Asymptotics for a class of generalized multicast autoregressive processes |
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Authors: | S.Y. Hwang Kee-Hoon Kang |
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Affiliation: | 1. Department of Statistics, Sookmyung Women’s University, Seoul 140-742, Republic of Korea;2. Department of Statistics, Hankuk University of Foreign Studies, Yongin 449-791, Republic of Korea |
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Abstract: | We propose a new class of generalized multicast autoregressive (GMCAR, for short, hereafter) models indexed by a multi-casting tree where each individual produces exactly the same number of offspring. This class includes standard bifurcating autoregressive processes (BAR, cf. Cowan and Staudte (1986)) and multicast autoregressive (MCAR, cf. Hwang and Choi (2009)) models as special cases. Accommodating non-Gaussian, non-negative and count data, the class includes various models such as nonlinear autoregression, conditionally heteroscedastic process and conditional exponential family. The pathwise stationarity of the GMCAR model is discussed. A law of large numbers and a central limit theorem are established which are in turn used to derive asymptotic distributions associated with martingale estimating functions. |
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