To perform hydrological forecasting, time series methods are often employed. In univariate time series, the autoregressive integrated moving average (ARIMA) model, the seasonal autoregressive moving average (SARMA) model, the deseasonalized model and the periodic autoregressive (PAR) model are often used. These models are based on the assumption that the influence of lagged riverflows on the riverflow is linear. In reality the assumption is often questionable. In this paper, the functional-coefficient autoregression (FCAR) model, which is a nonlinear model, is introduced to forecast riverflows. To explore the influence of the inflow on the outflow in a river system and to exploit the internal interaction of the outflows, bivariate time series models are needed. The transfer function (TF) model and the semi-parametric regression (SPR) model are often employed. In this paper, a new model, the non-parametric and functional-coefficient autoregression (NFCAR) model, is proposed. It consists of two parts: the first part, the non-parametric part explains the influences of the inflows on the outflow in a river system; the second part, the functional-coefficient linear part reveals the interactions among the outflows in a river system. By comparing the calibration and forecasting of the models, it is found that the NFCAR model performs very well.

Varying-coefficient models are popular multivariate nonparametric fitting techniques. When all coefficient functions in a varyingcoefficient model share the same smoothing variable, inference tools available include the F-test, the sieve empirical likelihood ratio test and the generalized likelihood ratio (GLR) test. However, when the coefficient functions have different smoothing variables, these tools cannot be used directly to make inferences on the model because of the differences in the process of estimating the functions. In this paper, the GLR test is extended to models of the latter case by the efficient estimators of these coefficient functions. Under the null hypothesis the new proposed GLR test follows the 2-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Further, we have derived its asymptotic power which is shown to achieve the optimal rate of convergence for nonparametric hypothesis testing.A simulation study is conducted to evaluate the test procedure empirically.

The functional-coefficient regression models with different smoothing variables in different coefficient functions are discussed in this paper. The averaged estimates of coefficient functions are defined by averaging the sample on the initial value obtained by a local linear technique. Their asymptotic normality is studied. The efficiency of the proposed method is shown by a simulated example.

本文探讨具有不同光滑变量的变系数模型的建模、估计和估计的渐近性。首先，从实际出发建立模型；然后，使用局部线性方法给出模型中未知函数的初始估计，再使用平均方法，给出它们的平均估计；进一步，给出这些平均估计的渐近正态性。两个模拟例子说明这一估计方法是有效的。

本文讨论在数据是强相依的情况下函数系数部分线性模型的估计。首先，采用局部线性方法，给出该模型函数是项函数的估计；然后，使用两阶段方法给出系数函数的估计。并且讨论了函数项函数估计的渐近正态性，以及系数函数估计的弱相合性的渐近正态性。模拟研究显示，这些估计是较为理想的。