bilinear models and white noise and, in general, linear models. Furthermore, they give an indication of the type combination (k, l) in the above model. The modulus of the bispectral density function of the above bilinear time series model for different combinations of (k, l) and values ofβare computed and the properties are studied.Keywords
This publication has 7 references indexed in Scilit:
- ON THE IDENTIFICATION OF SOME BILINEAR TIME SERIES MODELSJournal of Time Series Analysis, 1986
- ON THE AUTOCORRELATION STRUCTURE AND IDENTIFICATION OF SOME BILINEAR TIME SERIESJournal of Time Series Analysis, 1984
- A note on bilinear time series modelsStochastic Processes and their Applications, 1982
- Stationarity and invertibility of simple bilinear modelsStochastic Processes and their Applications, 1982
- THE ESTIMATION AND PREDICTION OF SUBSET BILINEAR TIME SERIES MODELS WITH APPLICATIONSJournal of Time Series Analysis, 1981
- On the Theory of Bilinear Time Series ModelsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1981
- Non-Linear Models in Time Series AnalysisJournal of the Royal Statistical Society: Series D (The Statistician), 1978