Smoothed L-estimation of Regression Function

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data.This sensitivity can be reduced, for example, by using local L-estimates of regression.Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function.The asymptotic distribution of the proposed estimator is derived under mild ¯-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical ¯nite-sample improvements.Finally, the proposed method is applied to the modelling of implied volatilitynonparametric regression;L-estimation;smoothed cumulative distribution function

Robust Estimation of Dimension Reduction Space

Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions.We show that the recently proposed methods by Xia et al.(2002) can be made robust in such a way that preserves all advantages of the original approach.Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.Dimension reduction;Nonparametric regression;M-estimation

Estimation of NAIRU with In ation Expectation Data

Estimating natural rate of unemployment (NAIRU) is important for understanding the joint dynamics of unemployment, inflation, and inflation expectation. However, existing literature falls short of endogenizing inflation expectation together with NAIRU in a model consistent way. We estimate a structural model with forward and backward looking Phillips curve. Inflation expectation is treated as a function of state variables and we use survey data as its noisy observations. Surprisingly, we find that the estimated NAIRU tracks unemployment rate closely, except for the high inflation period (late 1970s). Compared to the estimation without using the survey data, the estimated Bayesian credible sets are narrower and our model leads to better inflation and unemployment forecasts. These results suggest that monetary policy was very effective and there was not much room for policy improvement

Smoothed L-estimation of Regression Function

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data.This sensitivity can be reduced, for example, by using local L-estimates of regression.Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function.The asymptotic distribution of the proposed estimator is derived under mild ¯-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical ¯nite-sample improvements.Finally, the proposed method is applied to the modelling of implied volatilit

Testing Parametric versus Semiparametric Modelling in Generalized Linear Models

We consider a generalized partially linear model E(Y|X,T) = G{X'b + m(T)} where G is a known function, b is an unknown parameter vector, and m is an unknown function.The paper introduces a test statistic which allows to decide between a parametric and a semiparametric model: (i) m is linear, i.e. m(t) = t'g for a parameter vector g, (ii) m is a smooth (nonlinear) function.Under linearity (i) it is shown that the test statistic is asymptotically normal. Moreover, for the case of binary responses, it is proved that the bootstrap works asymptotically.Simulations suggest that (in small samples) bootstrap outperforms the calculation of critical values from the normal approximation.The practical performance of the test is shown in applications to data on East--West German migration and credit scoring.linear models

LASSO-Driven Inference in Time and Space

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak dependence. A sequence of large-scale regressions with LASSO is applied to reduce the dimensionality, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors

Localising temperature risk

On the temperature derivative market, modelling temperature volatility is an important issue for pricing and hedging. In order to apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that, after scale normalisation, a pure standardised Gaussian variable appears. Earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well. Therefore, we consider a local adaptive modelling approach to find, at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure for localised temperature risk by achieving nearly normal risk factors. We also employ our model to forecast the temperature in different cities and compare it to a model developed in Campbell and Diebold (2005)