Skip to main content

Nearest Neighbor Methods for Time Series, with Application to Rainfall/Runoff Prediction

  • Chapter
Advances in the Statistical Sciences: Stochastic Hydrology

Part of the book series: The University of Western Ontario Series in Philosophy of Science ((WONS,volume 37))

Abstract

The nearest neighbor technique is a general, powerful, intuitively-appealing approach to nonparametric estimation problems. We offer a rudimentary survey of this method, with special attention to recent results extending the theory to dependent random sequences. The classical rainfall/runoff prediction problem serves as focus for this study, but the methodology offered potentially has much wider application.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bras, R., and I. Rodríguez-Iturbe (1985), Random Functions and Hydrology. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Burnash, J. C., and R. L. Ferral (1980), “National Weather Service River Forecast System” (User’s Manual).

    Google Scholar 

  • Cooper, D. M., and E. W. Wood (1982a), “Identification on multivariate time series and multivariate input-output models”. Water Resources Research 18, 937–946.

    Article  Google Scholar 

  • Cooper, D. M., and E. W. Wood (1982b), “Parameter estimation of multiple input-output time series models: application to rainfall-runoff process”. Water Resources Research 18, 1352–1364.

    Article  Google Scholar 

  • Cover, T. M., and P. E. Hart (1967), “Nearest neighbor pattern classification”. IEEE Transactions on Information Theory IT-13, 21–27.

    Article  Google Scholar 

  • Crawford, N. H., and R. K. Linsley (1966), “Digital simulation in hydrology: Stanford watershed model IV”. Stanford University, Department of Civil Engineering, Technical Report 39.

    Google Scholar 

  • Davis, D. R., C. C. Kisiel, and L. Duckstein (1972), “Bayesian decision theory applied to design in hydrology”. Water Resources Research 8, 33–41.

    Article  Google Scholar 

  • Devroye, L. P. (1978), “The uniform convergence of nearest neighbor regression function estimators and their application in optimization”. IEEE Transactions on Information Theory IT-24, 142–150.

    Article  MathSciNet  Google Scholar 

  • Devroye, L. P. (1981), “On the almost everywhere convergence of nonparametric regression function estimates”. Annals of Statistics 9, 1310–1319.

    Article  MathSciNet  MATH  Google Scholar 

  • Devroye, L. P. (1982), “Necessary and sufficient conditions for the pointwise convergence of nearest neighbor regression function estimates”. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 467–481.

    Article  MathSciNet  MATH  Google Scholar 

  • Doob, J. L. (1953), Stochastic Processes. New York: Wiley and Sons.

    MATH  Google Scholar 

  • Fix, E., and J. L. Hodges, Jr. (1951), “Discriminatory analysis, nonparametric discrimination, consistency properties, Randolph fields”. Texas Project 21-49-004, Report No. 4.

    Google Scholar 

  • Karlsson, M. S. (1985), “Nearest neighbor regression estimators in rainfall-runoff forecasting”. Ph.D. thesis, University of Arizona.

    Google Scholar 

  • Kitanidis, P. K., and R. L. Bras (1980), “Real time forecasting with a conceptual hydrologic model”. Water Resources Research 16, 1025–1033.

    Article  Google Scholar 

  • Linsley, R. K., M. A. Kohler, and J. L. H. Paulhus (1982), Hydrology for Engineers. New York: McGraw-Hill.

    Google Scholar 

  • Ljung, L., and T. Soderstrom (1983), Theory and Practice of Recursive Identification. Cambridge, MA: MIT Press.

    MATH  Google Scholar 

  • Mack, Y. P. (1981), “Local properties of NN regression estimates”. SIAM Journal on Algebraic and Discrete Methods 2, 311–323.

    Article  MathSciNet  MATH  Google Scholar 

  • Mack, Y. P., and M. Rosenblatt (1979), “Multivariate k-nearest neighbor density estimates”. Journal of Multivariate Analysis 9, 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson, P. M. (1983), “Nonparametric estimators for time series”. Journal of Time Series Analysis 4, 185–207.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenblatt, M. (1970), “Density estimates and Markov sequences”. In Nonparametric Techniques in Statistical Inference. ed. M. Puri, pp. 109–213. Oxford: Cambridge University Press.

    Google Scholar 

  • Sorooshian, S. (1983), “Surface water hydrology: on-line estimation”. Reviews of Geophysics and Space Physics 21, 706–721, U.S. National Report to International Union of Geodesy and Geophysics 1979–1982.

    Article  Google Scholar 

  • Stone, C. (1977), “Consistent nonparametric regression”. Annals of Statistics 5, 595–645.

    Article  MathSciNet  MATH  Google Scholar 

  • Stone, C. (1980), “Optimal rates of convergence for nonparametric estimators”. Annals of Mathematics and Statistics 8, 1348–1360.

    MATH  Google Scholar 

  • Tou, J. T., and R. T. Gonzales (1974), Pattern Recognition Principles. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  • Watson, G. S. (1964) “Smooth regression analysis”. Sankhya, Series A 26, 359–372.

    MATH  Google Scholar 

  • Yakowitz, S. (1985a), “Markov flow models and the flood warning problem”. Water Resources Research 21, 81–88.

    Article  Google Scholar 

  • Yakowitz, S. (1985b), “Nonparametric density estimation, precision, and regression for Markov sequences”. Journal of the American Statistical Association 80, 215–221.

    Article  MathSciNet  MATH  Google Scholar 

  • Yakowitz, S. (1985c), “Nearest neighbor methods for time series analysis”. To appear, Journal of Time Series Analysis.

    Google Scholar 

  • Yakowitz, S. (1985d), “Almost sure convergence of nearest neighbor regression for ergodic Markov sequences”. Working paper.

    Google Scholar 

  • Yakowitz, S., and M. Karlsson (1985), “Pattern recognition methods for time series”. Proceedings of the IEEE Conference on Systems, Man, and Cybernetics, pp. 441–444.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Yakowitz, S., Karlsson, M. (1987). Nearest Neighbor Methods for Time Series, with Application to Rainfall/Runoff Prediction. In: MacNeill, I.B., Umphrey, G.J., McLeod, A.I. (eds) Advances in the Statistical Sciences: Stochastic Hydrology. The University of Western Ontario Series in Philosophy of Science, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4792-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4792-4_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8625-7

  • Online ISBN: 978-94-009-4792-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics