Defining a trend for time series using the intrinsic time-scale decomposition
We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/8/085004 |
| _version_ | 1797751366266912768 |
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| author | Juan M Restrepo Shankar Venkataramani Darin Comeau Hermann Flaschka |
| author_facet | Juan M Restrepo Shankar Venkataramani Darin Comeau Hermann Flaschka |
| author_sort | Juan M Restrepo |
| collection | DOAJ |
| description | We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition. |
| first_indexed | 2024-03-12T16:48:27Z |
| format | Article |
| id | doaj.art-47ff9819458b4946ac72e4f0838a7985 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:48:27Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-47ff9819458b4946ac72e4f0838a79852023-08-08T11:28:33ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116808500410.1088/1367-2630/16/8/085004Defining a trend for time series using the intrinsic time-scale decompositionJuan M Restrepo0Shankar Venkataramani1Darin Comeau2Hermann Flaschka3Mathematics Department, University of Arizona , Tucson, AZ 85716, USA; Program of Applied Mathematics, University of Arizona , Tucson, AZ 85716, USA; Physics Department, University of Arizona , Tucson, AZ 85716, USAMathematics Department, University of Arizona , Tucson, AZ 85716, USA; Program of Applied Mathematics, University of Arizona , Tucson, AZ 85716, USAProgram of Applied Mathematics, University of Arizona , Tucson, AZ 85716, USAMathematics Department, University of Arizona , Tucson, AZ 85716, USA; Program of Applied Mathematics, University of Arizona , Tucson, AZ 85716, USAWe propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.https://doi.org/10.1088/1367-2630/16/8/085004tendencytrendnon-stationarynon-parametrticmulti-scaleintrinsic time-scale decomposition |
| spellingShingle | Juan M Restrepo Shankar Venkataramani Darin Comeau Hermann Flaschka Defining a trend for time series using the intrinsic time-scale decomposition New Journal of Physics tendency trend non-stationary non-parametrtic multi-scale intrinsic time-scale decomposition |
| title | Defining a trend for time series using the intrinsic time-scale decomposition |
| title_full | Defining a trend for time series using the intrinsic time-scale decomposition |
| title_fullStr | Defining a trend for time series using the intrinsic time-scale decomposition |
| title_full_unstemmed | Defining a trend for time series using the intrinsic time-scale decomposition |
| title_short | Defining a trend for time series using the intrinsic time-scale decomposition |
| title_sort | defining a trend for time series using the intrinsic time scale decomposition |
| topic | tendency trend non-stationary non-parametrtic multi-scale intrinsic time-scale decomposition |
| url | https://doi.org/10.1088/1367-2630/16/8/085004 |
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