
on Econometric Time Series 
By:  Gunnar Bårdsen; Niels Haldrup (Department of Economics, University of Aarhus, Denmark) 
Abstract:  In static single equation cointegration regression models the OLS estimator will have a nonstandard distribution unless regressors are strictly exogenous. In the literature a number of estimators have been suggested to deal with this problem, especially by the use of seminonparametric estimators. Theoretically ideal instruments can be defined to ensure a limiting Gaussian distribution of IV estimators, but unfortunately such instruments are unlikely to be found in real data. In the present paper we suggest an IV estimator where the HodrickPrescott filtered trends are used as instruments for the regressors in cointegrating regressions. These instruments are almost ideal and simulations show that the IV estimator using such instruments alleviate the endogeneity problem extremely well in both finite and large samples. 
Keywords:  Cointegration, Instrumental variables, Mixed Gaussianity. 
JEL:  C2 C22 C32 
Date:  2006–02–16 
URL:  http://d.repec.org/n?u=RePEc:aah:aarhec:200603&r=ets 
By:  Svend Hylleberg (Department of Economics, University of Aarhus, Denmark) 
Abstract:  The main objective behind the production of seasonally adjusted time series is to give an easy access to a common time series data set purged of what is considered seasonal noise. Although the application of o¢ cially seasonally adjusted data may have the advantage of being cost saving it may also imply a less e¢ cient use of the information available, and one may apply a distorted set of data. Hence, in many cases, there may be a need for treating seasonality as an integrated part of an econometric analysis. In this article we present several di¤erent ways to integrate the seasonal adjustment into the econometric analysis in addition to applying data adjusted by the two most popular adjustment methods. 
Keywords:  Seasonality 
JEL:  C10 
Date:  2006–02–22 
URL:  http://d.repec.org/n?u=RePEc:aah:aarhec:200604&r=ets 
By:  Javier Hidalgo 
Abstract:  We consider the estimation of the location of the pole and memory parameter, ?0 and a respectively, of covariance stationary linear processes whose spectral density function f(?) satisfies f(?) ~ C?  ?0a in a neighbourhood of ?0. We define a consistent estimator of ?0 and derive its limit distribution Z?0 . As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that Z?0 is distributed as a normal random variable when ?0 ? (0, p), whereas for ?0 = 0 or p, Z?0 is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when ?0 = 0, Z?0 is distributed as a normal random variable truncated at zero. Moreover, we describe and examine a twostep estimator of the memory parameter a, showing that neither its limit distribution nor its rate of convergence is affected by the estimation of ?0. Thus, we reinforce and extend previous results with respect to the estimation of a when ?0 is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators. 
Keywords:  spectral density estimation, long memory processes, Gaussian processes 
JEL:  C14 G22 
Date:  2005–01 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/481&r=ets 
By:  Miguel A. Delgado; Javier Hidalgo; Carlos Velasco 
Abstract:  This article proposes a class of goodnessoffit tests for the autocorrelation function of a time series process, including those exhibiting longrange dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett's Tpprocess with estimated parameters, which converges in distribution to the standard Brownian Motion under the null hypothesis. We discuss tests of different nature such as omnibus, directional and Portmanteautype tests. A Monte Carlo study illustrates the performance of the different tests in practice. 
Keywords:  Nonparametric model checking, spectral distribution, linear processes, martingale decomposition, local alternatives, omnibus, smooth and directional tests, longrange alternatives 
JEL:  C14 C22 
Date:  2005–01 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/482&r=ets 
By:  Myunghwan Seo 
Abstract:  There is a growing literature on unit root testing in threshold autoregressive models. This paper makes two contributions to the literature. First, an asymptotic theory is developed for unit root testing in a threshold autoregression, in which the errors are allowed to be dependent and heterogeneous, and the lagged level of the dependent variable is employed as the threshold variable. The asymptotic distribution of the proposed Wald test is nonstandard and depends on nuisance parameters. Second, the consistency of the proposed residualbased block bootstrap is established based on a newly developed asymptotic theory for this bootstrap. It is demonstrated by a set of Monte Carlo simulations that the Wald test exhibits considerable power gains over the ADF test that neglects threshold effects. The law of one price hypothesis is investigated among used car markets in the US. 
Keywords:  Threshold autoregression, unit root test, threshold cointegration, residualbased block bootstrap 
JEL:  C12 C15 C22 
Date:  2005–01 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/484&r=ets 
By:  Andrew J. Patton; Allan Timmermann 
Abstract:  Evaluation of forecast optimality in economics and finance has almost exclusively been conducted on the assumption of mean squared error loss under which forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. This paper considers properties of optimal forecasts under general loss functions and establishes new testable implications of forecast optimality. These hold when the forecaster's loss function is unknown but testable restrictions can be imposed on the data generating process, trading off conditions on the data generating process against conditions on the loss function. Finally, we propose flexible parametric estimation of the forecaster's loss function, and obtain a test of forecast optimality via a test of overidentifying restrictions. 
Keywords:  forecast evaluation, loss function, rationality tests 
JEL:  C53 C22 C52 
Date:  2005–01 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/485&r=ets 
By:  Violetta Dalla; Javier Hidalgo 
Abstract:  The paper proposes a simple test for the hypothesis of strong cycles and as a byproduct a test for weak dependence for linear processes. We show that the limit distribution of the test is the maximum of a (semi)Gaussian process G(t), t ? [0; 1]. Because the covariance structure of G(t) is a complicated function of t and model dependent, to obtain the critical values (if possible) of maxt?[0;1] G(t) may be difficult. For this reason we propose a bootstrap scheme in the frequency domain to circumvent the problem of obtaining (asymptotically) valid critical values. The proposed bootstrap can be regarded as an alternative procedure to existing bootstrap methods in the time domain such as the residualbased bootstrap. Finally, we illustrate the performance of the bootstrap test by a small Monte Carlo experiment and an empirical example. 
Keywords:  Cyclical data, strong and weak dependence, spectral density functions, Whittle estimator, bootstrap algorithms 
JEL:  C15 C22 
Date:  2005–02 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/486&r=ets 
By:  Peter M Robinson 
Abstract:  Much time series data are recorded on economic and financial variables. Statistical modelling of such data is now very well developed, and has applications in forecasting. We review a variety of statistical models from the viewpoint of 'memory', or strength of dependence across time, which is a helpful discriminator between different phenomena of interest. Both linear and nonlinear models are discussed. 
Keywords:  Long memory, short memory, stochastic volatility 
JEL:  C22 
Date:  2005–03 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/487&r=ets 
By:  Peter M Robinson; Paolo Zaffaroni 
Abstract:  Strong consistency and asymptotic normality of the Gaussian pseudomaximumlikelihood estimate of the parameters in a wide class of ARCH(8) processesare established. We require the ARCH weights to decay at least hyperbolically,with a faster rate needed for the central limit theorem than for the law of largenumbers. Various rates are illustrated in examples of particular parameterizations in which our conditions are shown to be satisfied. 
Keywords:  ARCH(8,)models, pseudomaximum likelihoodestimation, asymptotic inference 
Date:  2005–10 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2005/495&r=ets 
By:  Violetta Dalla; Liudas Giraitis; Javier Hidalgo 
Abstract:  For linear processes, semiparametric estimation of the memory parameter, based on the logperiodogramand local Whittle estimators, has been exhaustively examined and their properties are well established.However, except for some specific cases, little is known about the estimation of the memory parameter fornonlinear processes. The purpose of this paper is to provide general conditions under which the localWhittle estimator of the memory parameter of a stationary process is consistent and to examine its rate ofconvergence. We show that these conditions are satisfied for linear processes and a wide class of nonlinearmodels, among others, signal plus noise processes, nonlinear transforms of a Gaussian process ?tandEGARCH models. Special cases where the estimator satisfies the central limit theorem are discussed. Thefinite sample performance of the estimator is investigated in a small MonteCarlo study. 
Keywords:  Long memory, semiparametric estimation, local Whittle estimator. 
JEL:  C14 C22 
Date:  2006–01 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:\2006\497&r=ets 
By:  Helena Veiga 
Abstract:  In this paper we fit the main features of financial returns by means of a two factor long memory stochastic volatility model (2FLMSV). Volatility, which is not observable, is explained by both a shortrun and a longrun factor. The first factor follows a stationary AR(1) process whereas the second one, whose purpose is to fit the persistence of volatility observable in data, is a fractional integrated process as proposed by Breidt et al. (1998) and Harvey (1998). We show formally that this model (1) creates more kurtosis than the long memory stochastic volatility (LMSV) of Breidt et al. (1998) and Harvey (1998), (2) deals with volatility persistence and (3) produces small first order autocorrelations of squared observations. In the empirical analysis, we use the estimation procedure of Gallant and Tauchen (1996), the Efficient Method of Moments (EMM), and we provide evidence that our specification performs better than the LMSV model in capturing the empirical facts of data. 
Date:  2006–02 
URL:  http://d.repec.org/n?u=RePEc:cte:wsrepe:ws061303&r=ets 
By:  P. Jeganathan (Indian Statistical Institute) 
Date:  2006–02 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1558&r=ets 
By:  Konstantin A. Kholodilin 
URL:  http://d.repec.org/n?u=RePEc:diw:diwwpp:dp554&r=ets 
By:  Alejandro Justiniano; Giorgio E. Primiceri 
Abstract:  In this paper we investigate the sources of the important shifts in the volatility of U.S. macroeconomic variables in the postwar period. To this end, we propose the estimation of DSGE models allowing for time variation in the volatility of the structural innovations. We apply our estimation strategy to a largescale model of the business cycle and find that investment specific technology shocks account for most of the sharp decline in volatility of the last two decades. 
JEL:  E30 C32 
Date:  2006–02 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:12022&r=ets 
By:  Gunnar Bårdsen (Department of Economics, Norwegian University of Science and Technology, Norway); Niels Haldrup (Department of Economics, University of Aarhus, Denmark) 
Abstract:  In static single equation cointegration regression models the OLS estimator will have a nonstandard distribution unless regressors are strictly exogenous. In the literature a number of estimators have been suggested to deal with this problem, especially by the use of seminonparametric estimators. Theoretically ideal instruments can be defined to ensure a limiting Gaussian distribution of IV estimators, but unfortunately such instruments are unlikely to be found in real data. In the present paper we suggest an IV estimator where the HodrickPrescott filtered trends are used as instruments for the regressors in cointegrating regressions. These instruments are almost ideal and simulations show that the IV estimator using such instruments alleviate the endogeneity problem extremely well in both finite and large samples. 
Keywords:  Cointegration; Instrumental variables; Mixed Gaussianity 
JEL:  C2 C22 C32 
Date:  2006–02–13 
URL:  http://d.repec.org/n?u=RePEc:nst:samfok:6706&r=ets 
By:  Joseph P. Romano; Michael Wolf 
Abstract:  Confidence intervals in econometric time series regressions suer from notorious coverage problems. This is especially true when the dependence in the data is noticeable and sample sizes are small to moderate, as is often the case in empirical studies. This paper suggests using the studentized block bootstrap and discusses practical issues, such as the choice of the block size. A particular datadependent method is proposed to automate the method. As a side note, it is pointed out that symmetric confidence intervals are preferred over equaltailed ones, since they exhibit improved coverage accuracy. The improvements in small sample performance are supported by a simulation study. 
Keywords:  Bootstrap, Confidence Intervals, Studentization, Time Series Regressions, Prewhitening 
JEL:  C14 C15 C22 C32 
Date:  2006–02 
URL:  http://d.repec.org/n?u=RePEc:zur:iewwpx:273&r=ets 
By:  Katsumi Shimotsu (Department of Economics, Queen's University); Morten Ørregaard Nielsen (Department of Economics, Cornell University) 
Abstract:  We propose to extend the cointegration rank determination procedure of Robinson and Yajima (2002) to accommodate both (asymptotically) stationary and nonstationary fractionally integrated processes as the common stochastic trends and cointegrating errors by applying the exact local Whittle analysis of Shimotsu and Phillips (2005). The proposed method estimates the cointegrating rank by examining the rank of the spectral density matrix of the d’th differenced process around the origin, where the fractional integration order, d, is estimated by the exact local Whittle estimator. Similar to other semiparametric methods, the approach advocated here only requires information about the behavior of the spectral density matrix around the origin, but it relies on a choice of (multiple) bandwidth(s) and threshold parameters. It does not require estimating the cointegrating vector(s) and is easier to implement than regressionbased approaches, but it only provides a consistent estimate of the cointegration rank, and formal tests of the cointegration rank or levels of confidence are not available except for the special case of no cointegration. We apply the proposed methodology to the analysis of exchange rate dynamics among a system of seven exchange rates. Contrary to both fractional and integerbased parametric approaches, which indicate at most one cointegrating relation, our results suggest three or possibly four cointegrating relations in the data. 
Keywords:  ` 
JEL:  C14 C32 
Date:  2006–01 
URL:  http://d.repec.org/n?u=RePEc:qed:wpaper:1029&r=ets 