Applications of distance correlation to time series

By Richard A. Davis, Muneya Matsui, Thomas Mikosch, Phyllis Wan. Bernoulli, 2016

70 citations recorded by the source corpus.

The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and Mureika (1977), Csorgo (1981a,1981b,1981c), Feuerverger (1993)). More recently, there has been renewed interest in using empirical characteristic functions in other inference settings. The distance covariance and correlation, developed by Szekely and Rizzo (2009) for measuring dependence and testing independence between two random vectors, are perhaps the best known illustrations of this. We apply these ideas to stationary univariate and multivariate time series to measure lagged auto- and cross-dependence in a time series. Assuming strong mixing, we establish the relevant asymptotic theory for the sample auto- and cross-distance correlation functions. We also apply the auto-distance correlation function (ADCF) to the residuals of an autoregressive processes as a test of goodness of fit. Under the null that an autoregressive model is true, the limit distribution of the empirical ADCF can differ markedly from the corresponding one based on an iid sequence. We illustrate the use of the empirical auto- and cross-distance correlation functions for testing dependence and cross-dependence of time series in a variety of different contexts.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c20a28cd0aa980e37ee48550a9770d6346b57eae

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Haakon Otneim
2. Baard Stove
3. Dag Tjøstheim
4. Jiti Gao
5. Christian Francq
6. A. Ahmad
7. Michael Vogt

In Statistics and Probability

1. Dag Tjøstheim
2. Haakon Otneim
3. Baard Stove
4. Christian Francq
5. A. Ahmad

Citations in the corpus

• Statistical Dependence: Beyond Pearson’s ρ (2018, methodology): “It has been extended to time series and multiple dependencies by Davis et al. (2018), Fokianos and Pitsillou (2017), Zhou (2012), and Dueck et al. (2014), Dueck, Edelman, and Richards (2015) and Yao, Zhang, and Shao (2018).”
• An Updated Literature Review of Distance Correlation and Its Applications to Time Series (2017, unknown): “Davis et al. (2018) also proved strong consistency for ADCV, under various choices of finite and infinite weight functions ω ( , · ) .”