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Zhang, Q., Pan, W., Li, C. and Wang, X. (2021), The conditional distance autocovariance function. Can J Statistics. https://doi.org/10.1002/cjs.11610
Conditional autocorrelation measures are of essential importance in time series research fields. How do we define such measures? What properties should such measures possess? How do we choose an appropriate measure in applications? The most commonly used measure is the partial autocorrelation function (PACF), which is based on Pearson correlation. However, the Pearson correlation performs poorly for variables with nonlinear relationship or heavy-tailed. Therefore, new techniques become necessary in order to detect the nonlinear relationship in time series.
In this paper, the authors propose the conditional distance autocovariance function (CDACF), which is zero if and only if the measured time series components are conditionally independent. The properties of the CDACF are fully explored. Theoretical results on efficiency and asymptotics are obtained. In contrast to several existing methods, the proposed method shows outstanding performance in the simulation studies. The proposed CDACF provides an attractive option for measuring correlation.