"Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes"

This paper considers a nonstandard kernel regression for strongly mixing processes when the regressor is nonnegative. The nonparametric regression is implemented using asymmetric kernels [Gamma (Chen, 2000b), Inverse Gaussian and Reciprocal Inverse Gaussian (Scaillet, 2004) kernels] that possess some appealing properties such as lack of boundary bias and adaptability in the amount of smoothing. The paper investigates the asymptotic and finite-sample properties of the asymmetric kernel Nadaraya-Watson, local linear, and re-weighted Nadaraya-Watson estimators. Pointwise weak consistency, rates of convergence and asymptotic normality are established for each of these estimators. As an important economic application of asymmetric kernel regression estimators, we reexamine the problem of estimating scalar diffusion processes.

Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels

This paper proposes a nonparametric regression using asymmetric kernel functions for nonnegative, absolutely regular processes, and specializes this technique to estimating scalar diffusion models of spot interest rate. We illustrate the advantages of asymmetric kernel estimators for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed estimators are evaluated in the context of bond and option pricing. We also present estimation results from empirical analysis of the term structure of U.S. interest rates.Nonparametric regression; Gamma kernel; diffusion estimation; spot interest rate; derivative pricing

APARCH Models Estimated by Support Vector Regression

This thesis presents a comprehensive study of asymmetric power autoregressive conditional heteroschedasticity (APARCH) models for modelling volatility in financial return data. The goal is to estimate and forecast volatility in financial data with excess kurtosis, volatility clustering and asymmetric distribution. Models based on maximum likelihood estimation (MLE) will be compared to the kernel based support vector regression (SVR). The popular Gaussian kernel and a wavelet based kernel will be used for the SVR. The methods will be tested on empirical data, including stock index prices, credit spreads and electric power prices. The results indicate that asymmetric power models are needed to capture the asseymtry in the data. Furthermore, SVR models are able to improve estimation and forecasting accuracy, compared with the APARCH models based on MLE.Masteroppgave i statistikkSTAT399MAMN-STA

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

Exploring Prediction Uncertainty in Machine Translation Quality Estimation

Machine Translation Quality Estimation is a notoriously difficult task, which lessens its usefulness in real-world translation environments. Such scenarios can be improved if quality predictions are accompanied by a measure of uncertainty. However, models in this task are traditionally evaluated only in terms of point estimate metrics, which do not take prediction uncertainty into account. We investigate probabilistic methods for Quality Estimation that can provide well-calibrated uncertainty estimates and evaluate them in terms of their full posterior predictive distributions. We also show how this posterior information can be useful in an asymmetric risk scenario, which aims to capture typical situations in translation workflows.Comment: Proceedings of CoNLL 201

Contour projected dimension reduction

In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace Cook [Regression Graphics (1998b) Wiley]. Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation and CP-directional regression to estimate the generalized contour subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.Comment: Published in at http://dx.doi.org/10.1214/08-AOS679 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Reproducing Kernel Perspective of Smoothing Spline Estimators

Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures.equivalent kernels, nonparametric regression, Hilbert spaces, time series filtering, spectral properties