
on Econometric Time Series 
By:  Pami Dua (Department of Economics, Delhi School of Economics, Delhi, India); Lokendra Kumawat (Department of Economics, Ramjas College,University of Delhi, Delhi) 
Abstract:  This paper models the seasonal dynamics in quarterly industrial production for India. For this, we extend the timevarying smooth transition autoregression (TVSTAR) model to allow for independent regimeswitching behaviour in the deterministic seasonal and cyclical components. This yields the timevarying seasonal smooth transition (TVSEASTAR) model. We find evidence of the effect of rainfall growth on seasonal dynamics of industrial production. We also find that the seasonal dynamics have changed over the past decade, one aspect of this being the significant narrowing down of seasonals. The timing of these changes coincides with the changes in the character of the economy as it progressed towards a freemarket economy in the post liberalization period. 
Keywords:  Seasonality, Smooth transition autoregression, Economic reforms. 
JEL:  C22 
Date:  2007–08 
URL:  http://d.repec.org/n?u=RePEc:cde:cdewps:162&r=ets 
By:  Myung Hwan Seo 
Abstract:  Asymptotic inference in nonlinear vector error correction models (VECM) thatexhibit regimespecific shortrun dynamics is nonstandard and complicated. Thispaper contributes the literature in several important ways. First, we establish theconsistency of the least squares estimator of the cointegrating vector allowing forboth smooth and discontinuous transition between regimes. This is a nonregularproblem due to the presence of cointegration and nonlinearity. Second, we obtainthe convergence rates of the cointegrating vector estimates. They differ dependingon whether the transition is smooth or discontinuous. In particular, we find that therate in the discontinuous threshold VECM is extremely fast, which is n^{3/2},compared to the standard rate of n: This finding is very useful for inference onshortrun parameters. Third, we provide an alternative inference method for thethreshold VECM based on the smoothed least squares (SLS). The SLS estimatorof the cointegrating vector and threshold parameter converges to a functional of avector Brownian motion and it is asymptotically independent of that of the slopeparameters, which is asymptotically normal. 
Keywords:  Threshold Cointegration, Smooth Transition Error Correction,Least Squares, Smoothed Least Squares, Consistency,Convergence Rate. 
JEL:  C32 
Date:  2007–03 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2007/517&r=ets 
By:  Peter Robinson 
Abstract:  We consider a multivariate continuous time process, generated by a system of linear stochastic differential equations, driven by white noise and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equallyspaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is deduced. Initially we focus on a firstorder model, but higherorder ones are discussed in case of equallyspaced observations. Some discussion of issues of statistical inference is included. 
Keywords:  Stochastic differential equations, timevarying coefficients, discrete sampling, irregular sampling. 
JEL:  C32 
Date:  2007–06 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2007/520&r=ets 
By:  Peter Robinson 
Abstract:  We develop a sequence of tests for specifying the cointegrating rank of, possiblyfractional, multiple time series. Memory parameters of observables are treated asunknown, as are those of possible cointegrating errors. The individual test statisticshave standard null asymptotics, and are related to Hausman specification teststatistics: when the memory parameter is common to several series, an estimate ofthis parameter based on the assumption of no cointegration achieves an efficiencyimprovement over estimates based on individual series, whereas if the series arecointegrated the former estimate is generally inconsistent. However, acomputationally simpler but asymptotically equivalent approach, which avoidsexplicit computation of the "efficient" estimate, is instead pursued here. Twoversions of it are initially proposed, followed by one that robustifies to possibleinequality between memory parameters of observables. Throughout, asemiparametric approach is pursued, modelling serial dependence only atfrequencies near the origin, with the goal of validity under broad circumstances andcomputational convenience. The main development is in terms of stationary series,but an extension to nonstationary ones is also described. The algorithm forestimating cointegrating rank entails carrying out such tests based on potentially allsubsets of two or more of the series, though outcomes of previous tests mayrender some or all subsequent ones unnecessary. A Monte Carlo study of finitesample performance is included. 
Keywords:  Fractional cointegration, Diagnostic testing, Specificationtesting, Cointegrating rank, Semiparametric estimation. 
JEL:  C32 
Date:  2007–09 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2007/522&r=ets 
By:  Ilze Kalnina; Oliver Linton 
Abstract:  We investigate the use of subsampling for conducting inference about the quadratic variation of a discretely observed diffusion process under an infill asymptotic scheme. We show that the usual subsampling method of Politis and Romano (1994) is inconsistent when applied to our inference question. Recently, a type of subsampling has been used to do an additive bias correction to obtain a consistent estimator of the quadratic variation of a diffusion process subject to measurement error, Zhang, Mykland, and AitSahalia (2005). This subsampling scheme is also inconsistent when applied to the inference question above. This is due to a high correlation between estimators on different subsamples. We discuss an alternative approach that does not have this correlation problem; however, it has a vanishing bias only under smoothness assumptions on the volatility path. Finally, we propose a subsampling scheme that delivers consistent inference without any smoothness assumptions on the volatility path. This is a general method and can be potentially applied to conduct inference for quadratic variation in the presence of jumps and/or microstructure noise by subsampling appropriate consistent estimators. 
Keywords:  Realised Volatility, Semimartingale, Subsampling, Infill Asymptotic Scheme 
JEL:  C12 
Date:  2007–09 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2007/523&r=ets 
By:  Peter M Robinson 
Abstract:  Moving from univariate to bivariate jointly dependent long memory time seriesintroduces a phase parameter (?), at the frequency of principal interest, zero; for shortmemory series ? = 0 automatically. The latter case has also been stressed under longmemory, along with the "fractional differencing" case ( ) / 2; 2 1 ? = d  d p where 1 2 d , dare the memory parameters of the two series. We develop time domain conditionsunder which these are and are not relevant, and relate the consequent properties ofcrossautocovariances to ones of the (possibly bilateral) moving averagerepresentation which, with martingale difference innovations of arbitrary dimension,is used in asymptotic theory for local Whittle parameter estimates depending on asingle smoothing number. Incorporating also a regression parameter (ß) which, whennonzero, indicates cointegration, the consistency proof of these implicitlydefinedestimates is nonstandard due to the ß estimate converging faster than the others. Wealso establish joint asymptotic normality of the estimates, and indicate how thisoutcome can apply in statistical inference on several questions of interest. Issues ofimplementation are discussed, along with implications of knowing ß and of correct orincorrect specification of ? , and possible extensions to higherdimensional systemsand nonstationary series. 
Keywords:  Long memory, phase, cointegration, semiparametricestimation, consistency, asymptotic normality. 
JEL:  C32 
Date:  2007–10 
URL:  http://d.repec.org/n?u=RePEc:cep:stiecm:/2007/525&r=ets 
By:  Franses, Ph.H.B.F.; Legerstee, R. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University) 
Abstract:  We study the performance of sales forecasts which linearly combine modelbased forecasts and expert forecasts. Using a unique and very large database containing monthly modelbased forecasts for many pharmaceutical products and forecasts given by thirtyseven different experts, we document that a combination almost always is most accurate. When correlating the specific weights in these "best" linear combinations with experts' experience and behaviour, we find that more experience is beneficial for forecasts for nearby horizons. And, when the rate of bracketing increases the relative weights converge to a 50%50% distribution, when there is some slight variation across forecasts horizons. 
Keywords:  modelbased forecasts;experts forecast;combining forecasts 
Date:  2007–12–06 
URL:  http://d.repec.org/n?u=RePEc:dgr:eureri:1765010769&r=ets 
By:  Palm Franz C.; Smeekes Stephan; Urbain JeanPierre (METEOR) 
Abstract:  In this paper we propose a bootstrap version of the Wald test for cointegration in a singleequation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid.We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. It also performs at least as well as the alternative bootstrap tests considered in terms of size and power.The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic componentsincluded are insensitive to the true value of the trends in the model, and retain correct size. 
Keywords:  econometrics; 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:dgr:umamet:2007054&r=ets 
By:  Amado, Cristina (University of Minho and NIPE); Teräsvirta, Timo (CREATES, University of Aarhus) 
Abstract:  In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the conditional variance to have a smooth timevarying structure of either additive or multiplicative type. The suggested parameterizations describe both nonlinearity and structural change in the conditional and unconditional variances where the transition between regimes over time is smooth. A modelling strategy for these new timevarying parameter GARCH models is developed. It relies on a sequence of Lagrange multiplier tests, and the adequacy of the estimated models is investigated by Lagrange multiplier type misspecification tests. Finitesample properties of these procedures and tests are examined by simulation. An empirical application to daily stock returns and another one to daily exchange rate returns illustrate the functioning and properties of our modelling strategy in practice. The results show that the long memory type behaviour of the sample autocorrelation functions of the absolute returns can also be explained by deterministic changes in the unconditional variance. 
Keywords:  Conditional heteroskedasticity; Structural change; Lagrange multiplier test; Misspecification test; Nonlinear time series; Timevarying parameter model. 
JEL:  C12 C22 C51 C52 
Date:  2008–01–24 
URL:  http://d.repec.org/n?u=RePEc:hhs:hastef:0691&r=ets 
By:  J. Isaac Miller (Department of Economics, University of MissouriColumbia) 
Abstract:  We consider a cointegrating regression in which the integrated regressors are messy in the sense that they contain data that may be mismeasured, missing, observed at mixed frequencies, or have other irregularities that cause the econo metrician to observe them with possibly nonstationary noise. We motivate the notion of messy data with a nontechnical example using linear interpolation. Even with such a straightforward DGP, we show that the resulting noise is mildly nonstationary. We adopt a unified theoretical approach to avoid strict distributional assumptions and to allow for such nonstationarity. Least squares estimation of the cointegrating vector is consistent under general conditions, even though the estimator is neither asymptotically normal nor unbiased. In order to allow valid statistical inference, we construct a canonical cointegrating regression (CCR) using standard consistent nonparametric variance estimators, and we show that least squares estimation of the CCR provides consistent and asymptotically normal estimation even with nonstationary disturbances. We briefly examine large and smallsample properties of the estimator when linear interpolation is the specific driver behind the messiness. 
Keywords:  cointegration, canonical cointegrating regression, messy data, miss ing data, mixedfrequency data, nonclassical measurement error, interpolation, nearepoch dependence 
JEL:  C13 C14 C32 
Date:  2007–11–27 
URL:  http://d.repec.org/n?u=RePEc:umc:wpaper:0722&r=ets 
By:  Monica Billio (Department of Economics, University Of Venice Cà Foscari); Roberto Casarin (University of Brescia); Domenico Sartore (Department of Economics, University Of Venice Cà Foscari) 
Abstract:  In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction. 
Keywords:  Bayesian Dynamic Models, Simulation Based Inference, Particle Filters, Latent Factors, Business Cycle 
JEL:  C11 C15 C22 C63 O40 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:ven:wpaper:34_07&r=ets 
By:  Proietti, Tommaso 
Abstract:  The chapter deals with parametric models for the measurement of the business cycle in economic time series. It presents univariate methods based on parametric trend{cycle decom positions and multivariate models featuring a Phillips type relationship between the output gap and inflation and the estimation of the gap using mixed frequency data. We finally address the issue of assessing the accuracy of the output gap estimates. 
Keywords:  State Space Models. Kalman Filter and Smoother. Bayesian Estimation. 
JEL:  C32 E32 C22 
Date:  2008–01–20 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:6854&r=ets 
By:  Proietti, Tommaso 
Abstract:  The paper estimates a largescale mixedfrequency dynamic factor model for the euro area, using monthly series along with Gross Domestic Product (GDP) and its main components, obtained from the quarterly national accounts. The latter define broad measures of real economic activity (such as GDP and its decomposition by expenditure type and by branch of activity) that we are willing to include in the factor model, in order to improve its coverage of the economy and thus the representativeness of the factors. The main problem with their inclusion is not one of model consistency, but rather of data availability and timeliness, as the national accounts series are quarterly and are available with a large publication lag. Our model is a traditional dynamic factor model formulated at the monthly frequency in terms of the stationary representation of the variables, which however becomes nonlinear when the observational constraints are taken into account. These are of two kinds: nonlinear temporal aggregation constraints, due to the fact that the model is formulated in terms of the unobserved monthly logarithmic changes, but we observe only the sum of the monthly levels within a quarter, and nonlinear crosssectional constraints, since GDP and its main components are linked by the national accounts identities, but the series are expressed in chained volumes. The paper provides an exact treatment of the observational constraints and proposes iterative algorithms for estimating the parameters of the factor model and for signal extraction, thereby producing nowcasts of monthly gross domestic product and its main components, as well as measures of their reliability. 
Keywords:  Dynamic Factor Models; EM algorithm; Non Linear State Space Models; Temporal Disaggregation; Nonlinear Smoothing; Monthly GDP; Chainlinking. 
JEL:  C32 E32 
Date:  2008–01–22 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:6860&r=ets 
By:  Buncic, Daniel 
Abstract:  We show that long horizon forecasts from the nonlinear models that are considered in the study by Rapach andWohar (2006) cannot generate any forecast gains over a simple AR(1) specification. This is contrary to the findings reported in Rapach and Wohar (2006). Moreover, we illustrate graphically that the nonlinearity in the forecasts from the ESTAR model is the strongest when forecasting one stepahead and that it diminishes as the forecast horizon increases. There exists, therefore, no potential whatsoever for the considered nonlinear models to outperform linear ones when forecasting far ahead. We also illustrate graphically why one stepahead forecasts from the nonlinear ESTAR model fail to yield superior predictions to a simple AR(1). 
Keywords:  PPP; regime modelling; nonlinear real exchange rate models; ESTAR; forecast evaluation. 
JEL:  C53 C52 F47 C22 F31 
Date:  2008–01–24 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:6904&r=ets 