### Testing independence for multivariate time series via the auto-distance correlation matrix

Statistics Seminar

15th March 2019, 3:00 pm – 3:45 pm

Main Maths Building, SM3

There has been a considerable recent interest in measuring dependence by employing the concept of distance covariance function, a new and appealing measure of dependence for random variables. This tool has been recently extended to time series analysis but since then a limited number of works are discussing its properties. Distance covariance and its normalized form, the so-called distance correlation can identify interesting links among the data, whereas the traditional correlation coefficient cannot unless the data are Gaussian and/or linearly related. We extend the notion of distance covariance to multivariate time series by defining its matrix version. The information contained in this matrix is useful for identifying any possible relationships within and between the time series components. Based on this new concept, we introduce a multivariate Ljung-Box type test statistic with an increasing number of lags, suitable for testing independence.

*Organiser*: Henry Reeve

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