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Applications of Distance Correlation to Time Series | | Richard A. Davis
; Muneya Matsui
; Thomas Mikosch
; Phyllis Wan
; | | Date: |
17 Jun 2016 | | Abstract: | 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. | | Source: | arXiv, 1606.5481 | | Services: | Forum | Review | PDF | Favorites | |
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