### Abstract

It should be noted that for linear bivariate models, the third order cross moments γ

xy (k, 1)= 0 for all k and 1. Hence looking at a table of the third order cross moments one can

easily distinguish bivariate bilinear models from linear bivariate models (assuming the

distribution of noise is Gaussian and series xt had been prewhitened). Again, one can also

distinguish between Tables 2, 3, and 4, ie, between diagonal, subdiagonal, and

superdiagonal bivariate bilinear models by looking at these tables. It may also be possible to

distinguish the lags of the particular model by carefully looking at the table. It may be more

interesting to look at the third order cross moment table for a few more general bivariate

bilinear models.

xy (k, 1)= 0 for all k and 1. Hence looking at a table of the third order cross moments one can

easily distinguish bivariate bilinear models from linear bivariate models (assuming the

distribution of noise is Gaussian and series xt had been prewhitened). Again, one can also

distinguish between Tables 2, 3, and 4, ie, between diagonal, subdiagonal, and

superdiagonal bivariate bilinear models by looking at these tables. It may also be possible to

distinguish the lags of the particular model by carefully looking at the table. It may be more

interesting to look at the third order cross moment table for a few more general bivariate

bilinear models.

Original language | English |
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Title of host publication | Nonlinear Time Series and Signal Processing |

Editors | R R Mohler |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 59-74 |

Number of pages | 15 |

ISBN (Electronic) | 978-3-540-38837-1 |

ISBN (Print) | 978-3-540-18861-2 |

DOIs | |

Publication status | Published - 1988 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 106 |

ISSN (Print) | 0170-8643 |

### Fingerprint

### Cite this

Kumar, K. (1988). Bivariate bilinear models and their specification. In R. R. Mohler (Ed.),

*Nonlinear Time Series and Signal Processing*(pp. 59-74). (Lecture Notes in Control and Information Sciences; Vol. 106). Berlin: Springer. https://doi.org/10.1007/BFb0044275