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A test for independence based on the correlation dimension. (English) Zbl 0893.62034
Summary: This paper presents a test of independence that can be applied to the estimated residuals of any time series model that can be transformed into a model driven by independent and identically distributed errors. The first order asymptotic distribution of the test statistic is independent of estimation error provided that the parameters of the model under test can be estimated $$\sqrt{n}$$-consistently. Because of this, our method can be used as a model selection tool and as a specification test.
Widely used software (written by W. D. Dechert and B. LeBaron) can be used to implement the test. Also, this software is fast enough that the null distribution of our test statistic can be estimated with bootstrap methods. Our method can be viewed as a nonlinear analog of the Box-Pierce $$Q$$ statistic used in ARIMA analysis.

##### MSC:
 62G10 Nonparametric hypothesis testing 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62E20 Asymptotic distribution theory in statistics
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