부산대학교 도서관

Let $x(t)$ be a real stationary process with vanishing mean. Define $$\multline\widehat m_n=\widehat m_n(t_1,\dots,t_{n-1})=\\ (1/T)\sum_{t=0}^{T-1} x(t_1+t)x(t_2+t)\cdots x(t_{n-1}+t)x(t).\endmultline$$ Then $\widehat m_n$ is an estimator of the corresponding theoretical moment $m_n(t_1,\dots,t_{n-1})$. The author proves that, under some conditions on cumulants of the process $x(t)$, the estimator $\widehat m_n$ is asymptotically normally distributed.