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The intrinsic predictability of ecological time series and its potential to guide forecasting


Pennekamp, Frank; Iles, Alison; Garland, Joshua; Brennan, Georgina; Brose, Ulrich; Gaedke, Ursula; Jacob, Ute; Kratina, Pavel; Matthews, Blake; Munch, Stephan; Novak, Mark; Palamara, Gian Marco; Rall, Bjorn; Rosenbaum, Benjamin; Tabi, Andrea; Ward, Colette; Williams, Richard; Ye, Hao; Petchey, Owen (2019). The intrinsic predictability of ecological time series and its potential to guide forecasting. Ecological Monographs:Epub ahead of print.

Abstract

Successfully predicting the future states of systems that are complex, stochastic and potentially chaotic is a major challenge. Model forecasting error (FE) is the usual measure of success; however model predictions provide no insights into the potential for improvement. In short, the realized predictability of a specific model is uninformative about whether the system is inherently predictable or whether the chosen model is a poor match for the system and our observations thereof. Ideally, model proficiency would be judged with respect to the systems’ intrinsic predictability – the highest achievable predictability given the degree to which system dynamics are the result of deterministic v. stochastic processes. Intrinsic predictability may be quantified with permutation entropy (PE), a model‐free, information‐theoretic measure of the complexity of a time series. By means of simulations we show that a correlation exists between estimated PE and FE and show how stochasticity, process error, and chaotic dynamics affect the relationship. This relationship is verified for a dataset of 461 empirical ecological time series. We show how deviations from the expected PE‐FE relationship are related to covariates of data quality and the nonlinearity of ecological dynamics. These results demonstrate a theoretically‐grounded basis for a model‐free evaluation of a system's intrinsic predictability. Identifying the gap between the intrinsic and realized predictability of time series will enable researchers to understand whether forecasting proficiency is limited by the quality and quantity of their data or the ability of the chosen forecasting model to explain the data. Intrinsic predictability also provides a model‐free baseline of forecasting proficiency against which modeling efforts can be evaluated.

Abstract

Successfully predicting the future states of systems that are complex, stochastic and potentially chaotic is a major challenge. Model forecasting error (FE) is the usual measure of success; however model predictions provide no insights into the potential for improvement. In short, the realized predictability of a specific model is uninformative about whether the system is inherently predictable or whether the chosen model is a poor match for the system and our observations thereof. Ideally, model proficiency would be judged with respect to the systems’ intrinsic predictability – the highest achievable predictability given the degree to which system dynamics are the result of deterministic v. stochastic processes. Intrinsic predictability may be quantified with permutation entropy (PE), a model‐free, information‐theoretic measure of the complexity of a time series. By means of simulations we show that a correlation exists between estimated PE and FE and show how stochasticity, process error, and chaotic dynamics affect the relationship. This relationship is verified for a dataset of 461 empirical ecological time series. We show how deviations from the expected PE‐FE relationship are related to covariates of data quality and the nonlinearity of ecological dynamics. These results demonstrate a theoretically‐grounded basis for a model‐free evaluation of a system's intrinsic predictability. Identifying the gap between the intrinsic and realized predictability of time series will enable researchers to understand whether forecasting proficiency is limited by the quality and quantity of their data or the ability of the chosen forecasting model to explain the data. Intrinsic predictability also provides a model‐free baseline of forecasting proficiency against which modeling efforts can be evaluated.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Evolutionary Biology and Environmental Studies
Dewey Decimal Classification:570 Life sciences; biology
590 Animals (Zoology)
Language:English
Date:2019
Deposited On:21 Feb 2019 10:10
Last Modified:17 Sep 2019 20:04
Publisher:Ecological Society of America
ISSN:0012-9615
OA Status:Green
Publisher DOI:https://doi.org/10.1101/350017

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Content: Accepted Version
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Size: 1MB