Surrogate data

Short description: Time series data technique

Surrogate data, sometimes known as analogous data,[1] usually refers to time series data that is produced using well-defined (linear) models like ARMA processes that reproduce various statistical properties like the autocorrelation structure of a measured data set.[2] The resulting surrogate data can then for example be used for testing for non-linear structure in the empirical data; this is called surrogate data testing.

Surrogate or analogous data also refers to data used to supplement available data from which a mathematical model is built. Under this definition, it may be generated (i.e., synthetic data) or transformed from another source.[1]

## Contents

* 1 Uses
* 2 Methods
* 3 See also
* 4 References
* 5 Further reading

## Uses

Surrogate data is used in environmental and laboratory settings, when study data from one source is used in estimation of characteristics of another source.[3] For example, it has been used to model population trends in animal species.[4] It can also be used to model biodiversity, as it would be difficult to gather actual data on all species in a given area.[5]

Surrogate data may be used in forecasting. Data from similar series may be pooled to improve forecast accuracy.[6] Use of surrogate data may enable a model to account for patterns not seen in historical data.[7]

Another use of surrogate data is to test models for non-linearity. The term surrogate data testing refers to algorithms used to analyze models in this way.[8] These tests typically involve generating data, whereas surrogate data in general can be produced or gathered in many ways.[1]

## Methods

One method of surrogate data is to find a source with similar conditions or parameters, and use those data in modeling.[4] Another method is to focus on patterns of the underlying system, and to search for a similar pattern in related data sources (for example, patterns in other related species or environmental areas).[5]

Rather than using existing data from a separate source, surrogate data may be generated through statistical processes,[2] which may involve random data generation[1] using constraints of the model or system.[8]

## See also

* Bootstrapping (statistics)
* Data augmentation
* Jackknife resampling
* Synthetic data

## References

1. ↑ 1.0 1.1 1.2 1.3 Kaefer, Paul E. (2015). Transforming Analogous Time Series Data to Improve Natural Gas Demand Forecast Accuracy (M.Sc. thesis). Marquette University. Archived from the original on 2016-03-12. Retrieved 2016-02-18.
2. ↑ 2.0 2.1 Prichard; Theiler (1994). "Generating surrogate data for time series with several simultaneously measured variables". Physical Review Letters 73 (7): 951–954. doi:10.1103/physrevlett.73.951. PMID 10057582. Bibcode: 1994PhRvL..73..951P. http://public.lanl.gov/jt/Papers/SurrogateMultiple.pdf.
3. ↑ "Surrogate Data Meaning". Columbia Analytical Services, Inc., now ALS Environmental. http://www.caslab.com/Surrogate_Data_Meaning/. "What is Surrogate Data? Data from studies of test organisms or a test substance that are used to estimate the characteristics or effects on another organism or substance."
4. ↑ 4.0 4.1 Hernández-Camacho, Claudia J.; Bakker, Victoria. J.; Aurioles-Gamboa, David; Laake, Jeff; Gerber, Leah R. (September 2015). Aaron W. Reed. ed. "The Use of Surrogate Data in Demographic Population Viability Analysis: A Case Study of California Sea Lions". PLOS ONE 10 (9). doi:10.1371/journal.pone.0139158. PMID 26413746. Bibcode: 2015PLoSO..1039158H.
5. ↑ 5.0 5.1 Faith, D.P.; Walker, P.A. (1996). "Environmental diversity: on the best-possible use of surrogate data for assessing the relative biodiversity of sets of areas". Biodiversity and Conservation (Springer Nature) 5 (4): 399–415. doi:10.1007/BF00056387. Bibcode: 1996BiCon...5..399F.
6. ↑ Duncan, George T.; Gorr, Wilpen L.; Szczypula, Janusz (2001). "Forecasting Analogous Time Series". in J. Scott Armstrong. Principles of Forecasting: A Handbook for Researchers and Practitioners. Kluwer Academic Publishers. pp. 195–213. ISBN 0-7923-7930-6.
7. ↑ Kaefer, Paul E.; Ishola, Babatunde; Brown, Ronald H.; Corliss, George F. (2015). "Using Surrogate Data to Mitigate the Risks of Natural Gas Forecasting on Unusual Days". International Institute of Forecasters: 35th International Symposium on Forecasting. https://forecasters.org/wp-content/uploads/gravity_forms/7-621289a708af3e7af65a7cd487aee6eb/2015/07/Kaefer_Paul_ISF2015.pdf. Retrieved 2022-07-20.
8. ↑ 8.0 8.1 Schreiber, Thomas; Schmitz, Andreas (1999). "Surrogate time series". Physica D 142 (3–4): 346–382. doi:10.1016/s0167-2789(00)00043-9. Bibcode: 2000PhyD..142..346S.

## Further reading

* Schreiber, T.; Schmitz, A. (1996). "Improved Surrogate Data for Nonlinearity Tests". Physical Review Letters 77 (4): 635–638. doi:10.1103/PhysRevLett.77.635. PMID 10062864. Bibcode: 1996PhRvL..77..635S.

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