Abstract
Various time series forecasting methods have been successfully applied for the water-stage forecasting problem. Graphical time series models are a class of multivariate time series to model the spatio-temporal dependencies between the sensors. Constructing graph-based models involve data pre-processing and correlation analysis to capture the dynamics of different water flow scenarios, which is not scalable for a large network of sensors. This paper presents a novel approach to model spatio-temporal dependencies across river network stations using a partial correlation graph. We also provide a method to enrich this partial correlation graph by eliminating the spurious correlations. We demonstrate the utility of enriched partial correlation graphs in multivariate forecasting for various scenarios and state-of-the-art multivariate forecasting models. We observe that the forecasting techniques that use information from the enriched partial correlation graph outperform standard time series forecasting approaches for river network forecasting.
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Data Availability
The data used for this experiment is available at https://github.com/SatyaKatragadda/RiverStageForecasting
References
Ahmed NK, Atiya AF, Gayar NE, El-Shishiny H (2010) An empirical comparison of machine learning models for time series forecasting. Economet Rev 29(5–6):594–621
Athanasopoulos G, Poskitt DS, Vahid F (2012) Two canonicalvarma forms: Scalar component models vis-‘a-vis the echelon form. Economet Rev 31(1):60–83
Barigozzi M, Brownlees C (2019) Nets: Network estimation for time-series. J Appl Economet 34(3):347–364
Bowden GJ, Dandy GC, Maier HR (2005) Input determination for neural network models in water resources applications. part 1–background and methodology. J Hydrol 301(1–4):75–92
Chau K (2004) River stage forecasting with particle swarm optimization. In: International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems. Springer, pp 1166–1173
Cohen J, Cohen P, West SG, Aiken LS (2013) Applied multiple regression/correlation analysis for the behavioral sciences. Routledge
Dahlhaus R (2000) Graphical interaction models for multivariate time-series 1. Metrika 51(2):157–172
De La Fuente A, Bing N, Hoeschele I, Mendes P (2004) Discovery of meaningful associations in genomic data using partial correlation coefficients. Bioinformatics 20(18):3565–3574
Diebold FX (2015) Comparing predictive accuracy twenty years later: a personal perspective on the use and abuse of diebold-mariano tests. J Bus Econ Stat 33(1):1
Diebold FX, Mariano RS (2002) Comparing predictive accuracy. J Bus Econ Stat 20(1):134–144
Epskamp S, Fried EI (2018) A tutorial on regularized partial correlation networks. Psychol Methods 23(4):617
Fernando T, Maier H, Dandy G (2009) Selection of input variables for data driven models: an average shifted histogram partial mutual information estimator approach. J Hydrol 367(3–4):165–176
Fildes R (1992) The evaluation of extrapolative forecasting methods. Int J Forecast 8(1):81–98
Fu J-C, Huang H-Y, Jang J-H, Huang P-H (2019) River stage forecasting using multiple additive regression trees. Water Resour Manage 33(13):4491–4507
Galelli S, Castelletti A (2013) Tree-based iterative input variable selection for hydrological modeling. Water Resour Res 49(7):4295–4310
Harvey D, Leybourne S, Newbold P (1997) Testing the equality of prediction mean squared errors. Int J Forecast 13(2):281–291
Irvine KN, Eberhardt AJ (1992) Multiplicative, seasonal arima models for lake erie and lake ontario water levels 1. JAWRA J Am Water Resour Assoc 28(2):385–396
Kenett DY, Tumminello M, Madi A, Gur-Gershgoren G, Mantegna RN, Ben-Jacob E (2010) Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market. PLoS One 5(12):e15032
Knight MI, Nunes MA, Nason GP (2016) Modelling, detrending and decorrelation ofnetwork time-series. arxiv. preprint
Lohani AK, Goel N, Bhatia K (2014) Improving real time flood forecasting using fuzzy inference system. J Hydrol 509:25–41
Maier HR, Jain A, Dandy GC, Sudheer KP (2010) Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ Model Software 25(8):891–909
Marrelec G, Krainik A, Duffau H, Pélégrini-Issac M, Lehéricy S, Doyon J, Benali H (2006) Partial correlation for functional brain interactivity investigation in functional mri. Neuroimage 32(1):228–237
Millington T, Niranjan M (2020) Partial correlation financial networks. Appl Netw Sci 5(1):1–19
Min W, Wynter L, Amemiya Y (2007) Road traffic prediction with spatio-temporal correlations. In: Proceedings of the Sixth Triennial Symposium on Transportation Analysis (Thailand (June 2007), vol. 65), Phuket Island, p 85
Opgen-Rhein R, Strimmer K (2007) From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Syst Biol 1(1):1–10
Panda RK, Pramanik N, Bala B (2010) Simulation of river stageusing artificial neural network and mike 11 hydrodynamic model. Comput Geosci 36(6):735–745
Papamichail DM, Georgiou PE (2001) Seasonal arima inflow models for reservoir sizing 1. JAWRA J Am Water Resour Assoc 37(4):877–885
Reich NG, Lessler J, Sakrejda K, Lauer SA, Iamsirithaworn S, Cummings DA (2016) Case study in evaluating time-series prediction models using the relative mean absolute error. Am Stat
Ruck DW, Rogers SK, Kabrisky M (1990) Feature selection using a multilayer perceptron. J Neural Netw Comput 2(2):40–48
Surface-Water U (2019) Data for the nation. [Online]. Available at https://waterdata.usgs.gov/nwis/sw. Accessed 24 Jun 2019
Ursu E, Pereau J-C (2016) Application of periodic autoregressive pro-cess to the modeling of the garonne river flows. Stoch Env Res Risk Assess 30(7):1785–1795
Wang G-J, Xie C, Stanley HE (2018) Correlation structure and evolution of world stock markets: Evidence from pearson and partial correlation-based networks. Comput Econ 51(3):607–635
Wang J, Wang J, Zeng G, Tu Z, Gan R, Li S (2012) Scalable k-nn graph construction for visual descriptors. IEEE Conference on Computer Vision and Pattern Recognition 2012 1106–1113
Yaseen ZM, Sulaiman SO, Deo RC, Chau K-W (2019) An enhanced extreme learning machine model for river flow forecasting: State-of-the-art, practical applications in water resource engineering area and future research direction. J Hydrol 569:387–408
Yu P-S, Chen S-T, Chang I-F (2006) Support vector regression for real-time flood stage forecasting. J Hydrol 328(3–4):704–716
Zellner A (ed) (1978) Seasonal analysis of economic time-series. US Department of Commerce, Bureau of the Census
Funding
This project is funded by NSF grant CNS-1429526
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Problem formulation: S.V.; Conceptualization: S.V.; Methodology: S.V., R.G., and V.R.; Software: S.V. and S.K.; Validation: S.K. and S.V.; Formal analysis: S.K., V.R., and S.V.; Resources: R.G.; Data curation: S.K. and S.V.; Writing–original draft preparation: S.V., R.G., and S.K.; Writing–review and editing: S.K. and R.G.; Visualization: S.K.; Supervision: R.G.; Project administration: R.G.; All authors reviewed the manuscript.
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Venna, S.R., Katragadda, S., Raghavan, V. et al. River Stage Forecasting using Enhanced Partial Correlation Graph. Water Resour Manage 35, 4111–4126 (2021). https://doi.org/10.1007/s11269-021-02933-0
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DOI: https://doi.org/10.1007/s11269-021-02933-0