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Kim, Won Kyung; Billard, L.; Basawa, I. V.

Estimation for the first-order diagonal bilinear time series model. (English) Zbl 0711.62078

J. Time Ser. Anal. 11, No. 3, 215-229 (1990).
The problem of estimation of the parameter b in the simple diagonal bilinear model \(\{X_ t\}\), \[ X_ t=e_ t+be_{t-1}X_{t-1}, \] is considered, where \(\{e_ t\}\) is Gaussian white noise with zero mean and possibly unknown variance \(\sigma^ 2\). The asymptotic normality of the moment estimator of b is established for the two cases when \(\sigma^ 2\) is known and \(\sigma^ 2\) is unknown. It is noted that the limit distribution of the least-squares cannot easily be derived analytically. A bootstrap comparison of the sampling distributions of the least-squares and moment estimates shows that both are asymptotically normal with the least-squares estimate being the more efficient.

Cited in 8 Documents

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
62F10 Point estimation

Keywords:

diagonal bilinear model; Gaussian white noise; asymptotic normality; moment estimator; bootstrap comparison; least-squares estimate
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\textit{W. K. Kim} et al., J. Time Ser. Anal. 11, No. 3, 215--229 (1990; Zbl 0711.62078)
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