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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]

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]

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]

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

• Schreiber, T.; Schmitz, A. (1996). "Improved Surrogate Data for Nonlinearity Tests". Physical Review Letters. 77 (4): 635–638. arXiv:chao-dyn/9909041. Bibcode:1996PhRvL..77..635S. doi:10.1103/PhysRevLett.77.635. PMID 10062864. S2CID 13193081.