自回归序列的穿带率

The Band-crossing Rate of Pth-oraer Autoregressive Processes

穿零问题是时间序列分析中的一个重要研究内容，被广泛应用于语音识别、信号探测等科学研究领域．统计学者已经给出了二阶自回归序列AR（2）的渐进穿零率与一阶渐进相关函数的关系，以及均方渐近穿零率与自回归序列AR（P）的特征根的关系等一系列研究成果．在此基础上，本文引入了白回归序列AR（P）的渐近穿带率（BCR）的概念，建立了序列的2邻点渐近穿带率与一阶渐近相关函数之间的关系．当带宽足够窄时，用2邻点穿带率可以近似穿带率，从而建立了渐近穿带率和一阶渐近相关函数与方差的关系式．

Zero-crossing rate （ZCR） is an important research content in time series analy- sis, and it is widely used in speech recognition, signal detection and other scientific research field. So far, many statistical scholars have proposed a series of research achievements, such as the relationship between asymptotic zero-crossing rate of 2th-oraer autoregressive process and lth-oraer asymptotic correlative function, and the relationship between the mean square asymptotic zero-crossing rate and the characteristic roots of Pth-oraer autoregressive pro- cesses, etc. In this paper the concept of asymptotic band-crossing rate （BCR） of Pth-oraer autoregressive processes is introduced and the relationship between the asymptotic BCR of 2 consecutive points and the lth-oraer asymptotic correlative function is investigated. In most cases, it brings about little error for taking the asymptotic BCR of 2 consecutive points as the asymptotic BCR as long as the band is chosen narrow enough. Further the links between the asymptotic BCR and the lth-oraer asymptotic correlative function and the variance are set up.