Causality in Time Series - ClopiNet
Causality in Time Series - ClopiNet
Causality in Time Series - ClopiNet
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PopescuH. White and X. Lu. Granger <strong>Causality</strong> and Dynamic Structural Systems. Journal ofF<strong>in</strong>ancial Econometrics, 8(2):193, 2010.N. Wiener. The theory of prediction. Modern mathematics for eng<strong>in</strong>eers, <strong>Series</strong>, 1:125–139, 1956.H. O. Wold. A Study <strong>in</strong> the Analysis of Stationary <strong>Time</strong> <strong>Series</strong>. Stockholm: Almqvistand Wiksell., 1938.A. Yatchew. Nonparametric regression techniques <strong>in</strong> economics. Journal of EconomicLiterature, 36(2):669–721, 1998.G. U. Yule. Why do we sometimes get nonsense correlations between time series?a study <strong>in</strong> sampl<strong>in</strong>g and the nature of time series. Journal of the Royal StatisticalSociety, 89:1–64, 1926.A. Ziehe and K.-R. Mueller. Tdsep- an efficient algorithm for bl<strong>in</strong>d separation us<strong>in</strong>gtime structure. ICANN Proceed<strong>in</strong>gs, pages 675–680, 1998.S. T. Ziliak and D. N. McCloskey. The Cult of Statistical Significance: How the StandardError Costs Us Jobs, Justice, and Lives. University of Michigan Press, February2008. ISBN 0472050079.Appendix A. Statistical significance tables for Type I and Type III errorsIn order to assist practitioners <strong>in</strong> evaluat<strong>in</strong>g the statistical significance of bivariatecausality test<strong>in</strong>g, tables were prepared for type I and type III error probabilities as def<strong>in</strong>ed<strong>in</strong> (1) for different values of the base statistic. Below tables are provided for boththe jacknifed statistic Ψ/std(Ψ) and for the raw statistic Ψ, which is needed <strong>in</strong> case thenumber of po<strong>in</strong>ts is too low to allow a jackknife/cross-validation/bootstrap or computationalspeed is at a premium. The spectral evaluation method is Welch’s method asdescribed <strong>in</strong> Section 6. There were 2000 simulations for each condition. The tables <strong>in</strong>this Appendix differ <strong>in</strong> one important aspect with respect to those <strong>in</strong> the ma<strong>in</strong> text. Inorder to avoid non-<strong>in</strong>formative comparison of datasets which are, for example, analysesof the same physical process sampled at different sampl<strong>in</strong>g rates, the number of po<strong>in</strong>tsis scaled by the ‘effective’ number of po<strong>in</strong>ts which is essentially the number of samplesrelative to a simple estimate of the observed signal bandwidth:N * = Nτ S /̂︂BŴ︂BW =‖X‖ F‖∆X/∆T‖ FThe values marked with an asterisk have values of both α and γ which are less than5%. Note also that Ψ is non-dimensional <strong>in</strong>dex.70