Time Series and Distance Correlation
Gábor J. Székely, Maria L. Rizzo · 2022
Correlation theory and distance correlation theory applies to iid observations. What can go wrong if the data are serially dependent? An example of “nonsense correlation” is discussed in “Yule&s;s ‘nonsense correlation’ solved!” [Ernst et al., 2017] . This nonsense correlation is a problem for distance correlation, too. This phenomenon is caused by two factors: the observations are serially correlated and the random walks (Wiener processes) are not stationary.