Testing for structural breaks via ordinal pattern dependence
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Date
2015
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Abstract
We propose new concepts in order to analyze and model the dependence structure
between two time series. Our methods rely exclusively on the order structure of the
data points. Hence, the methods are stable under monotone transformations of the
time series and robust against small perturbations or measurement errors. Ordinal
pattern dependence can be characterized by four parameters. We propose estimators
for these parameters, and we calculate their asymptotic distributions. Furthermore,
we derive a test for structural breaks within the dependence structure. All results
are supplemented by simulation studies and empirical examples.
For three consecutive data points attaining different values, there are six possibil-
ities how their values can be ordered. These possibilities are called ordinal patterns.
Our first idea is simply to count the number of coincidences of patterns in both time
series, and to compare this with the expected number in the case of independence. If
we detect a lot of coincident patterns, this means that the up-and-down behavior is
similar. Hence, our concept can be seen as a way to measure non-linear ‘correlation’.
We show in the last section, how to generalize the concept in order to capture various
other kinds of dependence.
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Keywords
time series, non-linear correlation, near epoch dependence, limit theorems