
on Econometric Time Series 
By:  Nielsen, Morten (Cornell U and CREATES) 
Abstract:  This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung's (2002) test as the special case d = 1. It is shown that (i) each member of the family with d > 0 is consistent, (ii) the asymptotic distribution depends on d, and thus reects the parameter chosen to implement the test, and (iii) since the asymptotic distribution depends on d and the test remains consistent for all d > 0, it is possible to analyze the power of the test for different values of d. The usual PhillipsPerron or DickeyFuller type tests are characterized by tuning parameters (bandwidth, lag length, etc.), i.e. parameters which change the test statistic but are not reected in the asymptotic distribution, and thus have none of these three properties. It is shown that members of the family with d < 1 have higher asymptotic local power than the Breitung (2002) test, and when d is small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear timetrend. Furthermore, GLS detrending is shown to improve power when d is small, which is not the case for Breitung's (2002) test. Simulations demonstrate that, apart from some size distortion in the presence of large negative AR or MA coefficients, the proposed test has good finite sample properties in the presence of both linear and nonlinear shortrun dynamics. When applying a sieve bootstrap procedure, the proposed test has very good size properties, with finite sample power that is higher than that of Breitung's (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented DickeyFuller test with lag length chosen by an information criterion. 
JEL:  C22 
Date:  2008–05 
URL:  http://d.repec.org/n?u=RePEc:ecl:corcae:0805&r=ets 
By:  Jorda, Oscar (U of California, Davis); Marcellino, Massimiliano (Universita Bocconi) 
Abstract:  A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffe's (1953) Smethod. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy. 
JEL:  C32 
Date:  2008–07 
URL:  http://d.repec.org/n?u=RePEc:ecl:ucdeco:085&r=ets 
By:  Alexander Chudik (European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.); M. Hashem Pesaran (University of Cambridge, CIMF and USC; Faculty of Economics, Austin Robinson Building, Sidgwick Avenue, Cambridge, CB3 9DD, United Kingdom.) 
Abstract:  This paper introduces a novel approach for dealing with the 'curse of dimensionality' in the case of large linear dynamic systems. Restrictions on the coefficients of an unrestricted VAR are proposed that are binding only in a limit as the number of endogenous variables tends to infinity. It is shown that under such restrictions, an infinitedimensional VAR (or IVAR) can be arbitrarily well characterized by a large number of finitedimensional models in the spirit of the global VAR model proposed in Pesaran et al. (JBES, 2004). The paper also considers IVAR models with dominant individual units and shows that this will lead to a dynamic factor model with the dominant unit acting as the factor. The problems of estimation and inference in a stationary IVAR with unknown number of unobserved common factors are also investigated. A cross section augmented least squares estimator is proposed and its asymptotic distribution is derived. Satisfactory small sample properties are documented by Monte Carlo experiments. JEL Classification: C10, C33, C51. 
Keywords:  Large N and T Panels, Weak and Strong Cross Section Dependence, VAR, Global VAR, Factor Models. 
Date:  2009–01 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20090998&r=ets 
By:  Frederik Herzberg (Institute of Mathematical Economics, Bielefeld University) 
Abstract:  This article shows that the nonstandard approach to stochastic integration with respect to Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to jumpdiffusions with finitevariation jump part. It is proven that internal stochastic integrals with respect to hyperfinite Lévy processes possess right standard parts, and that these standard parts coincide with the classical pathwise stochastic integrals, provided the integrator's jump part is of finite variation. If the integrator's Lévy measure is bounded from below, one can obtain a similar result for stochastic integrals with respect to C^2 functions of Lévy processes. As a byproduct, this yields a short, direct nonstandard proof of the generalized Ito's formula for stochastic differentials of smooth functions of Lévy processes. 
Keywords:  Lévy processes, stochastic integration, nonstandard analysis, ItÃ´ formula 
Date:  2008–06 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:404&r=ets 
By:  Jing, Li 
Abstract:  This paper examines the performance of prediction intervals based on bootstrap for threshold autoregressive models. We consider four bootstrap methods to account for the variability of estimates, correct the smallsample bias of autoregressive coefficients and allow for heterogeneous errors. Simulation shows that (1) accounting for the sampling variability of estimated threshold values is necessary despite superconsistency, (2) biascorrection leads to better prediction intervals under certain circumstances, and (3) twosample bootstrap can improve long term forecast when errors are regimedependent. 
Keywords:  Bootstrap; Interval Forecasting; Threshold Autoregressive Models; Time Series; Simulation 
JEL:  C53 C22 C15 
Date:  2009–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:13086&r=ets 
By:  Buncic, Daniel 
Abstract:  The forecast performance of the empirical ESTAR model of Taylor et al. (2001) is examined for 4 bilateral real exchange rate series over an outofsample evaluation period of nearly 12 years. Point as well as density forecasts are evaluated relative to a simple AR(1) specification, considering horizons up to 22 steps head. The results of this study suggest that no forecast gains over a simple AR(1) model exist at any of the forecast horizons that are considered, regardless of whether point or density forecasts are used. Using simulation and nonparametric techniques in conjunction with graphical methods, this study shows that the nonlinearity in the point forecasts of the ESTAR model decrease as the forecast horizon increases. Multiple steps ahead density forecasts of the ESTAR model are approximately normal looking, with no signs of skewness or bimodality. For an applied forecaster, there do not appear to exist any gains in using the nonlinear ESTAR model over a simple AR(1) specification. 
Keywords:  Purchasing power parity; regime modelling; nonlinear real exchange rate models; ESTAR; forecast evaluation; density forecasts; nonparametric methods. 
JEL:  C53 C52 C22 F47 F31 
Date:  2009–02–03 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:13121&r=ets 