Statistical Fourier Analysis: Clarifications and Interpretations

David Pollock ()

No 08/36, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

Abstract: This paper expounds some of the results of Fourier theory that are essential to the statistical analysis of time series. It employs the algebra of circulant matrices to expose the structure of the discrete Fourier transform and to elucidate the filtering operations that may be applied to finite data sequences. An ideal filter with a gain of unity throughout the pass band and a gain of zero throughout the stop band is commonly regarded as incapable of being realised in finite samples. It is shown here that, to the contrary, such a filter can be realised both in the time domain and in the frequency domain. The algebra of circulant matrices is also helpful in revealing the nature of statistical processes that are band limited in the frequency domain. In order to apply the conventional techniques of autoregressive moving-average modelling, the data generated by such processes must be subjected to antialiasing filtering and sub sampling. These techniques are also described. It is argued that band-limited processes are more prevalent in statistical and econometric time series than is commonly recognised.

Date: 2008-10
New Economics Papers: this item is included in nep-ecm and nep-hpe
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp08-36.pdf (application/pdf)

Related works:
Journal Article: Statistical Fourier Analysis: Clarifications and Interpretations (2009)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:lec:leecon:08/36

Ordering information: This working paper can be ordered from
https://www2.le.ac.u ... -1/discussion-papers

Access Statistics for this paper

More papers in Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester School of Business, University of Leicester, University Road. Leicester. LE1 7RH. UK Provider-Homepage: https://le.ac.uk/school-of-business. Contact information at EDIRC.
Bibliographic data for series maintained by Abbie Sleath ().