Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages

Let $X_t = \sum^\infty_{j=-\infty} c_jZ_{t-j}$ be a moving average process where the $Z_t$ 's are iid and have regularly varying tail probabilities with index $\alpha > 0$ . The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite fourth moment. Furthermore, in the infinite variance case $(0 < \alpha < 2)$ , the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices $\alpha$ and $\alpha/2$ , respectively. This result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process.Let $X_t = \sum^\infty_{j=-\infty} c_jZ_{t-j}$ be a moving average process where the $Z_t$'s are iid and have regularly varying tail probabilities with index $\alpha > 0$. The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite fourth moment. Furthermore, in the infinite variance case $(0 < \alpha < 2)$, the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices $\alpha$ and $\alpha/2$, respectively. This result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process.

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笔记与分组

分类依据与纠错

Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages

代码、数据与补充材料

移动平均过程样本协方差与相关函数的极限理论

原文摘要

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同方向的基础文献