Locally weighted polynomial regression: Parameter choice and application to forecasts of the Great Salt Lake

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. Cross-validatory procedures for the selection of the size of the neighborhood over which this approximation should take place and for the order of the local polynomial to use are provided and shown for some simple situations. The utility of this nonparametric regression approach is demonstrated through an application to nonparametric short-term forecasts of the biweekly Great Salt Lake volume. Blind forecasts up to 1 year in the future using the 1847-2004 time series of the Great Salt Lake are presented.