
on Econometric Time Series 
By:  G.M. Gallo; Edoardo Otranto 
Abstract:  The empirical evidence behind the dynamics of high frequency based measures of volatility is that they exhibit persistence and at times abrupt changes in the average level by subperiods. In the past ten years this pattern has a clear interpretation in reference to the dot com bubble, the quiet period of expansion of credit and then the harsh times after the burst of the subprime mortgage crisis. We conjecture that the inadequacy of many econometric volatility models (a very high level of estimated persistence, serially correlated residuals) can be solved with an adequate representation of such a pattern. We insert a Markovian dynamics in a Multiplicative Error Model to represent the conditional expectation of the realized volatility, allowing us to address the issues of a slow moving average level of volatility and of a different dynamics across regime. We apply the model to realized volatility of the S&P500 index and we gauge the usefulness of such an approach by a more interpretable persistence, better residual properties, and an increased goodness of fit. 
Keywords:  MEM models; regime switching; realized volatility; volatility persistence 
JEL:  C22 C24 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:cns:cnscwp:201205&r=ets 
By:  Eo, Yunjong; Kim, ChangJin 
Abstract:  In this paper, we relax the assumption of constant regimespecific mean growth rates in Hamilton's (1989) twostate Markovswitching model of the business cycle. We first present a benchmark model, in which each regimespecific mean growth rate evolves according to a random walk process over different episodes of booms or recessions. We then present a model with vector error correction dynamics for the regimespecific mean growth rates, by deriving and imposing a condition for the existence of a longrun equilibrium growth rate for real output. In the Bayesian Markov Chain Monte Carlo (MCMC) approach developed in this paper, the counterfactual priors, as well as the hierarchical priors for the regimespecific parameters, play critical roles. By applying the proposed model and approach to the postwar real GDP growth data (1947Q42011Q3), we uncover the evolving nature of the regimespecific mean growth rates of real output in the U.S. business cycle. An additional feature of the postwar U.S. business cycle that we uncover is a steady decline in the longrun equilibrium output growth. The decline started in the mid1950s and ended in the mid1980s, coinciding with the beginning of the Great Moderation. Our empirical results also provide partial, if not decisive, evidence that the central bank has been more successful in restoring the economy back to its longrun equilibrium growth path after unusually severe recessions than after unusually good booms. 
Keywords:  State Space Model; MCM; Hamilton Model; Markov Switching; Hierarchical Prior; Evolving Regime Specific Parameters; Counterfactual Prior; Business Cycle; Bayesian Approach 
Date:  2012–02 
URL:  http://d.repec.org/n?u=RePEc:syd:wpaper:2123/8150&r=ets 
By:  Eo, Yunjong 
Abstract:  I propose a Bayesian approach to making an inference about complicated patterns of structural breaks in time series. Structural break models in the literature are mainly considered for a simple case in which all the parameters under the structural changes are restricted to have breaks at the same dates. Unlike the existing literature, the proposed method in this paper allows multiple parameters such as intercept, persistence, and/or residual variance to undergo mutually independent structural breaks at different dates with the different number of breaks across parameters. To estimate the complex structural break models considered in this paper, structural breaks in the multiple parameters are interpreted as regime transitions as in Chib (1998). The regime for each parameter is then indicated by a corresponding discrete latent variable which follows a firstorder Markov process. A Markovchain Monte Carlo scheme is developed to estimate and compare the complex structural break models, which are potentially nonnested, in an efficient and tractable way. I apply this approach to postwar U.S. inflation and find strong support for an autoregressive model with two structural breaks in residual variance and no break in intercept and persistence. 
Keywords:  Inflation Dynamics; MultipleParameter Changepoint; Structural Breaks; Bayesian Analysis 
Date:  2012–02 
URL:  http://d.repec.org/n?u=RePEc:syd:wpaper:2123/8149&r=ets 
By:  Andrea Carriero; Todd E. Clark; Massimiliano Marcellino 
Abstract:  The estimation of large vector autoregressions with stochastic volatility using standard methods is computationally very demanding. In this paper we propose to model conditional volatilities as driven by a single common unobserved factor.> This is justified by the observation that the pattern of estimated volatilities in empirical analyses is often very similar across variables. Using a combination of a standard natural conjugate prior for the VAR coefficients and an independent prior on a common stochastic volatility factor, we derive the posterior densities for the parameters of the resulting BVAR with common stochastic volatility (BVARCSV). Under the chosen prior, the conditional posterior of the VAR coefficients features a Kroneker structure that allows for fast estimation, even in a large system. Using US and UK data, we show that, compared to a model with constant volatilities, our proposed common volatility model significantly improves model fit and forecast accuracy. The gains are comparable to or as great as the gains achieved with a conventional stochastic volatility specification that allows independent volatility processes for each variable. But our common volatility specification greatly speeds computations. 
Keywords:  Economic forecasting ; Bayesian statistical decision theory ; Econometric models ; Estimation theory 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:fip:fedcwp:1206&r=ets 
By:  Yuta Kurose (Graduate School of Economics, University of Tokyo); Yasuhiro Omori (Faculty of Economics, University of Tokyo) 
Abstract:  A smoothing spline is considered to propose a novel model for the timevarying quantile of the univariate time series using a state space approach. A correlation is further incorporated between the dependent variable and its onestepahead quantile. Using a Bayesian approach, an efficient Markov chain Monte Carlo algorithm is described where we use the multimove sampler, which generates simultaneously latent timevarying quantiles. Numerical examples are provided to show its high sampling efficiency in comparison with the simple algorithm that generates one latent quantile at a time given other latent quantiles. Furthermore, using Japanese inflation rate data, an empirical analysis is provided with the model comparison. </table> 
Date:  2012–03 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2012cf845&r=ets 
By:  Aleksei NETSUNAJEV 
Abstract:  The paper reconsiders the conflicting results in the debate connected to the effects of technology shocks on hours worked in the bivariate system. Given major dissatisfaction with the justidentifying longrun restrictions, I analyze whether the restrictions used in the literature are consistent with the data. Modeling volatility of shocks using Markov switching structure allows to obtain additional identifying information and perform tests of the restrictions that were justidentifying in classical structural vector autoregression analysis. Using four datasets where hours worked are modeled differently, I find that the standard restriction, identifying the technology shocks as the only sources of variation in labor productivity, has major support by the data. Taking into account important low frequency movements in the hours worked series yields a result consistent with the recent findings: hours decline in response to a positive technology shock. I also show that the use of a standard HodrickPrescott filter may be problematic in the context. 
Keywords:  Technology shocks; Markov switching model; heteroskedasticity; 
JEL:  C32 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:eui:euiwps:eco2012/13&r=ets 
By:  Peter Reinhard HANSEN; Allan TIMMERMANN 
Abstract:  Outofsample tests of forecast performance depend on how a given data set is split into estimation and evaluation periods, yet no guidance exists on how to choose the split point. Empirical forecast evaluation results can therefore be di cult to interpret, particularly when several values of the split point might have been considered. When the sample split is viewed as a choice variable, rather than being fixed ex ante, we show that very large size distortions can occur for conventional tests of predictive accuracy. Spurious rejections are most likely to occur with a short evaluation sample, while conversely the power of forecast evaluation tests is strongest with long outofsample periods. To deal with size distortions, we propose a test statistic that is robust to the effect of considering multiple sample split points. Empirical applications to predictability of stock returns and inflation demonstrate that outofsample forecast evaluation results can critically depend on how the sample split is determined. 
Keywords:  C12; C53 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:eui:euiwps:eco2012/10&r=ets 
By:  Claudia FORONI; Massimiliano MARCELLINO 
Abstract:  Forecast models that take into account unbalanced datasets have recently attracted substantial attention. In this paper, we focus on different methods pro posed so far in the literature to deal with mixedfrequency and raggededge datasets: bridge equations, mixeddata sampling (MIDAS), and mixedfrequency (MF) models. We discuss their performance on now and forecasting the quarterly growth rate of Euro area GDP and its components, using a very large set of monthly indicators taken from Eurostat dataset of Principal European Economic Indicators (PEEI). We both investigate the behavior of single indicator models and combine first the forecasts within each class of models and then the information in the dataset by means of factor models, in a pseudo realtime framework. Anticipating some of the results, MIDAS without an AR component performs worse than the corresponding approach which incorporates it, and MFVAR seems to outperform the MIDAS approach only at longer horizons. Bridge equations have overall a good performance. Pooling many indicators within each class of models is overall superior to most of the single indicator models. Pooling information with the use of factor models gives even better results, at least at short horizons. A battery of robustness checks high lights the importance of monthly information during the crisis more than in stable periods. Extending the analysis to a realtime context highlights that revisions do not influence substantially the results. 
Keywords:  mixedfrequency data; mixedfrequency VAR; MIDAS; factor models; nowcasting; forecasting 
JEL:  E37 C53 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:eui:euiwps:eco2012/07&r=ets 
By:  Carlos Fuertes; Andrew Papanicolaou 
Abstract:  We explore the inversion of derivatives prices to obtain an implied probability measure on volatility's hidden state. Stochastic volatility is a hidden Markov model (HMM), and HMMs ordinarily warrant filtering. However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute an \textit{implied distribution} by inverting the market's option prices. Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show. When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX, and also pick up some of the monthly effects that occur from option expiration. We find that parsimony of the Heston model is beneficial because we are able to decipher behavior in estimated parameters and implied measures, whereas the richer Heston model with jumps produces a better fit but also has implied behavior that is less revealing. 
Date:  2012–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1203.6631&r=ets 
By:  Georgiadis, Georgios 
Abstract:  In the panel conditionally homogenous vectorautoregressive model, the crosssectional units' dynamics are generally heterogenous, but homogenous if units share the same structural characteristics. The panel conditionally homogenous vectorautoregressive model thus allows (i) to account for heterogeneity in dynamic panel data sets, (ii) to nevertheless exploit the panel nature of the data, and (iii) to analyze the relationship between the units' observed heterogeneities and structural characteristics. I show how standard least squares estimation can be applied, how impulse responses can be computed, how multivariate conditioning is implemented, and how polynomial order restrictions can be incorporated. Finally, I present an easytouse Matlab routine which can be used to estimate the panel conditionally homogenous vectorautoregressive model and produce impulse responses as well as forecast error variance decompositions. 
Keywords:  Panel VAR; Heterogeneity; Conditional Pooling 
JEL:  C51 C33 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:37755&r=ets 
By:  Lanne, Markku; Saikkonen, Pentti 
Abstract:  This is a supplementary appendix to "Noncausal Vector Autoregression". 
Keywords:  Vector autoregression; Noncausal time series; NonGaussian time series 
JEL:  C32 E43 C52 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:37732&r=ets 
By:  Qiankun Zhou (School of Economics, Singapore Management University); Jun Yu (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business) 
Abstract:  The asymptotic distributions of the least squares estimator of the mean reversion parameter (κ) are developed in a general class of diffusion models under three sampling schemes, namely, longspan, infill and the combination of longspan and infill. The models have an affine structure in the drift function, but allow for nonlinearity in the diffusion function. The limiting distributions are quite different under the alternative sampling schemes. In particular, the infill limiting distribution is nonstandard and depends on the initial condition and the time span whereas the other two are Gaussian. Moreover, while the other two distributions are discontinuous at κ = 0, the infill distribution is continuous in κ. This property provides an answer to the Bayesian criticism to the unit root asymptotics. Monte Carlo simulations suggest that the infill asymptotic distribution provides a more accurate approximation to the finite sample distribution than the other two distributions in empirically realistic settings. The empirical application using the U.S. Federal fund rates highlights the difference in statistical inference based on the alternative asymptotic distributions and suggests strong evidence of a unit root in the data. 
Keywords:  Vasicek Model, Onefactor Model, Mean Reversion, Infill Asymptotics, Longspan Asymptotics, Unit Root Test 
JEL:  C12 C22 G12 
Date:  2012–01 
URL:  http://d.repec.org/n?u=RePEc:siu:wpaper:112012&r=ets 