On studying relations between time series in climatology
Relationships between time series are often studied on the basis of cross-correlation coefficients and regression equations. This approach is generally incorrect for time series, irrespective of the cross-correlation coefficient value, because relations between time series are frequency-dependent. M...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2015-06-01
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| Series: | Earth System Dynamics |
| Online Access: | http://www.earth-syst-dynam.net/6/389/2015/esd-6-389-2015.pdf |
| Summary: | Relationships between time series are often studied on the basis of
cross-correlation coefficients and regression equations. This approach is
generally incorrect for time series, irrespective of the cross-correlation
coefficient value, because relations between time series are
frequency-dependent. Multivariate time series should be analyzed in both
time and frequency domains, including fitting a parametric (preferably,
autoregressive) stochastic difference equation to the time series and then
calculating functions of frequency such as spectra and coherent spectra,
coherences, and frequency response functions. The example with a bivariate
time series "Atlantic Multidecadal Oscillation (AMO) – sea surface
temperature in Niño area 3.4 (SST3.4)" proves that even when the
cross correlation is low, the time series' components can be closely related
to each other. A full time and frequency domain description of this
bivariate time series is given. The AMO–SST3.4 time series is shown to
form a closed-feedback loop system with a 2-year memory. The coherence
between AMO and SST3.4 is statistically significant at intermediate
frequencies where the coherent spectra amount up to 55 % of the total
spectral densities. The gain factors are also described. Some
recommendations are offered regarding time series analysis in climatology. |
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| ISSN: | 2190-4979 2190-4987 |