Zudi Lu

Kernel density estimation for spatial processes: the L 1 theory

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc.

Local linear spatial quantile regression

Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.

Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution

A parametric approach to estimating and forecasting Value-at-Risk (VaR) and expected shortfall (ES) for a heteroscedastic financial return series is proposed. The well-known GJR-GARCH form models the volatility process, capturing the leverage effect. To capture potential skewness and heavy tails, the model assumes an asymmetric Laplace form as the conditional distribution of the series. Furthermore, dynamics in higher moments are modeled by allowing the shape parameter in this distribution to be time-varying. Estimation is via an adaptive Markov chain Monte Carlo (MCMC) sampling scheme, employing the Metropolis-Hastings (MH) algorithm with a mixture of Gaussian proposal distributions. A simulation study highlights accurate estimation and improved inference compared to a single-Gaussian-proposal MH method. The model is illustrated by applying it to four international stock market indices and two exchange rates, generating one-step-ahead forecasts of VaR and ES. Standard and non-standard tests are applied to these forecasts, and the finding is that the proposed model performs favourably compared to some popular competitors: in particular it is the only conservative model of risk over the period studied, which includes the recent global financial crisis.

NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a bootstrap simulation scheme for the selection of suitable bandwidth parameters involved in the kernel test as well as the choice of simulated critical values. An example of implementation is given to show that the proposed test works in practice.

Specification testing in nonlinear and nonstationary time series autoregression

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting and the results differ from earlier work on nonparametric autoregression with stationarity. In addition, we develop a new bootstrap simulation scheme for the selection of a suitable bandwidth parameter involved in the kernel test as well as the choice of a simulated critical value. The finitesample performance of the proposed test is assessed using one simulated example and one real data example.

LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE

Local linear fitting of nonlinear processes under strong (i.e., I±-) mixing conditions has been investigated extensively. However, it is often a difficult step to establish the strong mixing of a nonlinear process composed of several parts such as the popular combination of autoregressive moving average (ARMA) and generalized autoregressive conditionally heteroskedastic (GARCH) models. In this paper we develop an asymptotic theory of local linear fitting for near epoch dependent (NED) processes. We establish the pointwise asymptotic normality of the local linear kernel estimators under some restrictions on the amount of dependence. Simulations and application examples illustrate that the proposed approach can work quite well for the medium size of economic time series.We thank Yuichi Kitamura and two referees for helpful comments. This research was partially supported by a Leverhulme Trust research grant, the National Natural Science Foundation of China, and the Economic and Social Science Research Council of the UK.

A semiparametric spatial dynamic model

Stimulated by the Boston house price data, in this paper, we propose a semiparametric spatial dynamic model, which extends the ordinary spatial autoregressive models to accommodate the effects of some covariates associated with the house price. A profile likelihood based estimation procedure is proposed. The asymptotic normality of the proposed estimators are derived. We also investigate how to identify the parametric/nonparametric components in the proposed semiparametric model. We show how many unknown parameters an unknown bivariate function amounts to, and propose an AIC/BIC of nonparametric version for model selection. Simulation studies are conducted to examine the performance of the proposed methods. The simulation results show our methods work very well. We finally apply the proposed methods to analyze the Boston house price data, which leads to some interesting findings

Coordination in a Single-Retailer Two-Supplier Supply Chain under Random Demand and Random Supply with Disruption

This paper studies the coordination issue of a supply chain consisting of one retailer and two suppliers, a main supplier and a backup supplier. The main supplier’s yield is subject to disruption and the retailer faces a random demand. We determine the retailer’s optimal ordering policy and the main supplier’s production quantity that maximize expected profit of the centralized supply chain. We also analyze the decentralized scenario, and a combination of overproduction risk sharing and buy-back contracts with a side payment from/to the backup supplier is provided to coordinate the supply chain. Numerical examples are given to gain some qualitative insights.

Optimal production and procurement decisions in a supply chain with an option contract and partial backordering under uncertainties

This paper considers a decentralized supply chain including one retailer and one manufacturer, where the manufacturer’s production yield and the retailer’s demand are both stochastic. At the beginning of the selling season, the retailer places an order and purchases an option contract with the manufacturer. After the selling season, the excess demand is partially backordered, and the retailer exercises his option order and then place an instant order for the backorders. The optimal ordering policy for the retailer and the corresponding production decision for the manufacturer are studied. Numerical examples are carried out to show the impact of the model parameters on the optimal policies.

Local Linear Fitting Under Near Epoch Dependence: Uniform consistency with Convergence Rates

Local linear fitting is a popular nonparametric method in nonlinear statistical and econometric modelling. Lu and Linton (2007) established the point wise asymptotic distribution (central limit theorem) for the local linear estimator of nonparametric regression function under the condition of near epoch dependence. We further investigate the uniform consistency of this estimator. The uniformly strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results of uniform convergence rates for nonparametric kernel-based estimators are provided. Applications of our results to conditional variance function estimation and some economic time series models are also discussed. The results of this paper will be of widely potential interest in time series semiparametric modelling.