Multivariate flexible least squares analysis of hydrological time series

Abstract Models with coefficients which change with time can be developed by using Kalman filter techniques and these have been applied to model river flow, rainfall and other hydrological time series. However, application of Kalman filter techniques requires assumptions about the statistics of processes and state variables which may depend on unknown factors, and these assumptions may not be valid. A new approach to this problem is the flexible least squares (FLS) method. In this approach, the parameters are assumed to evolve slowly over time. The parameters of the model are estimated by minimizing the sums of squared measurement and dynamic errors conditional on the given observations. The method is based on a cost efficient frontier and is called the generalized flexible least squares method. The objective of this study is to apply the FLS method to hydrological time series. Data from the Green River basin in Kentucky in the USA are used in the study. The method is found to perform well.