| Using "Surrogate Surrogate Data" to Calibrate the Actual Rate of False Positives in Tests for Nonlinearity in Time Series (2007) | |||||||||||||||
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| . A distinction can be drawn between two approaches for using surrogate data to test for nonlinearity in a time series. The first is a "typical realizations" model which can be implemented in terms of a direct autoregressive (AR) fit to the data, and the second is a "constrained realizations" model which is implemented using a Fourier transform (FT). Earlier comparisons of these two methods found that that the FT surrogate data test was the more powerful of the two for the same nominal false-positive rate, but that the actual false-positive rate was much lower for the AR test. In this paper, further comparisons are made of the FT and AR tests. A kind of "double bootstrap" approach (that involves taking surrogate data of surrogate data) is suggested for calibrating hypothesis tests so that their actual rate of false positives matches a specified nominal false-positive rate. Numerical experiments are performed using a noise-corrupted high-dimensional strange attractor to generate the dat... | |||||||||||||||
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