
on Econometric Time Series 
By:  Juan Jose Dolado; Jesus Gonzalo; Laura Mayoral 
Abstract:  This paper presents an overview of some new results regarding an easily implementable Wald teststatistic (EFDF test) of the null hypotheses that a timeseries process is I(1) or I(0) against fractional I(d) alternatives, with d?(0,1), allowing for unknown deterministic components and serial correlation in the error term. Specifically, we argue that the EFDF test has better power properties under fixed alternatives than other available tests for fractional roots, as well as analyze how to implement this test when the deterministic components or the longmemory parameter are subject to structural breaks. 
Keywords:  Fractional processes, Deterministic components, Power, Structural breaks 
JEL:  C12 C22 
Date:  2008–01 
URL:  http://d.repec.org/n?u=RePEc:cte:werepe:we20080129&r=ets 
By:  Lennart Hoogerheide (Erasmus University Rotterdam); Herman K. van Dijk (Erasmus University Rotterdam) 
Abstract:  Highly nonelliptical posterior distributions may occur in several econometric models, in particular, when the likelihood information is allowed to dominate and data information is weak. We explain the issue of highly nonelliptical posteriors in a model for the effect of education on income using data from the wellknown Angrist and Krueger (1991) study and discuss how a socalled Information Matrix or Jeffreys' prior may be used as a `regularization prior' that in combination with the likelihood yields posteriors with desirable properties. We further consider an 8dimensional bimodal posterior distribution in a 2regime mixture model for the real US GNP growth. In order to perform a Bayesian posterior analysis using indirect sampling methods in these models, one has to find a good candidate density. In a recent paper  Hoogerheide, Kaashoek and Van Dijk (2007)  a class of neural network functions was introduced as candidate densities in case of nonelliptical posteriors. In the present paper, the connection between canonical model structures, nonelliptical credible sets, and more sophisticated neural network simulation techniques is explored. In all examples considered in this paper – a bimodal distribution of Gelman and Meng (1991) and posteriors in IV and mixture models  the mixture of Student's <I>t</I> distributions is clearly a much better candidate than a Student's <I>t</I> candidate, yielding far more precise estimates of posterior means after the same amount of computing time, whereas the Student's <I>t</I> candidate almost completely misses substantial parts of the parameter space. 
Keywords:  instrumental variables; vector error correction model; mixture model; importance sampling; Markov chain Monte Carlo; neural network 
JEL:  C11 C15 C45 
Date:  2008–04–08 
URL:  http://d.repec.org/n?u=RePEc:dgr:uvatin:20080036&r=ets 
By:  Erik Hjalmarsson 
Abstract:  This paper analyzes the asymptotic properties of longhorizon estimators under both the null hypothesis and an alternative of predictability. Asymptotically, under the null of no predictability, the longrun estimator is an increasing deterministic function of the shortrun estimate and the forecasting horizon. Under the alternative of predictability, the conditional distribution of the longrun estimator, given the shortrun estimate, is no longer degenerate and the expected pattern of coefficient estimates across horizons differs from that under the null. Importantly, however, under the alternative, highly endogenous regressors, such as the dividendprice ratio, tend to deviate much less than exogenous regressors, such as the short interest rate, from the pattern expected under the null, making it more difficult to distinguish between the null and the alternative. 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgif:928&r=ets 
By:  Mohamed Boutahar (GREQAM  Groupement de Recherche en Économie Quantitative d'AixMarseille  Université de la Méditerranée  AixMarseille II  Université Paul Cézanne  AixMarseille III  Ecole des Hautes Etudes en Sciences Sociales  CNRS : UMR6579); Gilles Dufrénot (GREQAM  Groupement de Recherche en Économie Quantitative d'AixMarseille  Université de la Méditerranée  AixMarseille II  Université Paul Cézanne  AixMarseille III  Ecole des Hautes Etudes en Sciences Sociales  CNRS : UMR6579); Anne PeguinFeissolle (GREQAM  Groupement de Recherche en Économie Quantitative d'AixMarseille  Université de la Méditerranée  AixMarseille II  Université Paul Cézanne  AixMarseille III  Ecole des Hautes Etudes en Sciences Sociales  CNRS : UMR6579) 
Abstract:  This paper generalizes the standard long memory modeling by assuming that the long memory parameter d is stochastic and time varying: we introduce a STAR process on this parameter characterized by a logistic function. We propose an estimation method of this model. Some simulation experiments are conducted. The empirical results suggest that this new model offers an interesting alternative competing framework to describe the persistent dynamics in modelling some financial series. 
Keywords:  Longmemory, Logistic function, STAR 
Date:  2008–04–23 
URL:  http://d.repec.org/n?u=RePEc:hal:papers:halshs00275254_v1&r=ets 
By:  Ibrahim Ahamada (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, Ecole d'économie de Paris  Paris School of Economics  Université PanthéonSorbonne  Paris I); Philippe Jolivaldt (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, Ecole d'économie de Paris  Paris School of Economics  Université PanthéonSorbonne  Paris I) 
Abstract:  Test for unit root based in wavelets theory is recently defined (Genay and Fan, 2007). While the new test is supposed to be robust to the initial value, we bring out by contrast the significant effects of the initial value in the size and the power. We found also that both the wavelets unit root test and ADF test give the same efficiency if the data are corrected of the initial value. Our approach is based in monte carlo experiment. 
Keywords:  Unit root tests, wavelets, monte carlo experiments, sizepower curve. 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:hal:papers:halshs00275767_v1&r=ets 
By:  Prof D.S.G. Pollock 
Abstract:  An account is given of some techniques of linear filtering that can be used for extracting the business cycle from economic data sequences of limited duration. It is argued that there can be no definitive definition of the business cycle. Both the definition of the business cycle and the methods that are used to extract it must be adapted to the purposes of the analysis; and different definitions may be appropriate to different eras. 
Keywords:  Linear filtering; Frequencydomain analysis; Flexible trends 
JEL:  C22 
Date:  2008–04 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:08/12&r=ets 
By:  Prof D.S.G. Pollock 
Abstract:  This paper shows how a frequencyselective filter that is applicable to short trended data sequences can be implemented via a frequencydomain approach. A filtered sequence can be obtained by multiplying the Fourier ordinates of the data by the ordinates of the frequency response of the filter and by applying the inverse Fourier transform to carry the product back into the time domain. Using this technique, it is possible, within the constraints of a finite sample, to design an ideal frequencyselective filter that will preserve all elements within a specified range of frequencies and that will remove all elements outside it. Approximations to ideal filters that are implemented in the time domain are commonly based on truncated versions of the infinite sequences of coefficients derived from the Fourier transforms of rectangular frequency response functions. An alternative to truncating an infinite sequence of coefficients is to wrap it around a circle of a circumference equal in length to the data sequence and to add the overlying coefficients. The coefficients of the wrapped filter can also be obtained by applying a discrete Fourier transform to a set of ordinates sampled from the frequency response function. Applying the coefficients to the data via circular convolution produces results that are identical to those obtained by a multiplication in the frequency domain, which constitutes a more efficient approach. 
Keywords:  Linear filtering; Frequencydomain analysis 
JEL:  C22 
Date:  2008–04 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:08/13&r=ets 
By:  Beatrice Pataracchia 
Abstract:  In this paper we propose a method to derive the spectral representation in the case of a particular class of nonlinear models: Markov Switching ARMA models. The procedure simply relies on the application of the RieszFisher Theorem which describes the spectral density as the Fourier transform of the autocovariance functions. We explicitly show the analytical structure of the spectral density in the simple Markov Switching AR(1). Finally, a monetary policy application of a Markov Switching VAR(4) is presented 
Keywords:  Multivariate ARMA models; Regimeswitching models; Markov switching models; Frequency Domain 
JEL:  C32 C44 E52 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:usi:wpaper:528&r=ets 
By:  Eduardo Mendes; Les Oxley (University of Canterbury); William Rea; Marco Reale 
Abstract:  It is now recognised that long memory and structural change can be confused because the statistical properties of times series of lengths typical of financial and econometric series are similar for both models. We propose a new set of methods aimed at distinguishing between long memory and structural change. The approach, which utilises the computational efficient methods based upon Atheoretical Regression Trees (ART), establishes through simulation the bivariate distribution of the fractional integration parameter, d, with regime length for simulated fractionally integrated series. This bivariate distribution is then compared with the data for the time series. We also combine ART with the established goodness of fit test for long memory series due to Beran. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average. We show that in these series the value of the fractional integration parameter is not constant with time. The mathematical consequence of this is that the definition of H selfsimilarity is violated. We present evidence that these series have structural breaks. 
Keywords:  Longrange dependence; Strong dependence; Global dependence; Hurst phenomena 
JEL:  C22 
Date:  2008–01–29 
URL:  http://d.repec.org/n?u=RePEc:cbt:econwp:08/04&r=ets 
By:  Viktor Winschel; Markus Krätzig 
Abstract:  We present an objectoriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The imple mented solution methods for nding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev polynomial approximation with the Smolyak op erator to overcome the course of dimensionality. The operator is also useful for numerical integration and we use it for the integrals arising in rational expecta tions and in nonlinear state space lters. The estimation step is done by a parallel MetropolisHastings (MH) algorithm, using a linear or nonlinear lter. Implemented are the Kalman, Extended Kalman, Particle, Smolyak Kalman, Smolyak Sum, and Smolyak Kalman Particle lters. The MH sampling step can be interactively moni tored and controlled by sequence and statistics plots. The number of parallel threads can be adjusted to benet from multiprocessor environments. JBendge is based on the framework JStatCom, which provides a standardized ap plication interface. All tasks are supported by an elaborate multithreaded graphical user interface (GUI) with project management and data handling facilities. 
Keywords:  Dynamic Stochastic General Equilibrium (DSGE) Models, Bayesian Time Series Econometrics, Java, Software Development 
JEL:  C11 C13 C15 C32 C52 C63 C68 C87 
Date:  2008–04 
URL:  http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2008034&r=ets 
By:  Lanne, Markku; Saikkonen, Pentti 
Abstract:  This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregressive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly show how the considered economic variable is affected by expectations and how expectations are formed. Noncausal autoregressive models can also be used to examine the related issue of backwardlooking or forwardlooking dynamics of an economic variable. We show in the paper how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and how related test procedures can be obtained. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a detailed discussion on their specification is provided. Motivated by economic applications we explicitly use a forwardlooking autoregressive polynomial in the formulation of the model. This is different from the practice used in previous statistics literature on noncausal autoregressions and, in addition to its economic motivation, it is also convenient from a statistical point of view. In particular, it facilitates obtaining likelihood based diagnostic tests for the specified orders of the backwardlooking and forwardlooking autoregressive polynomials. Such test procedures are not only useful in the specification of the model but also in testing economically interesting hypotheses such as whether the considered variable only exhibits forwardlooking behavior. As an empirical application, we consider modeling the U.S. inflation dynamics which, according to our results, is purely forwardlooking. 
Keywords:  Noncausal autoregression; expectations; inflation persistence 
JEL:  C52 E31 C22 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:8411&r=ets 