The partial autocorrelation function (PACF) is often used in time series analysis to identify the extent of the lag in an autoregressive model. However, the PACF is only suitable for detecting linear correlations. This article proposes the conditional distance autocovariance function (CDACF), which is zero if and only if measured time series components are conditionally independent. Due to the lack of this property, traditional tools for measuring partial correlations such as the PACF cannot work well for nonlinear sequences. Based on the CDACF, we introduce a tool known as an integrated conditional distance autocovariance function (ICDACF), which can test conditional temporal dependence structures of a sequence and estimate the order of an autoregressive process. Simulation studies reveal that the ICDACF can detect the conditional dependence of nonlinear autoregressive models efficiently while controlling for type-I error rates. Finally, an analysis of a Bitcoin price dataset using the ICDACF demonstrates that our method has considerable advantages over other state-of-the-art methods.

中文翻译：

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条件距离自协方差函数

偏自相关函数 (PACF) 通常用于时间序列分析，以识别自回归模型中的滞后程度。然而，PACF 仅适用于检测线性相关。本文提出条件距离自协方差函数 (CDACF)，当且仅当测量的时间序列分量条件独立时，该函数为零。由于缺乏这一特性，传统的偏相关测量工具（如 PACF）不能很好地用于非线性序列。基于 CDACF，我们引入了一种称为集成条件距离自协方差函数 (ICDACF) 的工具，它可以测试序列的条件时间依赖结构并估计自回归过程的阶数。仿真研究表明，ICDACF 可以有效地检测非线性自回归模型的条件依赖性，同时控制 I 类错误率。最后，使用 ICDACF 对比特币价格数据集的分析表明，我们的方法比其他最先进的方法具有相当大的优势。