A Note on the Third-Order Moment Structure of a Bilinear Model with Non-Independent Shocks

C.M. Martins

Abstract: Formulas for the third-order theoretical moments are obtained for the bilinear time series $X_t=\beta\,X_{t-k}\,\varepsilon_{t-l}+\varepsilon_t$, $k\ge l\ge 1$, 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; third-order moments.

Classification (MSC2000): 62M10.

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