
on Econometric Time Series 
By:  Emilio Zanetti Chini (University of Rome "Tor Vergata") 
Abstract:  This paper introduces a variant of the smooth transition autoregression (STAR). The proposed model is able to parametrize the asymmetry in the tails of the transition equation by using a particular generalization of the logistic function. The null hypothesis of symmetric adjustment toward a new regime is tested by building two different LMtype tests. The first one maintains the original parametrization, while the second one is based on a thirdorder expanded auxiliary regression. Three diagnostic tests for no error autocorrelation, no additive asymmetry and parameter constancy are also discussed. The empirical size and power of the new symmetry as well as diagnostic tests are investigated by an extensive Monte Carlo experiment. An empirical application of the so generalized STAR (GSTAR) model to four economic time series reveals that the asymmetry in the transition between two regimes is a feature to be considered for economic analysis. 
Keywords:  Dynamic Asymmetry, GSTAR, LMtype Tests, Business Cycle, LongTerm Interest Spread, CO2 Emissions 
JEL:  C22 C51 C52 
Date:  2013–04–10 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201332&r=ets 
By:  Mark Podolskij (Heidelberg University and CREATES); Nakahiro Yoshida (Graduate School of Mathematical Science) 
Abstract:  This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations. 
Keywords:  diffusion processes, Edgeworth expansion, high frequency observations, power variation. 
JEL:  C10 C13 C14 
Date:  2013–10–21 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201333&r=ets 
By:  Tommaso Proietti (University of Rome “Tor Vergata” and Creates); Alessandra Luati (University of Bologna) 
Abstract:  The exponential model for the spectrum of a time series and its fractional extensions are based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion form the cepstrum of the time series. After deriving the cepstrum of important classes of time series processes, also featuring long memory, we discuss likelihood inferences based on the periodogram, for which the estimation of the cepstrum yields a generalized linear model for exponential data with logarithmic link, focusing on the issue of separating the contribution of the long memory component to the logspectrum. We then propose two extensions. The first deals with replacing the logarithmic link with a more general BoxCox link, which encompasses also the identity and the inverse links: this enables nesting alternative spectral estimation methods (autoregressive, exponential, etc.) under the same likelihoodbased framework. Secondly, we propose a gradient boosting algorithm for the estimation of the logspectrum and illustrate its potential for distilling the long memory component of the logspectrum. 
Keywords:  Frequency Domain Methods, Generalized linear models, Long Memory, Boosting. 
JEL:  C22 C52 
Date:  2013–10–16 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201334&r=ets 
By:  Bent Jesper Christensen (Aarhus University and CREATES); Robinson Kruse (Leibniz University Hannover and CREATES); Philipp Sibbertsen (Leibniz University Hannover) 
Abstract:  We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional integration. We propose a Lagrange Multipliertype test whose limiting distribution is independent of the order of integration of the errors. Different testing scenarios for the case of deterministic and stochastic regressors are considered. Simulations demonstrate that the proposed test works well for a variety of different cases, thereby emphasizing its generality. 
Keywords:  Long memory, linear time series regression, Lagrange Multiplier test 
JEL:  C12 C22 
Date:  2013–05–24 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201335&r=ets 
By:  Juan Luis Lopez; Jesus Guillermo Contreras 
Abstract:  The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series. As an application the series of the daily exchange rate between the U.S. dollar and the euro is studied. 
Date:  2013–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1311.2278&r=ets 
By:  Maximo Camacho (Universidad de Murcia); Gabriel PerezQuiros (Banco de España); Pilar Poncela (Universidad Autónoma de MAdrid) 
Abstract:  Practitioners do not always use research findings, as the research is not always conducted in a manner relevant to realworld practice. This survey seeks to close the gap between research and practice in respect of shortterm forecasting in real time. To this end, we review the most relevant recent contributions to the literature, examining their pros and cons, and we take the liberty of proposing some avenues of future research. We include bridge equations, MIDAS, VARs, factor models and Markovswitching factor models, all allowing for mixedfrequency and ragged ends. Using the four constituent monthly series of the StockWatson coincident index, industrial production, employment, income and sales, we evaluate their empirical performance to forecast quarterly US GDP growth rates in real time. Finally, we review the main results having regard to the number of predictors in factorbased forecasts and how the selection of the more informative or representative variables can be made. 
Keywords:  Forecasting, GDP growth, time series 
JEL:  E32 C22 E27 
Date:  2013–11 
URL:  http://d.repec.org/n?u=RePEc:bde:wpaper:1318&r=ets 
By:  Dimitrios D. Thomakos (University of Peloponnese); Konstantinos Nikolopoulos (Bangor Business School) 
Abstract:  In this study building on earlier work on the properties and performance of the univariate Theta method for a unit root data generating process we: (a) derive new theoretical formulations for the application of the method on multivariate time series, (b) investigate the conditions for which the multivariate Theta method is expected to forecast better than the univariate one, (c) evaluate through simulations the bivariate form of the method, (d) evaluate this latter model in real macroeconomic and financial time series. The study provides sufficient empirical evidence to illustrate the suitability of the method for vector forecasting; furthermore it provides the motivation for further investigation of the multivariate Theta method for higher dimensions. 
Keywords:  Theta method; univariate; multivariate time series; unit roots; vector forecasting 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:bng:wpaper:13004&r=ets 
By:  Elisa Luciano; Marina Marena; Patrizia Semeraro 
Abstract:  The paper explores the theoretical and fit properties of a class of multivariate Lévy processes, which are characterized as timechanged correlated Brownian motions. The time change has a common and an idiosyncratic component, thus re ecting the properties of trade, which it represents. The resulting process is still Lévy; it may provide Variance Gamma, NormalInverseGaussian or GeneralizedHyperbolic margins. Linear and nonlinear dependence measures are studied. A nonpairwise calibration to a portfolio of ten US daily stockmarket returns over the period 20092013 shows that the fit of the Hyperbolic specification is very good, both in terms of margins and overall correlation matrix. 
Keywords:  Lévy processes, multivariate subordinators, dependence, correlation, multivariate asset modelling, multivariate timechanged processes, factorbased time changes. 
JEL:  G12 G13 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:cca:wpaper:307&r=ets 
By:  Jarociński, Marek; Maćkowiak, Bartosz 
Abstract:  A researcher is interested in a set of variables that he wants to model with a vector autoregression and he has a dataset with more variables. Which variables from the dataset to include in the VAR, in addition to the variables of interest? This question arises in many applications of VARs, in prediction and impulse response analysis. We develop a Bayesian methodology to answer this question. We rely on the idea of Grangercausalpriority, related to the wellknown concept of Grangernoncausality. The methodology is simple to use, because we provide closedform expressions for the relevant posterior probabilities. Applying the methodology to the case when the variables of interest are output, the price level, and the shortterm interest rate, we find remarkably similar results for the United States and the euro area. JEL Classification: C32, C52, E32 
Keywords:  Bayesian model choice, grangercausalpriority, grangernoncausality, structural vector autoregression, Vector autoregression 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20131600&r=ets 
By:  Fernández Macho, Francisco Javier 
Abstract:  In a recent paper LeongHuang:2010 {Journal of Applied Statistics 37, 215â€“233} proposed a waveletcorrelationbased approach to test for cointegration between two time series. However, correlation and cointegration are two different concepts even when wavelet analysis is used. It is known that statistics based on nonstationary integrated variables have nonstandard asymptotic distributions. However, wavelet analysis offsets the integrating order of nonstationary series so that traditional asymptotics on stationary variables suffices to ascertain the statistical properties of waveletbased statistics. Based on this, this note shows that wavelet correlations cannot be used as a test of cointegration. 
Keywords:  econometric methods, spectral analysis, integrated process, time series models, unit roots, wavelet analysis. 
JEL:  C22 C12 
URL:  http://d.repec.org/n?u=RePEc:ehu:biltok:10862&r=ets 
By:  Xibin Zhang; Maxwell L. King 
Abstract:  This paper aims to investigate a Bayesian sampling approach to parameter estimation in the GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the standard deviation. This study is motivated by the lack of robustness in GARCH models with a parametric assumption for the error density when used for errordensity based inference such as valueatrisk (VaR) estimation. A contribution of the paper is to construct the likelihood and posterior of the model and bandwidth parameters under the kernelform error density, and to derive the onestepahead posterior predictive density of asset returns. We also investigate the use and benefit of localized bandwidths in the kernelform error density. A Monte Carlo simulation study reveals that the robustness of the kernelform error density compensates for the loss of accuracy when using this density. Applying this GARCH model to daily return series of 42 assets in stock, commodity and currency markets, we find that this GARCH model is favored against the GARCH model with a skewed Student t error density for all stock indices, two out of 11 currencies and nearly half of the commodities. This provides an empirical justification for the value of the proposed GARCH model. 
Keywords:  Bayes factors, Gaussian kernel error density, localized bandwidths, Markov chain Monte Carlo, valueatrisk 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:201319&r=ets 
By:  Xiangjin B. Chen; Jiti Gao; Degui Li; Param Silvapulle 
Abstract:  This paper introduces a new specification for the heterogeneous autoregressive (HAR) model for the realized volatility of S&P500 index returns. In this new model, the coeffcients of the HAR are allowed to be timevarying with unknown functional forms. We propose a local linear method for estimating this TVCHAR model as well as a bootstrap method for constructing confidence intervals for the time varying coefficient functions. In addition, the estimated nonparametric TVCHAR was calibrated by fitting parametric polynomial functions by minimising the L2type criterion. The calibrated TVCHAR and the simple HAR models were tested separately against the nonparametric TVCHAR model. The test statistics constructed based on the generalised likelihood ratio method augmented with bootstrap method provide evidence in favour of calibrated TVCHAR model. More importantly, the results of conditional predictive ability test developed by Giacomini and White (2006) indicate that the nonparametric TVCHAR model consistently outperforms its calibrated counterpart as well as the simple HAR and the HARGARCH models in outofsample forecasting. 
Keywords:  Bootstrap method, heterogeneous autoregressive model, locally stationary process, nonparametric method 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:201321&r=ets 
By:  Peter C. B. Phillips; Degui Li; Jiti Gao 
Abstract:  This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These timevarying coefficient functions are wellsuited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernelinduced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a pathdependent local coordinate transformation to reorient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions (or combinations) of the (functional) parameter space. Both rates are faster than the usual (âˆšnh) rate for nonlinear models with smoothly changing coefficients and local stationarity. Hence two types of superconsistency apply in nonparametric kernel estimation of timevarying coefficient cointegration models. The higher rate of convergence (nâˆšh) lies in the direction of the nonstationary regressor vector at the local coordinate point. The lower rate (nh) lies in the degenerate directions but is still superconsistent for nonparametric estimators. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case. Simulations are conducted to explore the finite sample properties of the methods and a practical application is given to examine time varying empirical relationships involving consumption, disposable income, investment and real interest rates. 
Keywords:  Cointegration, Endogeneity, Kernel degeneracy, Nonparametric regression, Superconsistency, Time varying coefficients 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:201322&r=ets 
By:  Kim, ChangJin; Kim, Jaeho 
Abstract:  One goal of this paper is to develop an efficient MarkovChain Monte Carlo (MCMC) algorithm for estimating an ARMA model with a regimeswitching mean, based on a multimove sampler. Unlike the existing algorithm of Billio et al. (1999) based on a singlemove sampler, our algorithm can achieve reasonably fast convergence to the posterior distribution even when the latent regime indicator variable is highly persistent or when there exist absorbing states. Another goal is to appropriately investigate the dynamics of the latent exante real interest rate (EARR) in the presence of structural breaks, by employing the econometric tool developed. We argue Garcia and Perron's (1996) conclusion that the EARR rate is a constant subject to occasional jumps may be samplespecific. For an extended sample that includes recent data, Garcia and Perron's (1996) AR(2) model of EPRR may be misspecified, and we show that excluding the theoryimplied movingaverage terms may understate the persistence of the observed expost real interest rate (EPRR) dynamics. Our empirical results suggest that, even though we rule out the possibility of a unit root in the EARR, it may be more persistent and volatile than has been documented in some of the literature including Garcia and Perron (1996). 
Keywords:  ARMA model with Regime Switching, Multimove Sampler, SingleMove Sampler, MetropolisHastings Algorithm, Absorbing State, ExAnte Real Interest Rate. 
JEL:  C11 E4 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:51117&r=ets 
By:  Kim, ChangJin; Kim, Jaeho 
Abstract:  In the case of a flat prior, a conventional wisdom is that Bayesian inference may not be very different from classical inference, as the likelihood dominates the posterior density. This paper shows that there are cases in which this conventional wisdom does not apply. An ARMA model of real GDP growth estimated by Perron and Wada (2009) is an example. While their maximum likelihood estimation of the model implies that real GDP may be a trend stationary process, Bayesian estimation of the same model implies that most of the variations in real GDP can be explained by the stochastic trend component, as in Nelson and Plosser (1982) and Morley et al. (2003). We show such dramatically different results stem from the differences in how the nuisance parameters are handled between the two approaches, especially when the parameter estimate of interest is dependent upon the estimates of the nuisance parameters for small samples. For the maximum likelihood approach, as the number of the nuisance parameters increases, we have higher probability that the movingaverage root may be estimated to be one even when its true value is less than one, spuriously indicating that the data is `overdifferenced.' However, the Bayesian approach is relatively free from this pileup problem, as the posterior distribution is not dependent upon the nuisance parameters. 
Keywords:  pileup problem, ARMA model, UnobservedComponents Model, Profile likelihood, marginal powterior density, TrendCycle decomposition 
JEL:  C11 E32 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:51118&r=ets 
By:  Yuta Kurose (Center for the Study of Finance and Insurance, Osaka University,); Yasuhiro Omori (Faculty of Economics, University of Tokyo) 
Abstract:  ã€€ã€€ A multivariate stochastic volatility model with dynamic equicorrelation and cross leverage ef fect is proposed and estimated. Using a Bayesian approach, an ecient Markov chain Monte Carlo algorithm is described where we use the multimove sampler, which generates multiple latent variables simultaneously. Numerical examples are provided to show its sampling e ciency in comparison with the simple algorithm that generates one latent variable at a time given other latent variables. Furthermore, the proposed model is applied to the multivariate daily stock price index data. The empirical study shows that our novel model provides a substantial improvement in forecasting with respect to outofsample hedging performances 
Date:  2013–11 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2013cf907&r=ets 
By:  Fengler, Matthias R.; Mammen, Enno; Vogt, Michael 
Abstract:  For an additive autoregression model, we study two types of testing problems. First, a parametric specification of a component function is compared against a nonparametric fit. Second, two nonparametric fits of two different time periods are tested for equality. We apply the theory to a nonparametric extension of the linear heterogeneous autoregressive (HAR) model. The linear HAR model is widely employed to describe realized variance data. We find that the linearity assumption is often rejected, in particular on equity, fixed income, and currency futures data; in the presence of a structural break, nonlinearity appears to prevail on the sample before the outbreak of the financial crisis in mid2007. 
Keywords:  Additive models; Backfitting; Nonparametric time series analysis; Specification tests; Realized variance; Heterogeneous autoregressive model. 
JEL:  C14 C58 
Date:  2013–11 
URL:  http://d.repec.org/n?u=RePEc:usg:econwp:2013:32&r=ets 
By:  Monica Billio (Department of Economics, University Of Venice Cà Foscari, Italy); Maddalena Cavicchioli (Department of Economics, University Of Venice Cà Foscari, Italy) 
Abstract:  This paper is devoted to show duality in the estimation of Markov Switching (MS) processes for volatility. It is wellknown that MSGARCH models suffer of path dependence which makes the estimation step unfeasible with usual Maximum Likelihood procedure. However, by rewriting the MSGARCH model in a suitable linear State Space representation, we are able to give a unique framework to reconcile the estimation obtained by the Kalman Filter and with some auxiliary models proposed in the literature. Reasoning in the same way, we present a linear Filter for MSStochastic Volatility (MSSV) models on which different conditioning sets yield more flexibility in the estimation. Estimation on simulated data and on shortterm interest rates shows the feasibility of the proposed approach. 
Keywords:  Markov Switching, MSGARCH model, MSSV model, estimation, auxiliary model, Kalman Filter. 
JEL:  C01 C13 C58 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:ven:wpaper:2013:24&r=ets 