
on Econometric Time Series 
By:  Alessandro De Gregorio (Department of Economics, Business and Statistics, Università di Milano, Italy); Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT) 
Abstract:  A one dimensional diffusion process X={X_t, 0 <= t <= T}, with drift b(x) and diffusion coefficient s(theta, x)=sqrt(theta) s(x) known up to theta>0, is supposed to switch volatility regime at some point t* in (0,T). On the basis of discrete time observations from X, the problem is the one of estimating the instant of change in the volatility structure t* as well as the two values of theta, say theta_1 and theta_2, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length Delta_n with n*Delta_n=T. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant. 
Keywords:  discrete observations, diffusion process, change point problem, volatility regime switch, nonparametric estimator, 
Date:  2007–09–18 
URL:  http://d.repec.org/n?u=RePEc:bep:unimip:1063&r=ets 
By:  Luis Fernando Melo; John Jairo León; Dagoberto Saboya 
Abstract:  This paper extends the asymptotic results of the dynamic ordinary least squares (DOLS) cointegration vector estimator of Mark and Sul (2003) to a threedimensional panel. We use a balanced panel of N and M lengths observed over T time periods. The cointegration vector is homogenous across individuals but we allow for individual heterogeneity using different shortrun dynamics, individualspecific fixed effects and individualspecific time trends. Both individual effects are considered for the first two dimensions. We also model some degree of crosssectional dependence using timespecific effects. This paper was motivated by the threedimensional panel cointegration analysis used to estimate the total factor productivity for Colombian regions and sectors during 19752000 by Iregui, Melo and Ram´ırez (2007). They used the methodology proposed by Marrocu, Paci and Pala (2000); however, hypothesis testing is not valid under this technique. The methodology we are currently proposing allows us to estimate the longrun relationship and to construct asymptotically valid test statistics in the 3Dpanel context. 
Date:  2007–12–17 
URL:  http://d.repec.org/n?u=RePEc:col:000094:004391&r=ets 
By:  Maria S. Heracleous 
Abstract:  Econometric modeling based on the Student’s t distribution introduces an additional parameter — the degree of freedom. In this paper we use a simulation study to investigate the ability of (i) the GARCHt model (Bollerslev, 1987) to estimate the true degree of freedom parameter and (ii) the sample kurtosis coefficient to accurately determine the implied degrees of freedom. Simulation results reveal that the GARCHt model and the sample kurtosis coefficient provide biased and inconsistent estimates of the degree of freedom parameter. Moreover, by varying ó2, we find that only the constant term in the conditional variance equation is affected, while the other parameters remain unaffected. 
Keywords:  Student’s t distribution, Degree of freedom, Kurtosis coefficient, GARCH t model 
JEL:  C15 C16 C22 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:eui:euiwps:eco2007/60&r=ets 
By:  Sarantis Tsiaplias (Melbourne Institute of Applied Economic and Social Research, The University of Melbourne) 
Abstract:  A model incorporating common Markovian regimes and GARCH residuals in a persistent factor environment is considered. Given the intractable and approximate nature of the likelihood function, a MetropolisinGibbs sampler with Bayesian features is constructed for estimation purposes. The common factor drawing procedure is effectively an exact derivation of the Kalman filter with a Markovian regime component and GARCH innovations. To accelerate the drawing procedure, approximations to the conditional density of the common component are considered. The model is applied to equity data for 18 developed markets to derive global, European, and country specific equity market factors. 
Keywords:  Common factors, Kalman filter, Markov switching, Monte Carlo, GARCH, Equities 
JEL:  C32 C51 
Date:  2007–06 
URL:  http://d.repec.org/n?u=RePEc:iae:iaewps:wp2007n18&r=ets 
By:  Turgut Kisinbay 
Abstract:  The paper proposes an algorithm that uses forecast encompassing tests for combining forecasts. The algorithm excludes a forecast from the combination if it is encompassed by another forecast. To assess the usefulness of this approach, an extensive empirical analysis is undertaken using a U.S. macroecoomic data set. The results are encouraging as the algorithm forecasts outperform benchmark model forecasts, in a mean square error (MSE) sense, in a majority of cases. 
Keywords:  Forecasting models , Economic forecasting , 
Date:  2007–11–21 
URL:  http://d.repec.org/n?u=RePEc:imf:imfwpa:07/264&r=ets 
By:  Alexander Chudik (Cambridge University); M. Hashem Pesaran (Cambridge University, CIMF USC and IZA) 
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. An empirical application to modelling of real GDP growth and investmentoutput ratios provides an illustration of the proposed approach. Considerable heterogeneities across countries and significant presence of dominant effects are found. The results also suggest that increase in investment as a share of GDP predict higher growth rate of GDP per capita for nonnegligible fraction of countries and vice versa. 
Keywords:  large N and T panels, weak and strong cross section dependence, VAR, global VAR, factor models, capital accumulation, growth 
JEL:  C10 C33 C51 O40 
Date:  2007–12 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp3206&r=ets 
By:  Kevin D. Hoover (Duke University); Katarina Juselius (Department of Economics, University of Copenhagen); Søren Johansen (Department of Economics, University of Copenhagen) 
Abstract:  An explication of the key ideas behind the Cointegrated Vector Autoregression Approach. The CVAR approach is related to Haavelmo’s famous “Probability Approach in Econometrics” (1944). It insists on careful stochastic specification as a necessary groundwork for econometric inference and the testing of economic theories. In timeseries data, the probability approach requires careful specification of the integration and cointegration properties of variables in systems of equations. The relationship between the CVAR approach and wider methodological issues and between it and related approaches (e.g., the LSE approach) are explored. The specifictogeneral strategy of widening the scope of econometric models to identify stochastic trends and cointegrating relations and to nest theoretical economic models is illustrated with the example of purchasingpower parity 
Keywords:  cointegrated VAR; stochastic trends; Purchasing Power Parity 
JEL:  B41 C32 C51 
Date:  2007–11 
URL:  http://d.repec.org/n?u=RePEc:kud:kuiedp:0735&r=ets 
By:  Søren Johansen (Department of Economics, University of Copenhagen); Katarina Juselius (Department of Economics, University of Copenhagen); Roman Frydman (New York University); Michael Goldberg (University of New Hampshire) 
Abstract:  This paper discusses a number of likelihood ratio tests on longrun relations and common trends in the I(2) model and provide new results on the test of overidentifying restrictions on β’xt and the asymptotic variance for the stochastic trends parameters, α⊥1: How to specify deterministic components in the I(2) model is discussed at some length. Model specification and tests are illustrated with an empirical analysis of long and persistent swings in the foreign exchange market between Germany and USA. The data analyzed consist of nominal exchange rates, relative prices, US inflation rate, two longterm interest rates and two shortterm interest rates over the 19751999 period. One important aim of the paper is to demonstrate that by structuring the data with the help of the I(2) model one can achieve a better understanding of the empirical regularities underlying the persistent swings in nominal exchange rates, typical in periods of floating exchange rates 
Keywords:  PPP puzzle; forward premium puzzle; cointegrated VAR; likelihood inference 
JEL:  C32 C52 F41 
Date:  2007–12 
URL:  http://d.repec.org/n?u=RePEc:kud:kuiedp:0734&r=ets 
By:  Chun Liu; John M Maheu 
Abstract:  Constructed from highfrequency data, realized volatility (RV) provides an efficient estimate of the unobserved volatility of financial markets. This paper uses a Bayesian approach to investigate the evidence for structural breaks in reduced form timeseries models of RV. We focus on the popular heterogeneous autoregressive (HAR) models of the logarithm of realized volatility. Using Monte Carlo simulations we demonstrate that our estimation approach is effective in identifying and dating structural breaks. Applied to daily S&P 500 data from 19932004, we find strong evidence of a structural break in early 1997. The main effect of the break is a reduction in the variance of logvolatility. The evidence of a break is robust to different models including a GARCH specification for the conditional variance of log(RV). 
Keywords:  realized volatility, change point, marginal likelihood, Gibbs sampling, GARCH 
JEL:  C22 C11 G10 
Date:  2007–12–18 
URL:  http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa304&r=ets 
By:  Carlo Altavilla (University of Naples “Parthenope”, Via Medina, 40  80133 Naples, Italy.); Matteo Ciccarelli (Corresponding author: European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.) 
Abstract:  This paper explores the role of model and vintage combination in forecasting, with a novel approach that exploits the information contained in the revision history of a given variable. We analyse the forecast performance of eleven widely used models to predict inflation and GDP growth, in the three dimensions of accuracy, uncertainty and stability by using the realtime data set for macroeconomists developed at the Federal Reserve Bank of Philadelphia. Instead of following the common practice of investigating only the relationship between first available and fully revised data, we analyse the entire revision history for each variable and extract a signal from the entire distribution of vintages of a given variable to improve forecast accuracy and precision. The novelty of our study relies on the interpretation of the vintages of a real time data base as related realizations or units of a panel data set. The results suggest that imposing appropriate weights on competing models of inflation forecasts and output growth — reflecting the relative ability each model has over different subsample periods — substantially increases the forecast performance. More interestingly, our results indicate that augmenting the information set with a signal extracted from all available vintages of timeseries consistently leads to a substantial improvement in forecast accuracy, precision and stability. JEL Classification: C32, C33, C53. 
Keywords:  Realtime data, forecast combination, data and model uncertainty. 
Date:  2007–12 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20070846&r=ets 