The conditional distance autocovariance function

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.