Local Gaussian Cross-Spectrum Analysis
The ordinary spectrum is restricted in its applications, since it is based on the second-order moments (auto- and cross-covariances). Alternative approaches to spectrum analysis have been investigated based on other measures of dependence. One such approach was developed for univariate time series b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Econometrics |
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| Online Access: | https://www.mdpi.com/2225-1146/11/2/12 |
| _version_ | 1797595220833992704 |
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| author | Lars Arne Jordanger Dag Tjøstheim |
| author_facet | Lars Arne Jordanger Dag Tjøstheim |
| author_sort | Lars Arne Jordanger |
| collection | DOAJ |
| description | The ordinary spectrum is restricted in its applications, since it is based on the second-order moments (auto- and cross-covariances). Alternative approaches to spectrum analysis have been investigated based on other measures of dependence. One such approach was developed for univariate time series by the authors of this paper using the <i>local Gaussian auto-spectrum</i> based on the <i>local Gaussian auto-correlations</i>. This makes it possible to detect local structures in univariate time series that look similar to white noise when investigated by the ordinary auto-spectrum. In this paper, the <i>local Gaussian approach</i> is extended to a <i>local Gaussian cross-spectrum</i> for multivariate time series. The local Gaussian cross-spectrum has the desirable property that it coincides with the ordinary cross-spectrum for Gaussian time series, which implies that it can be used to detect non-Gaussian traits in the time series under investigation. In particular, if the ordinary spectrum is flat, then peaks and troughs of <i>the local Gaussian spectrum</i> can indicate nonlinear traits, which potentially might reveal <i>local periodic phenomena</i> that are undetected in an ordinary spectral analysis. |
| first_indexed | 2024-03-11T02:34:10Z |
| format | Article |
| id | doaj.art-ed00c4e8e92442a9bb74bafc8a1edb9a |
| institution | Directory Open Access Journal |
| issn | 2225-1146 |
| language | English |
| last_indexed | 2024-03-11T02:34:10Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj.art-ed00c4e8e92442a9bb74bafc8a1edb9a2023-11-18T10:05:16ZengMDPI AGEconometrics2225-11462023-04-011121210.3390/econometrics11020012Local Gaussian Cross-Spectrum AnalysisLars Arne Jordanger0Dag Tjøstheim1Department of Computer Science, Electrical Engineering and Mathematical Sciences, Faculty of Engineering and Science, Western Norway University of Applied Sciences, 5020 Bergen, NorwayDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Bergen, 5020 Bergen, NorwayThe ordinary spectrum is restricted in its applications, since it is based on the second-order moments (auto- and cross-covariances). Alternative approaches to spectrum analysis have been investigated based on other measures of dependence. One such approach was developed for univariate time series by the authors of this paper using the <i>local Gaussian auto-spectrum</i> based on the <i>local Gaussian auto-correlations</i>. This makes it possible to detect local structures in univariate time series that look similar to white noise when investigated by the ordinary auto-spectrum. In this paper, the <i>local Gaussian approach</i> is extended to a <i>local Gaussian cross-spectrum</i> for multivariate time series. The local Gaussian cross-spectrum has the desirable property that it coincides with the ordinary cross-spectrum for Gaussian time series, which implies that it can be used to detect non-Gaussian traits in the time series under investigation. In particular, if the ordinary spectrum is flat, then peaks and troughs of <i>the local Gaussian spectrum</i> can indicate nonlinear traits, which potentially might reveal <i>local periodic phenomena</i> that are undetected in an ordinary spectral analysis.https://www.mdpi.com/2225-1146/11/2/12local periodicitieslocal co-spectrumlocal quadrature-spectrumlocal amplitude-spectrumlocal phase-spectrumheatmap |
| spellingShingle | Lars Arne Jordanger Dag Tjøstheim Local Gaussian Cross-Spectrum Analysis Econometrics local periodicities local co-spectrum local quadrature-spectrum local amplitude-spectrum local phase-spectrum heatmap |
| title | Local Gaussian Cross-Spectrum Analysis |
| title_full | Local Gaussian Cross-Spectrum Analysis |
| title_fullStr | Local Gaussian Cross-Spectrum Analysis |
| title_full_unstemmed | Local Gaussian Cross-Spectrum Analysis |
| title_short | Local Gaussian Cross-Spectrum Analysis |
| title_sort | local gaussian cross spectrum analysis |
| topic | local periodicities local co-spectrum local quadrature-spectrum local amplitude-spectrum local phase-spectrum heatmap |
| url | https://www.mdpi.com/2225-1146/11/2/12 |
| work_keys_str_mv | AT larsarnejordanger localgaussiancrossspectrumanalysis AT dagtjøstheim localgaussiancrossspectrumanalysis |