
on Econometric Time Series 
By:  Michael Dueker 
Abstract:  A pair of simple modifications to the Kalman filter recursions makes possible the filtering of models in which one or more state variables is truncated normal. Such recursions are broadly applicable to macroeconometric models that have one or more probittype equation, such as vector autoregressions and estimated dynamic stochastic general equilibrium models. 
Keywords:  Macroeconomics  Econometric models 
Date:  2005 
URL:  http://d.repec.org/n?u=RePEc:fip:fedlwp:2005057&r=ets 
By:  Andrea Beltratti; Claudio Morana 
Abstract:  We study the time series properties of the FamaFrench factor returns volatility processes. Among the original findings of this paper, we point to structural breaks in the volatility of the factors, and strong coincidence between the timing of the breaks in the volatility of the market portfolio and the timing of the breaks in the volatility of SMB. Moreover, analyses of the break free series show that two common long memory factors drive the longrun evolution of the series. The first factor mainly affects the volatility of the market and the volatility of SMB, while the second one mainly affects the volatility of HML. These results imply that the timevaring volatility of stocks is driven mainly by the timevarying volatility of the market as a whole and of the HML portfolio, while the volatility of SMB does not seem to be an independent driving force. 
Keywords:  risk factors, structural change, long memory, fractional cointegration, portfolio allocation 
JEL:  C32 F30 G10 
Date:  2005–07 
URL:  http://d.repec.org/n?u=RePEc:icr:wpicer:232005&r=ets 
By:  D. Bond; M.J. Harrision; E.J. O, Brien (Department of Economics, Trinity College) 
Abstract:  This is a revised and extended version of the authors’ 2003 Trinity Economic Paper. It describes Hamilton’s (2001) approach to nonlinear econometric modelling and some of the methods of nonlinear optimization, as before, but adds significantly to the investigation of Hamilton’s Gauss program for the implementation of his methodology. Specifically, it reports on the performance of this program using data relating to Hamilton’s US Phillips curve example, the use of two versions of the Gauss software and a range of numerical optimization options. It also examines the impact of changes in initial parameter estimates, the use of algorithm switching strategies, and the e?ects of changes in the sample data on the results produced by Hamilton’s procedure. The new results presented suggest some further clear conclusions that will be of value to those using Hamilton’s method. 
JEL:  C13 C51 C61 
Date:  2005–08 
URL:  http://d.repec.org/n?u=RePEc:tcd:wpaper:tep4&r=ets 
By:  Bauer, Dietmar (arsenal research, Vienna, Austria); Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) 
Abstract:  We investigate autoregressive approximations of multiple frequency I(1) processes. The underlying data generating process is assumed to allow for an infinite order autoregressive representation where the coefficients of the Wold representation of the suitably filtered process satisfy mild summability constraints. An important special case of this process class are MFI(1) VARMA processes. The main results link the approximation properties of autoregressions for the nonstationary multiple frequency I(1) process to the corresponding properties of a related stationary process, which are well known. First, uniform error bounds on the estimators of the autoregressive coefficients are derived. Second, the asymptotic properties of order estimators obtained with information criteria are shown to be closely related to those for the associated stationary process obtained by suitable filtering. For multiple frequency I(1) VARMA processes we establish divergence of order estimators based on the BIC criterion at a rate proportional to the logarithm of the sample size. 
Keywords:  Unit roots, Multiple frequency I(1) process, Nonrational transfer function, Cointegration, VARMA process, Information criteria 
JEL:  C13 C32 
Date:  2005–09 
URL:  http://d.repec.org/n?u=RePEc:ihs:ihsesp:174&r=ets 
By:  Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) 
Abstract:  This paper reassesses the panel (unit root test) evidence for PPP on four monthly data sets. We discuss and illustrate that commonlyused first generation panel unit root tests are inappropriate for PPP analysis since they are constructed for crosssectionally uncorrelated panels. Given that real exchange rate panel data sets are – almost by construction – highly crosssectionally correlated, so called second generation panel unit root methods that allow for and model crosssectional dependence should be applied. Using inappropriate first generation tests, quite strong evidence for PPP is found. However, this evidence vanishes entirely when resorting to an appropriate method (e.g. the one developed in Bai and Ng, 2004a) for nonstationary crosssectionally correlated panels. We strongly believe that our findings are relevant beyond the data sets investigated here for illustration. 
Keywords:  PPP, Real exchange rate index, Unit root, Panel, Crosssectional dependence, Factor model 
JEL:  C23 F30 F31 
Date:  2005–09 
URL:  http://d.repec.org/n?u=RePEc:ihs:ihsesp:176&r=ets 
By:  Kunst, Robert M. (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and Department of Economics, University of Vienna) 
Abstract:  The occurrence of decision problems with changing roles of null and alternative hypotheses has increased interest in extending the classical hypothesis testing setup. Particularly, confirmation analysis has been in the focus of some recent contributions in econometrics. We emphasize that confirmation analysis is grounded in classical testing and should be contrasted with the Bayesian approach. Differences across the three approaches – traditional classical testing, Bayes testing, joint confirmation – are highlighted for a popular testing problem. A decision is searched for the existence of a unit root in a timeseries process on the basis of two tests. One of them has the existence of a unit root as its null hypothesis and its nonexistence as its alternative, while the roles of null and alternative are reversed for the other hypothesis test. 
Keywords:  Confirmation analysis, Decision contours, Unit roots 
JEL:  C11 C12 C22 C44 
Date:  2005–09 
URL:  http://d.repec.org/n?u=RePEc:ihs:ihsesp:177&r=ets 
By:  Francesca V. Monti 
Abstract:  This paper examines the feasibility of implementing Linear Quadratic Gaussian (LQG) Control in structural cointegrated VAR models and sheds some light on the two major problems generated by such implementation. The first aspect to be taken into account is the effect of the presence of unit roots in the system on the policymaker’s ability to control it, partially or thoroughly. Different control techniques are proposed according to the extent to which the policymaker can exercise his control on the overall dynamics of the economy, i.e. depending on whether he/she can stabilize the whole system, only part of it or none of it. The second issue involves the structural form of the model. It will be shown in this paper that, in general, a system’s features will change when implementing a new control rule. In particular, a controlled system will generally not retain features that should be intrinsecally invariant to policy changes (e.g., neutrality of money in the longrun). 
Keywords:  Optimal control; cointegration; policy invariance. 
JEL:  C32 C61 E52 
Date:  2003–11 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20030288&r=ets 
By:  Claudio Morana (University of Piemonte Orientale, Faculty of Economics, Via Perrone 18, I28100, Novara, Italy) 
Abstract:  In the paper we propose a new methodological approach to core inflation estimation,based on a frequency domain principal components estimator, suited to estimate systems of fractionally cointegrated processes. The proposed core inflation measure is the scaled common persistent factor in inflation and excess nominal money growth and bears the interpretation of monetary inflation. The proposed measure is characterised by all the properties that an “ideal” core inflation process should show, providing also a superior forecasting performance relative to other available measures. 
Keywords:  Long memory; Common factors; Fractional cointegration; Markov switching; Core inflation; Euro area. 
JEL:  C22 E31 E52 
Date:  2004–02 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040305&r=ets 
By:  Claudio Morana (University of Piemonte Orientale, Faculty of Economics,Via Perrone 18, 28100, Novara, Italy,) 
Abstract:  In this paper we study the zero frequency spectral properties of fractionally cointegrated long memory processes and introduce a new frequency domain principal components estimator of the cointegration space and the factor loading matrix for the long memory factors. We find that for fractionally differenced (fractionally) cointegrated processes the squared multiple coherence at the zero frequency is equal to one, the spectral density matrix at the zero frequency is singular, and the factor loading and cointegrating matrices can be obtained from the eigenvectors of the spectral matrix at the zero frequency, associated with the positive and zero roots, respectively. A Monte Carlo simulation reveals that the proposed principal components estimator has already good properties with relatively small sample sizes. 
Keywords:  Fractional cointegration, long memory, frequency domain analysis. 
JEL:  C22 
Date:  2004–03 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040321&r=ets 
By:  Gonzalo CambaMendez (European Central Bank, Kaiserstrasse 29, D60311 Frankfurt/Main, Germany.); George Kapetanios (Department of Economics, Queen Mary, University of London, Mile End Rd, London E1 4NS,) 
Abstract:  The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix whose rank is known. 
Keywords:  Tests of Ran; Spectral Density Matrix. 
JEL:  C12 C32 C52 
Date:  2004–04 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040349&r=ets 
By:  Matthias Mohr (European Central Bank, Kaiserstraße 29, D60311 Frankfurt am Main, Germany) 
Abstract:  This paper proposes a new univariate method to decompose a time series into a trend, a cyclical and a seasonal component: the TrendCycle filter (TC filter) and its extension, the TrendCycleSeason filter (TCS filter). They can be regarded as extensions of the HodrickPrescott filter (HP filter). In particular, the stochastic model of the HP filter is extended by explicit models for the cyclical and the seasonal component. The introduction of a stochastic cycle improves the filter in three respects  first, trend and cyclical components are more consistent with the underlying theoretical model of the filter. Second, the endofsample reliability of the trend estimates and the cyclical component is improved compared to the HP filter since the procyclical bias in endofsample trend estimates is virtually removed. Finally, structural breaks in the original time series can be easily accounted for. 
Keywords:  Economic cycles; time series; filtering; trendcycle decomposition; seasonality. 
JEL:  C13 C22 E32 
Date:  2005–07 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050499&r=ets 
By:  Christian Dreger; HansEggert Reimers 
Abstract:  In this paper the seasonal unit root test of Hylleberg et al. (1990) is generalized to cover a heterogenous panel. Test statistics are proposed and critical values are obtained by simulation. The new test is applied for unemployment behaviour in industrialized countries. 
Date:  2004–06 
URL:  http://d.repec.org/n?u=RePEc:iwh:dispap:191&r=ets 