A Time-Domain Test for Some Types of Non-Linearity
The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of non-linearity in stationary time series. This is because the bispectrum is the Fourier transform of the third order moment. An advantage of the bispectrum is that its estimator comprises terms which are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third order moment is that its values at any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third order moment is required to construct the Fourier transform. In this paper we propose a test for non-linearity based upon the estimated third order moment. We use the phase scrambling bootstrap method to give a non-parametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of non-linearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of non-stationarity.
|Date of creation:||20 Dec 2003|
|Date of revision:|
|Contact details of provider:|| Postal: GPO Box 2434, BRISBANE QLD 4001|
Web page: http://www.bus.qut.edu.au/faculty/economics/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nur, Darfiana & Wolff, Rodney C. & Mengersen, Kerrie L., 2001. "Phase randomisation: numerical study of higher cumulants behaviour," Computational Statistics & Data Analysis, Elsevier, vol. 37(4), pages 487-513, October.
When requesting a correction, please mention this item's handle: RePEc:qut:dpaper:168. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Angela Fletcher)
If references are entirely missing, you can add them using this form.