Yield Curve Estimation by Kernel Smoothing Methods

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various restrictions in the estimation. Our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not explicit and our estimation procedure is iterative, rather like the backfitting method of estimating additive nonparametric models. We establish the asymptotic normality of our methods using the asymptotic representation of our estimator as an infinite series with declining coefficients. The rate of convergence is standard for one dimensional nonparametric regression. We investigate the finite sample performance of our method, in comparison with other well-established methods, in a small simulation experiment.Coupon bonds, kernel estimation, Hilbert space, nonparametric regression, term structure estimation, yield curve, zero coupon.

KERNEL NONPARAMETRIC REGRESSION FOR THE MODELIZING OF THE PRODUCTIVITY WETLAND PADDY

Nonparametric regression can be used when the relationship between the response variable and the predictor variables have an unknown pattern form the regression curve. One of the method that can be used to predictproductivity of the wetland paddy is a nonparametric regression kernel. In kernel regression, there are severaltypes of estimator that can be used to modelling productivity of wetland paddy in Central Java, one of which isNadaraya-Watson estimator. Variables used in the study of the productivity of rice as the response variable,while the predictor variables that harvested area, production and rainfall. Based on estimates indicate that thekernel nonparametric regression optimum bandwidth value 1.2 and GCV = 1.7577. The coefficient ofdetermination (R2) of 94.23% and MSE of 0.8560. Keywords: Kernel Nonparametric Regression, Productivity, Wetland Padd

Kernel-based Estimation Method

Regression is a basic statistical tool for estimation task of data mining, which is to predict the relationship between a dependent variable and one or more independent variables. Parametric and nonparametric regressions are two kinds of regression approach used for various problems. This work proposes a kernel-based nonparametric regression method, which can solve nonlinear regression problem properly by mapping the data to a higher-dimensional space by kernel function. With this method, we conduct a series of experiment on nonlinear function and real world regression problems, and the results reveal the effectiveness of the model. The results reveal that the model is efficient on some data sets with similar or even higher precision than the prevalently used support vector regression and neural network regression method. Nevertheless, there are still other data sets which kernel-based method cannot works well, as water flow and forest fire data set

ESTIMATION OF A SEMIPARAMETRICIGARCH(1,1) MODEL

We propose a semiparametric IGARCH model that allows for persistence invariance but also allows for more flexible functional form. We assume that thedifference of the squared process is weakly stationary. We propose an estimationstrategy based on the nonparametric instrumental variable method. We establishthe rate of convergence of our estimator.Inverse Problem, Instrumental Variable, IGARCH,Kernel Estimation, Nonparametric regression

A note on kernel principal component regression

Kernel principal component regression (KPCR) was studied by Rosipal et al. [18, 19, 20], Hoegaerts et al. [7], and Jade et al. [8]. However, KPCR still encounters theoretical difficulties in the procedure for constructing KPCR and in the choice rule for the retained number of principal components. In this paper, we revise the method of KPCR to overcome the difficulties. The performance of the revised method is compared to linear regression, nonlinear regression based on Gompertz function, and nonparametric Nadaraya-Watson regression, and gives better results than those of the three methods

Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods

We investigate a class of semiparametric ARCH(8) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the 'news impact' function. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric and nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 daily returns. We find some evidence of asymmetric news impact functions in the data.ARCH, inverse problem, kernel estimation, news impact curve, nonparametric regression, profile likelihood, semiparametric estimation, volatility

NP-optimal kernels for nonparametric sequential detection rules

An attractive nonparametric method to detect change-points sequentially is to apply control charts based on kernel smoothers. Recently, the strong convergence of the associated normed delay associated with such a sequential stopping rule has been studied under sequences of out-of-control models. Kernel smoothers employ a kernel function to downweight past data. Since kernel functions with values in the unit interval are sufficient for that task, we study the problem to optimize the asymptotic normed delay over a class of kernels ensuring that restriction and certain additional moment constraints. We apply the key theorem to discuss several important examples where explicit solutions exist to illustrate that the results are applicable. --Control charts,financial data,nonparametric regression,quality control,statistical genetics