PORTUGALIAE MATHEMATICA Vol. 56, No. 1, pp. 115125 (1999) 

A Note on the ThirdOrder Moment Structure of a Bilinear Model with NonIndependent ShocksC.M. MartinsDep. de Matemática, Faculdade de Ciências e Tecnologia da Universidade de Coimbra,Universidade de Coimbra  PORTUGAL Abstract: Formulas for the thirdorder theoretical moments are obtained for the bilinear time series $X_t=\beta\,X_{tk}\,\varepsilon_{tl}+\varepsilon_t$, $k\ge l\ge 1$, assuming that $\{\varepsilon_t\}$ is a strictly stationary and ergodic sequence of random variables such that, for each $t\in\bkZ$, $\varepsilon_t$ has some conditional moments that are finite. Thus, Gabr's results (1988), obtained with an independent and identically distributed Gaussian sequence $\{\varepsilon_t\}$, are generalized. Keywords: Bilinear models; conditional expectation; ergodicity; stationarity; thirdorder moments. Classification (MSC2000): 62M10. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 1999 Sociedade Portuguesa de Matemática
