
on Econometric Time Series 
By:  Mariam Camarero; Josep Lluis CarrioniSilvestre; Cecilio Tamarit (Universitat de Barcelona) 
Abstract:  This paper tests for real interest parity (RIRP) among the nineteen major OECD countries over the period 1978:Q21998:Q4. The econometric methods applied consist of combining the use of several unit root or stationarity tests designed for panels valid under crosssection dependence and presence of multiple structural breaks. Our results strongly support the fulfilment of the weak version of the RIRP for the studied period once dependence and structural breaks are accounted for. 
Keywords:  crosssection dependence, economic integration, panel data, real interest rate parity, structural breaks, unit root tests 
JEL:  C32 C33 F21 F32 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:bar:bedcje:2006159&r=ets 
By:  Vanessa BerenguerRico; Josep Lluis CarrioniSilvestre (Universitat de Barcelona) 
Abstract:  The paper addresses the concept of multicointegration in panel data frame work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either crosssection independent or crosssection dependence can be re moved by crosssection demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. 
Keywords:  common factors, crosssection dependence, crossmulticointegration, i(2) processes, multicointegration, panel data 
JEL:  C12 C22 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:bar:bedcje:2006160&r=ets 
By:  Lawrence J. Christiano; Martin Eichenbaum; Robert Vigfusson 
Abstract:  This paper analyzes the quality of VARbased procedures for estimating the response of the economy to a shock. We focus on two key issues. First, do VARbased confidence intervals accurately reflect the actual degree of sampling uncertainty associated with impulse response functions? Second, what is the size of bias relative to confidence intervals, and how do coverage rates of confidence intervals compare with their nominal size? We address these questions using data generated from a series of estimated dynamic, stochastic general equilibrium models. We organize most of our analysis around a particular question that has attracted a great deal of attention in the literature: How do hours worked respond to an identified shock? In all of our examples, as long as the variance in hours worked due to a given shock is above the remarkably low number of 1 percent, structural VARs perform well. This finding is true regardless of whether identification is based on shortrun or longrun restrictions. Confidence intervals are wider in the case of longrun restrictions. Even so, longrun identified VARs can be useful for discriminating among competing economic models. 
Keywords:  Vector analysis ; Econometric models 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgif:866&r=ets 
By:  Todd E. Clark; Michael W. McCracken 
Abstract:  A body of recent work suggests commonly–used VAR models of output, inflation, and interest rates may be prone to instabilities. In the face of such instabilities, a variety of estimation or forecasting methods might be used to improve the accuracy of forecasts from a VAR. These methods include using different approaches to lag selection, different observation windows for estimation, (over) differencing, intercept correction, stochastically time–varying parameters, break dating, discounted least squares, Bayesian shrinkage, and detrending of inflation and interest rates. Although each individual method could be useful, the uncertainty inherent in any single representation of instability could mean that combining forecasts from the entire range of VAR estimates will further improve forecast accuracy. Focusing on models of U.S. output, prices, and interest rates, this paper examines the effectiveness of combination in improving VAR forecasts made with real–time data. The combinations include simple averages, medians, trimmed means, and a number of weighted combinations, based on: BatesGranger regressions, factor model estimates, regressions involving just forecast quartiles, Bayesian model averaging, and predictive least squares–based weighting. Our goal is to identify those approaches that, in real time, yield the most accurate forecasts of these variables. We use forecasts from simple univariate time series models and the Survey of Professional Forecasters as benchmarks. 
Keywords:  Economic forecasting ; Vector autoregression 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:fip:fedkrw:rwp0612&r=ets 
By:  Dean Croushore 
Abstract:  This paper carries out the task of evaluating inflation forecasts from the Livingston Survey and the Survey of Professional Forecasters, using the realtime data set for macroeconomists as a source of realtime data. The author examines the magnitude and patterns of revisions to the inflation rate based on the output price index and describe what data to use as “actuals” in evaluating forecasts. The author then runs tests on the forecasts from the surveys to see how good they are, using a variety of actuals. The author finds that much of the empirical work from 20 years ago was a misleading guide to the quality of forecasts because of unique events during the earlier sample period. Repeating that empirical work over a longer sample period shows no bias or other problems in the forecasts. The use of realtime data also matters for some key tests on some variables. If a forecaster had used the empirical results from the late 1970s and early 1980s to adjust survey forecasts of inflation, forecast errors would have increased substantially. 
Keywords:  Inflation (Finance) 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:fip:fedpwp:0619&r=ets 
By:  Jönsson, Kristian (Department of Economics, Lund University) 
Abstract:  In this paper, we study the size distortions of the KPSS test for stationarity when serial correlation is present and samples are small and mediumsized. It is argued that two distinct sources of the size distortions can be identified. The first source is the finitesample distribution of the longrun variance estimator used in the KPSS test, while the second source of the size distortions is the serial correlation not captured by the longrun variance estimator due to a too narrow choice of truncation lag parameter. When the relative importance of the two sources is studied, it is found that the size of the KPSS test can be reasonably well controlled if the finitesample distribution of the KPSS test statistic, conditional on the timeseries dimension and the truncation lag parameter, is found. Hence, finitesample critical values, that can be applied in order to reduce the size distortions of the KPSS test, are supplied. When the power of the test is studied, it is found that the price paid for the increased size control is a lower power against a nonstationary alternative hypothesis. 
Keywords:  Stationarity Testing; Unit Root; FiniteSample Inference; LongRun Variance; Monte Carlo Simulation; Permanent Income Hypothesis; Private Consumption 
JEL:  C12 C14 C15 C22 E21 
Date:  2006–10–30 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2006_020&r=ets 
By:  Eiji Kurozumi; Yoichi Arai 
Abstract:  This paper considers a single equation cointegrating model and proposes the locally best invariant and unbiased (LBIU) test for the null hypothesis of cointegration. We derive the asymptotic local power functions and compare them with the standard residualbased test, and we show that the LBIU test is more powerful in a wide range of local alternatives. Then, we conduct a Monte Carlo simulation to investigate the nite sample properties of the tests and show that the LBIU test outperforms the residualbased test in terms of both size and power. The advantage of the LBIU test is particularly patent when the error is highly autocorrelated. Further, we point out that nite sample performance of existing tests is largely affected by the initial value condition while our tests are immune to it. We propose a simple transformation of data that resolves the problem in the existing tests. 
Keywords:  Cointegration, locally best test, point optimal test 
JEL:  C12 C22 
Date:  2006–11 
URL:  http://d.repec.org/n?u=RePEc:hst:hstdps:d06190&r=ets 
By:  Luc Bauwens; Arie Preminger; Jeroen V.K. Rombouts (IEA, HEC Montréal) 
Abstract:  We develop univariate regimeswitching GARCH (RSGARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a timevarying probability, specified as a function of past information. We provide sufficient conditions for stationarity and existence of moments. Because of path dependence, maximum likelihood estimation is infeasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We apply this model using the NASDAQ daily return series. 
Keywords:  GARCH, regime switching, Bayesian inference. 
JEL:  C11 C22 C52 
Date:  2006–06 
URL:  http://d.repec.org/n?u=RePEc:iea:carech:0608&r=ets 
By:  Francis Y. Kumah 
Abstract:  Adequate modeling of the seasonal structure of consumer prices is essential for inflation forecasting. This paper suggests a new econometric approach for jointly determining inflation forecasts and monetary policy stances, particularly where seasonal fluctuations of economic activity and prices are pronounced. In an application of the framework, the paper characterizes and investigates the stability of the seasonal pattern of consumer prices in the Kyrgyz Republic and estimates optimal money growth and implied exchange rate paths along with a jointly determined inflation forecast. The approach uses two broad specifications of an augmented errorcorrection modelwith and without seasonal components. Findings from the paper confirm empirical superiority (in terms of information content and contributions to policymaking) of augmented errorcorrection models of inflation over singleequation, BoxJenkinstype general autoregressive seasonal models. Simulations of the estimated errorcorrection models yield optimal monetary policy paths for achieving inflation targets and demonstrate the empirical significance of seasonality and monetary policy in inflation forecasting. 
Keywords:  Inflation forecasting , seasonal unit roots , monetary policy stance , errorocorrection models and VAR , Monetary policy , Inflation , Forecasting models , 
Date:  2006–07–28 
URL:  http://d.repec.org/n?u=RePEc:imf:imfwpa:06/175&r=ets 
By:  Marcus Pramor; Natalia T. Tamirisa 
Abstract:  How much convergence has been achieved between Central and Eastern European (CEE) economies and the eurozone? We explore this question by comparing longrun volatility trends in CEE currencies and the euro. We find that these trends are closely correlated, pointing to convergence in the economic and financial structures of these economies. Nonetheless, the degree of commonality remains weaker than what had been found for major European currencies before the introduction of the euro. Spillovers of volatility across regional markets appear to have diminished over time, with the exception of the Hungarian forint, which remains a source of volatility shocks to regional currencies. 
Keywords:  Exchange rate , volatility , GARCH , convergence , Central Europe , 
Date:  2006–09–25 
URL:  http://d.repec.org/n?u=RePEc:imf:imfwpa:06/206&r=ets 
By:  Frank Gerhard (Barclays Capital, London); Nikolaus Hautsch (Department of Economics, University of Copenhagen) 
Abstract:  This paper proposes a dynamic proportional hazard (PH) model with nonspecified baseline hazard for the modelling of autoregressive duration processes. A categorization of the durations allows us to reformulate the PH model as an ordered response model based on extreme value distributed errors. In order to capture persistent serial dependence in the duration process, we extend the model by an observation driven ARMA dynamic based on generalized errors. We illustrate the maximum likelihood estimation of both the model parameters and discrete points of the underlying unspecified baseline survivor function. The dynamic properties of the model as well as an assessment of the estimation quality is investigated in a Monte Carlo study. It is illustrated that the model is a useful approach to estimate conditional failure probabilities based on (persistent) serial dependent duration data which might be subject to censoring structures. In an empirical study based on financial transaction data we present an application of the model to estimate conditional asset price change probabilities. Evaluating the forecasting properties of the model, it is shown that the proposed approach is a promising competitor to wellestablished ACD type models. 
Keywords:  autoregressive duration models; dynamic ordered response models; generalized residuals; censoring 
JEL:  C22 C25 C41 G14 
Date:  2006–10 
URL:  http://d.repec.org/n?u=RePEc:kud:kuiefr:200605&r=ets 
By:  Chihwa Kao (Center for Policy Research, Maxwell School, Syracuse University, Syracuse NY 132441020); Lorenzo Trapani (Cass Business School and Bergamo University); Giovanni Urga (Cass Business School) 
Abstract:  This paper develops a novel asymptotic theory for panel models with common shocks. We assume that contemporaneous correlation can be generated by both the presence of common regressors among units and weak spatial dependence among the error terms. Several characteristics of the panel are considered: cross sectional and time series dimensions can either be fixed or large; factors can either be observable or unobservable; the factor model can describe either cointegration relationship or a spurious regression, and we also consider the stationary case. We derive the rate of convergence and the distribution limits for the ordinary least squares (OLS) estimates of the model parameters under all the aforementioned cases. 
Keywords:  crosssectional dependence; common shocks; nonstationary panel 
JEL:  C13 C23 
Date:  2006–02 
URL:  http://d.repec.org/n?u=RePEc:max:cprwps:77&r=ets 
By:  Fabrizio Cipollini; Robert F. Engle; Giampiero M. Gallo 
Abstract:  The Multiplicative Error Model introduced by Engle (2002) for positive valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with positive support. In this paper we propose a multivariate extension of such a model, by taking into consideration the possibility that the vector innovation process be contemporaneously correlated. The estimation procedure is hindered by the lack of probability density functions for multivariate positive valued random variables. We suggest the use of copulafunctions and of estimating equations to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. Empirical applications on volatility indicators are used to illustrate the gains over the equation by equation procedure. 
Date:  2006–11 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberte:0331&r=ets 
By:  Enzo Giacomini; Wolfgang Härdle; Ekaterina Ignatieva; Vladimir Spokoiny 
Abstract:  Measuring dependence in a multivariate time series is tantamount to modelling its dynamic structure in space and time. In the context of a multivariate normally distributed time series, the evolution of the covariance (or correlation) matrix over time describes this dynamic. A wide variety of applications, though, requires a modelling framework different from the multivariate normal. In risk management the nonnormal behaviour of most financial time series calls for nonlinear (i.e. nongaussian) dependency. The correct modelling of nongaussian dependencies is therefore a key issue in the analysis of multivariate time series. In this paper we use copulae functions with adaptively estimated time varying parameters for modelling the distribution of returns, free from the usual normality assumptions. Further, we apply copulae to estimation of ValueatRisk (VaR) of a portfolio and show its better performance over the RiskMetrics approach, a widely used methodology for VaR estimation. 
Keywords:  ValueatRisk, time varying copula, adaptive estimation, nonparametric estimation. 
JEL:  C14 
Date:  2006–11 
URL:  http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2006075&r=ets 
By:  Joan Jasiak (Department of Economics, York University); R. Sufana (University of Toronto); C. Gourieroux (CREST, CEPREMAP, University of Toronto) 
Abstract:  The Wishart Autoregressive (WAR) process is a multivariate process of stochastic positive definite matrices. The WAR is proposed in this paper as a dynamic model for stochastic volatility matrices. It yields simple nonlinear forecasts at any horizon and has factor representation, which separates white noise directions from those that contain all information about the past. For illustration, the WAR is applied to a sequence of intraday realized volatility covolatility matrices. 
Keywords:  Stochastic Volatility, Car Process, Factor Analysis, Reduced Rank, Realized Volatility 
JEL:  G13 C51 
Date:  2005–09 
URL:  http://d.repec.org/n?u=RePEc:yca:wpaper:2005_2&r=ets 
By:  Alfred A. Haug (Department of Economics, York University); Syed A. Basher (Department of Economics, York University) 
Abstract:  We test long¨Crun PPP within a general model of cointegration of linear and nonlinear form. Nonlinear cointegration is tested with rank tests proposed by Breitung (2001). We start with determining the order of integration of each variable in the model, applying relatively powerful DF¨CGLS tests of Elliott, Rothenberg and Stock (1996). Using monthly data from the post¨CBretton Woods era for G¨C10 countries, the evidence leads to a rejection of PPP for almost all countries. In several cases the price variables are driven by permanent shocks that differ from the ones that drive the exchange rate. Also, nonlinear cointegration cannot solve the PPP puzzle. 
Keywords:  Purchasing power parity; unit roots; nonlinear cointegration 
JEL:  C22 F40 
Date:  2003–01 
URL:  http://d.repec.org/n?u=RePEc:yca:wpaper:2003_1&r=ets 
By:  Ruthira Naraidoo (Keele University, Centre for Economic Research and School of Economic and Management Studies); Patrick Minford (Cardiff Business School, Aberconway Building, Cardiff University); Ioannis A. Venetis (University of Patras, Department of Economics) 
Abstract:  This paper develops a political economy model of multiple unemployment equilibria to provide a theory of an endogenous natural rate of unemployment using a nonlinear threshold model for a number of OECD countries. The theory here sees the natural rate and the associated path of unemployment as a reaction to shocks (mainly demand in nature) and the institutional structure of the economy. The channel through which these two forces feed on each other is a political economy process whereby voters with limited information on the natural rate react to shocks by demanding more or less social protection. The empirical results obtained confirm the existence of multiple and ``moving'' equilibria (``vicious'' and ``virtuous'' circles). The nonlinear model is compared with a linear version with the nonlinear framework always exhibiting superior insample fit and generally better outofsample predictive accuracy. The conclusion is that macroeconomics and supply side policies feed on each other via the political economy. 
Keywords:  Equilibrium unemployment, political economy, threshold model, forecasting 
JEL:  E24 E27 P16 
Date:  2006–10 
URL:  http://d.repec.org/n?u=RePEc:kee:kerpuk:2006/21&r=ets 
By:  Matteo Pelagatti 
Abstract:  Duration dependent Markovswitching VAR (DDMSVAR) models are time series models with data generating process consisting in a mixture of two VAR processes. The switching between the two VAR processes is governed by a two state Markov chain with transition probabilities that depend on how long the chain has been in a state. In the present paper we analyze the second order properties of such models and propose a Markov chain Monte Carlo algorithm to carry out Bayesian inference on the model’s unknowns. Furthermore, a freeware software written by the author for the analysis of time series by means of DDMSVAR models is illustrated. The methodology and the software are applied to the analysis of the U.S. business cycle. 
Keywords:  Markovswitching, business cycle, Gibbs sampler, duration dependence, vector autoregression 
JEL:  C11 C15 C32 C41 E32 
Date:  2003–08 
URL:  http://d.repec.org/n?u=RePEc:mis:wpaper:20051101&r=ets 
By:  Gadea, Maria; Mayoral, Laura 
Abstract:  The statistical properties of inflation and, in particular, its degree of persistence and stability over time is a subject of intense debate, and no consensus has been achieved yet. The goal of this paper is to analyze this controversy using a general approach, with the aim of providing a plausible explanation for the existing contradictory results. We consider the inflation rates of twentyone OECD countries which are modeled as fractionally integrated (FI) processes. First, we show analytically that FI can appear in inflation rates after aggregating individual prices from firms that face different costs of adjusting their prices. Then, we provide robust empirical evidence supporting the FI hypothesis using both classical and Bayesian techniques. Next, we estimate impulse response functions and other scalar measures of persistence, achieving an accurate picture of this property and its variation across countries. It is shown that the application of some popular tools for measuring persistence, such as the sum of the AR coefficients, could lead to erroneous conclusions if fractional integration is present. Finally, we explore the existence of changes in inflation inertia using a novel approach. We conclude that the persistence of inflation is very high (although nonpermanent) in most postindustrial countries and that it has remained basically unchanged over the last four decades. 
JEL:  G00 G0 
Date:  2005–12–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:815&r=ets 
By:  Boivin, Jean; Ng, Serena 
Abstract:  Forecasting using "diffusion indices" has received a good deal of attention in recent years. The idea is to use the common factors estimated from a large panel of data to help forecast the series of interest. This paper assesses the extent to which the forecasts are influenced by (i) how the factors are estimated and/or (ii) how the forecasts are formulated. We find that for simple datagenerating processes and when the dynamic structure of the data is known, no one method stands out to be systematically good or bad. All five methods considered have rather similar properties, though some methods are better in longhorizon forecasts, especially when the number of time series observations is small. However, when the dynamic structure is unknown and for more complex dynamics and error structures such as the ones encountered in practice, one method stands out to have smaller forecast errors. This method forecasts the series of interest directly, rather than the common and idiosyncratic components separately, and it leaves the dynamics of the factors unspecified. By imposing fewer constraints, and having to estimate a smaller number of auxiliary parameters, the method appears to be less vulnerable to misspecification, leading to improved forecasts. 
JEL:  G00 G0 
Date:  2005–05–18 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:836&r=ets 
By:  Evans, Martin D 
Abstract:  This paper describes a method for calculating daily realtime estimates of the current state of the U.S. economy. The estimates are computed from data on scheduled U.S. macroeconomic announcements using an econometric model that allows for variable reporting lags, temporal aggregation, and other complications in the data. The model can be applied to find realtime estimates of GDP, inflation, unemployment, or any other macroeconomic variable of interest. In this paper, I focus on the problem of estimating the current level of and growth rate in GDP. I construct daily realtime estimates of GDP that incorporate public information known on the day in question. The realtime estimates produced by the model are uniquely suited to studying how perceived developments in the macroeconomy are linked to asset prices over a wide range of frequencies. The estimates also provide, for the first time, daily time series that can be used in practical policy decisions. 
JEL:  G00 G0 
Date:  2005–03–14 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:831&r=ets 