Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment
Abstract
:1. Introduction
2. Interpolation Methods
2.1. Deterministic Methods
2.1.1. Nearest-Neighbor Interpolation
2.1.2. Polynomial Interpolation
2.1.3. Methods Based on Distance Weighting
2.1.4. Methods Based on Fourier’s Theory: Use of Signal Analysis Methods
2.1.5. Other Deterministic Interpolation Method
2.2. Stochastic Methods
2.2.1. Regression Methods
2.2.2. AutoRegressive Methods
2.2.3. Machine Learning Methods
Artificial Neural Networks (ANN)
Kernel Methods
Tree Approaches
Meta-Algorithms of Machine Learning Methods
2.2.4. Methods Based on Data Dynamics
k-Nearest Neighbors (kNN)
Box-Jenkins Models
Method of Moment Fitting
Other Methods Based on Data Dynamic
2.2.5. Methods Based on Kriging
2.2.6. Other Stochastic Methods
3. Criteria Used to Compare Interpolation
4. Evaluation of Uncertainties
4.1. Law of Propagation of Uncertainties
4.2. Monte-Carlo Simulation
5. Discussion: From Literature Outcomes to a New Method
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Equations | Names | References |
---|---|---|
Coefficient of correlation (r) | [80] | |
Squared coefficient of correlation (r2) | [16] | |
Mean of autocorrelation function r(l) | [9] 1 | |
Mean Bias Error (MBE) | [9] | |
Bias | [80] | |
Mean Error (ME) | [12] | |
Absolute differences | [13] | |
Mean Absolute Error (MAE) | [9,77,80] | |
Mean Relative Error (MRE) | [77,80] | |
Mean Absolute Relative Error (MARE) | [77,80] | |
Mean Absolute Percentage Error (MAPE) | [4,54] | |
Sum of Squared Errors (SSE) | [45] | |
Quadratic differences | [13] | |
Standard errors | [16] | |
Prediction risk—leave one out MSE (RLOO) | [32] | |
Mean Square Error (MSE) | [32,39] | |
nc | [1,81] | |
[82] | ||
Root Mean Squares (RMS) | ||
[24] | ||
Root Mean Square Errors of Prediction (RMSEP) | [54] | |
Mean Squares Error (NMSE) | [4] | |
Reduction of Error (RE) | [81] | |
Nash-Sutcliffe coefficient (NS) | [3] | |
Mean Squared Forecast Error (MFSE(h)) | [45] 2 | |
Root Mean Squares Deviations (RMSD) | [9] | |
Root Mean Squares Errors (RMSE) | [12,77,80,83] | |
Normalized Root Mean Square Deviation | [27] | |
Root Mean Square Standardized error (RMSS) | [80] | |
Absolute Percent Error (APE) | [13] 3 | |
Chi-Square (X2) | [9] 4 | |
Coverage | [39] | |
Left Mis-coverage | [39] | |
Right Mis-coverage | [39] | |
Various equations | 95% confidence interval | [39] |
Percentage of Correctly Classified observations (PCC) | [18] | |
Percentage of correctly classified observations in the positive class (Sensitivity) | [18] | |
Percentage of correctly classified observations in the negative class (Specificity) | [18] | |
Top 10% lift (Lift) | [18] | |
H-measure (H) | [18] | |
No equation | Time of computation | [10,12,18,84] |
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Lepot, M.; Aubin, J.-B.; Clemens, F.H.L.R. Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment. Water 2017, 9, 796. https://doi.org/10.3390/w9100796
Lepot M, Aubin J-B, Clemens FHLR. Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment. Water. 2017; 9(10):796. https://doi.org/10.3390/w9100796
Chicago/Turabian StyleLepot, Mathieu, Jean-Baptiste Aubin, and François H.L.R. Clemens. 2017. "Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment" Water 9, no. 10: 796. https://doi.org/10.3390/w9100796