Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
권호 표지

Locally Weighted Polynomial Forecasting Model

지역가중다항식을 이용한 예측모형

  • 문영일 (서울시립대학교 토목공학과)
  • Published : 2000.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

Relationships between hydrologic variables are often nonlinear. Usually the functional form of such a relationship is not known a priori. A multivariate, nonparametric regression methodology is provided here for approximating the underlying regression function using locally weighted polynomials. Locally weighted polynomials consider the approximation of the target function through a Taylor series expansion of the function in the neighborhood of the point of estimate. The utility of this nonparametric regression approach is demonstrated through an application to nonparametric short term forecasts of the biweekly Great Salt Lake volume.volume.

수문변량 사이의 관계는 대부분 비선형 관계를 보이고 있다. 일반적으로 이런 비선형 관계는 어떤 선행하는 명백한 하나의 함수적인 형태로 표현할 수 없는 것이 일반적이다. 본 논문에서는, 비매개변수적 다변량 회귀분석 방법을 지역적으로 가중된 다항식을 이용하여 비선형 예상 함수를 추정하였다. 지역적으로 가중된 다항식은 추정치 각 점에서의 인접한 이웃자료를 가지고 목적 함수를 테일러 급수 확장을 통하여 고려하였다. 이런 비매개변수적 회귀분석을 실용성을 Great Salt Lake의 격주 체적자료에 대한 단기간 예측을 통하여 보여주었다.

Keywords

References

  1. Abarbanel, H.D.I., Brown, R. Sidorowich, J.J., and Tsimring, L.S. (1993). 'The analysis of observed chaotic data in physical systems.' Rev. of Modem Phys., Vol. 65, No. 4, 1331-1392 https://doi.org/10.1103/RevModPhys.65.1331
  2. Abarbanel, H.D.I., Lall, U, Moon, Young-Il, Mann, M., and Sangoyomi, T., 'Nonlinear dynamics of the Great Salt Lake: A predictable indicator of regional climate.' Energy, Vol. 21(7/8), pp. 655-665 https://doi.org/10.1016/0360-5442(96)00018-7
  3. Cleveland, W.S. (1979). 'Robust locally weighted regression and smoothing scatterplots.' J Amer. Stat. Assoc., Vol. 74, No. 368, pp. 829-836 https://doi.org/10.2307/2286407
  4. Cleveland, W.S., and Devlin, S.J. (1988). 'Locally weighted regression: An approach to regression. analysis by local fitting.' J Amer. Stat. Assn., Vol. 83, No. 403, pp. 596-610 https://doi.org/10.2307/2289282
  5. Cleveland, W.S., Devlin, S.J., and Grosse, E. (1988). 'Regression by local fitting.' J Econometrics, Vol. 37, pp. 87-114 https://doi.org/10.1016/0304-4076(88)90077-2
  6. Kember, G., Flower, AC., and Holubeshen, J. (1993). 'Forecasting river flow using nonlinear dynamics.' Stoch. Hydrol. Hydraul., Vol. 7, pp. 205-212 https://doi.org/10.1007/BF01585599
  7. Lall, U., Moon, Young-II, and Bosworth, K. (in press). 'Locally weighted polynomial regression: Parameter choice and application to forecasts of the Great Salt Lake.' J. of Hydrologic Engineering, ASCE
  8. Moon, Young-II, Rajagopalan, B., and Lall, U. (1995). 'Estimation of mutual information using kernel density estimators.' Physical Review E, Vol. 52 No. 3, pp. 2318-2321 https://doi.org/10.1103/PhysRevE.52.2318
  9. Moon, Young-II, and Lall, U. (1996). 'Atmospheric flow indices and interannual Great Salt Lake variability.' J. of Hydrologic Engineering, A3CE, Vol. 1, No. 2, pp. 55-62 https://doi.org/10.1061/(ASCE)1084-0699(1996)1:2(55)
  10. Moon, Young-II. (1997). 'A nonparametric nonlinear time series forecasting model application to selected hydrologic variables in Korea.' American Geophysical Union, Fall Meeting, Vol. 78, pp. 46
  11. Smith, J.A, (1991). 'Long-range streamflow forecasting using nonparametric regression.' Water Resour. Bull., Vol. 27, No. 1, pp. 39-46
  12. Yakowitz, S., and Karlsson, M. (1987). 'Nearest neighbor methods with application to rainfall/runoff prediction.' Stochastic hydrology, Edited by Macneil, J.B., and Humphries, G.J., D. Reidel, Hingham, MA, pp. 149-160