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On sequential spectral analysis of amplitude-modulated time series

机译：关于调幅时间序列的顺序频谱分析

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摘要

Consider a zero-mean and second-order stationary time series of interest that cannot be observed directly. Instead an amplitude-modulated time series is observed where is a stationary Bernoulli time series and is a time series of independent variables satisfying and Time series creates missing observations when A(t) = 0, and U-t modulates not missed X-t. There is bad and good news about spectral analysis of amplitude-modulated time series. The bad news is that in general consistent estimation of the spectral density is impossible. The good news is that the spectral shape (which is the spectral density minus ) multiplied by factor may be consistently estimated. This article, for the first time in the literature, explores a classical problem of sequential nonparametric estimation of the scaled shape with assigned mean integrated square error. It proposes an adaptive sequential estimator that solves the problem and whose mean stopping time matches the performance of a minimax oracle that knows an underlying spectral density and the amplitude-modulating mechanism. The asymptotic theory is complemented by numerical examples.
机译：考虑一个不能直接观测到的零均值和二阶平稳时间序列。而是观察到一个调幅时间序列，其中是一个平稳的伯努利时间序列，并且是一个满足自变量的时间序列，并且当A（t）= 0时，时间序列会创建丢失的观测值，而U-t会调制未丢失的X-t。关于调幅时间序列的频谱分析有好有坏。坏消息是，通常不可能对光谱密度进行一致的估计。好消息是，可以一致地估计光谱形状（即光谱密度减去）乘以系数。本文是文献中的第一次，探讨了分配均值积分平方误差的按比例缩放形状的顺序非参数估计的经典问题。它提出了一种自适应顺序估计器，可以解决该问题，并且其平均停止时间与知道基础频谱密度和幅度调制机制的minimax oracle的性能相匹配。渐近理论由数字示例补充。

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