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Computer intensive testing for the influence between time series. (English) Zbl 1268.62105

Schelter, Björn (ed.) et al., Handbook of time series analysis: Recent theoretical developments and applications. Weinheim: Wiley-VCH (ISBN 978-3-527-40623-4/hbk; 978-3-527-60997-0/ebook). 411-436 (2006).
Summary: Recent years have seen several different quantitative approaches to gauging the mutual influence between multiple simultaneously measured time series with applications that range from physiology to economics. Some of them, specially those that portray that influcence in the frequency domain, like partial directed coherence in connection to the parametric modeling of jointly stationary time series lead to estimators whose asymptotic behavior, even if known, is of limited practical value, as many times series of interest can only be often considered stationary over very limited time spans. This chapter examines how to use the actually observed data to: (a) set limits on the significance of the null hypothesis of absence of relationships between the observed time series and (b) to produce confidence interval estimates when the mutual influence is of significance. Two different strategies to produce bootstrapped estimates are considered. The first one is based on random model residual resampling and the second one on spectral phase shuffling. Their relative merits are examined and examples of their application to both real and simulated data are considered.
For the entire collection see [Zbl 1104.62328].

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
68U99 Computing methodologies and applications
65C60 Computational problems in statistics (MSC2010)
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