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Abstract:
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The classical nonparametric approach to studying dependence between time series is via cross-correlation. One limitation of cross-correlation is that it identifies only linear dependence. Often it fails to identify the presence of dependence between two time series when the dependence is non-linear. In this talk, we shall discuss mutual information (MI) as a general measure of dependence between time series. For a bivariate time series (X,Y), MI is the reduction in the entropy of the time series X when the time series Y is known. It is bounded below by 0 and attains the minimum value when X and Y are independent. Special cases of MI are cross-correlation which are derived when the time series is bivariate Gaussian. This talk will cover the methods of estimating mutual information, extension to MI in the frequency domain and applications to neuroscience and financial time series data.
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