Evaluation of Surrogate and Bootstrap Tests for Nonlinearity in Time Series

Dimitris Kugiumtzis 1 , 1
  • 1 Aristotle University of Thessaloniki, dkugiu@gen.auth.gr

The validity of any test for nonlinearity based on resampling techniques depends heavily on the consistency of the generated resampled data to the null hypothesis of linear stochastic process. The surrogate data generating algorithms AAFT, IAAFT and STAP, as well as a residual-based bootstrap algorithm, all used for the randomization or bootstrap test for nonlinearity, are reviewed and their performance is compared using different nonlinear statistics for the test. The simulations on linear and nonlinear stochastic systems, as well as chaotic systems, reveals a variation in the test outcome with the algorithm and statistic. Overall, the bootstrap algorithm led to smallest test power whereas the STAP algorithm gave consistently good results in terms of size and power of the test. The performance of the nonlinearity test with the resampling techniques is evaluated on volume and return time series of international stock exchange indices.

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SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.