A time-span-focussed test for independence of time-varying linear processes

A time-span-focussed testing procedure for independence of possibly non-causal multivariate linear processes with time-varying coefficients using a weighted distance composed of characteristic functions (CF) and its empirical version as a base is proposed. The distance covariance defined by Székely et al. [(2007), ‘Measuring and Testing Dependence by Correlation of Distances’, The Annals of Statistics, 35, 2769–2794] and its use by Jentsch et al. [(2020), ‘Empirical Characteristic Functions-Based Estimation and Distance Correlation for Locally Stationary Processes’, Journal of Time Series Analysis, 41, 110–133] inspired the essential idea of this concept. To be finally able to compile a testing procedure, the needed results with the notion of the beneficial effects of a bootstrap analogue to overcome the dependence of unknown quantities forming the testing threshold are provided. Therefore, bootstrap versions of the previously presented findings are established. Beforehand, the concept of empirical weighted CF-based distance is transferred to the bootstrap world. In the end, numerical examples as well as a real-world application show the validity of the proposed testing procedure.