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ON THE THIRD‐ORDER MOMENT STRUCTURE AND BISPECTRAL ANALYSIS OF SOME BILINEAR TIME SERIES
Author(s) -
Gabr M. M.
Publication year - 1988
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1988.tb00449.x
Subject(s) - mathematics , bilinear interpolation , white noise , order (exchange) , series (stratigraphy) , bilinear form , mathematical analysis , pure mathematics , statistics , paleontology , finance , economics , biology
For the bilinear time series model X t =βX t‐k e t‐t + e t , k > l, k = l and k < l formulae 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 of β are computed and the properties are studied.