
on Econometric Time Series 
By:  Dennis Kristensen (Columbia University and CREATES) 
Abstract:  A novel estimation method for two classes of semiparametric scalar diffusion models is proposed: In the first class, the diffusion term is parameterised and the drift is left unspecified, while in the second class only the drift term is specified. Under the assumption of stationarity, the unspecified term can be identified as a functional of the parametric component and the stationary density. Given a discrete sample with a fixed time distance, the parametric compo nent is then estimated by maximizing the associated likelihood with a preliminary estimator of the unspecified term plugged in. It is shown that this PseudoMLE (PMLE) is root nconsistent and asymptotically normally distributed under regularity conditions, and demonstrate how the models and estimators can be used in a twostep specification testing strategy of fully parametric models. Since the likelihood function is not available on closed form, the practical implementa tion of our estimator and tests will rely on simulated or approximate PMLE's. Under regularity conditions, it is verified that approximate/simulated versions of the PMLE inherits the prop erties of the actual but infeasible estimator. A simulation study investigates the finitesample performance of the PMLE, and finds that it performs well and is comparable to parametric MLE both in terms of bias and variance. 
Keywords:  Diffusion process, fixedtime distance asymptotics, kernel estimation, pseudolikelihood, semiparametric 
JEL:  C12 C13 C14 C22 
Date:  2009–09–18 
URL:  http://d.repec.org/n?u=RePEc:aah:create:200941&r=ets 
By:  Zhijie Xiao (Boston College); Roger Koenker (University of Illinois UrbanaChampaign) 
Abstract:  Conditional quantile estimation is an essential ingredient in modern risk management. Although GARCH processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this paper, we study estimation of conditional quantiles for GARCH models using quantile regression. Quantile regression estimation of GARCH models is highly nonlinear; we propose a simple and effective twostep approach of quantile regression estimation for linear GARCH time series. In the first step, we employ a quan tile autoregression sieve approximation for the GARCH model by combining information over different quantiles; second stage estimation for the GARCH model is then carried out based on the first stage minimum distance estimation of the scale process of the time series. Asymptotic properties of the sieve approximation, the minimum distance estimators, and the final quantile regression estimators employing generated regressors are studied. These results are of independent interest and have applications in other quantile regression settings. Monte Carlo and empirical application results indicate that the proposed estimation methods outperform some existing conditional quantile estimation methods. 
Keywords:  Quantile Regression, GARCH, ValueatRisk 
JEL:  C13 C21 C22 
Date:  2009–03–13 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:725&r=ets 
By:  Andros Kourtellos (Department of Economics,University of Cyprus); Thanasis Stengos (Department of Economics, University of Guelphy); Chih Ming Tan (Department of Economics,Tufts University) 
Abstract:  This paper extends the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for endogeneity of the threshold variable. We develop a concentrated least squares estimator of the threshold parameter based on an inverse Mills ratio bias correction. We show that our estimator is consistent and investigate its performance using a Monte Carlo simulation that indicates the applicability of the method in finite samples. 
JEL:  C13 C51 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:gue:guelph:20097.&r=ets 
By:  Pawel J. Szerszen 
Abstract:  In this paper I analyze a broad class of continuoustime jump diffusion models of asset returns. In the models, stochastic volatility can arise either from a diffusion part, or a jump part, or both. The jump component includes either compound Poisson or Lévy alphastable jumps. To be able to estimate the models with latent Lévy alphastable jumps, I construct a new Markov chain Monte Carlo algorithm. I estimate all model specifications with S&P500 daily returns. I find that models with Levy alphastable jumps perform well in capturing return characteristics if diffusion is a source of stochastic volatility. Models with stochastic volatility from jumps and models with Poisson jumps cannot represent excess kurtosis and tails of return distribution. In density forecast and VaR analysis, the model with Levy alphastable jumps and joint stochastic volatility performs the best among all other specifications, since both diffusion and infinite activity jump part provide information about latent volatility. 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:200940&r=ets 
By:  Christopher Gust; Robert Vigfusson 
Abstract:  Are structural vector autoregressions (VARs) useful for discriminating between macro models? Recent assessments of VARs have shown that these statistical methods have adequate size properties. In other words, in simulation exercises, VARs will only infrequently reject the true data generating process. However, in assessing a statistical test, we often also care about power: the ability of the test to reject a false hypothesis. Much less is known about the power of structural VARs. ; This paper attempts to fill in this gap by exploring the power of longrun structural VARs against a set of DSGE models that vary in degree from the true data generating process. We report results for two tests: the standard test of checking the sign on impact and a test of the shape of the response. For the models studied here, testing the shape is a more powerful test than simply looking at the sign of the response. In addition, relative to an alternative statistical test based on sample correlations, we find that the shapebased tests have greater power. Given the results on the power and size properties of longrun VARs, we conclude that these VARs are useful for discriminating between macro models. 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgif:978&r=ets 
By:  Heinen, Florian; Sibbertsen, Philipp; Kruse, Robinson 
Abstract:  We consider the problem of forecasting time series with long memory when the memory parameter is subject to a structural break. By means of a largescale Monte Carlo study we show that ignoring such a change in persistence leads to substantially reduced forecasting precision. The strength of this effect depends on whether the memory parameter is increasing or decreasing over time. A comparison of six forecasting strategies allows us to conclude that pretesting for a change in persistence is highly recommendable in our setting. In addition we provide an empirical example which underlines the importance of our findings. 
Keywords:  Long memory time series, Break in persistence, Structural change, Simulation, Forecasting competition 
JEL:  C15 C22 C53 
Date:  2009–11 
URL:  http://d.repec.org/n?u=RePEc:han:dpaper:dp433&r=ets 