
on Econometric Time Series 
By:  Michal Franta 
Abstract:  Iterated multistep forecasts are usually constructed assuming the same model in each forecasting iteration. In this paper, the model coefficients are allowed to change across forecasting iterations according to the insample prediction performance at a particular forecasting horizon. The technique can thus be viewed as a combination of iterated and direct forecasting. The superior point and density forecasting performance of this approach is demonstrated on a standard mediumscale vector autoregression employing variables used in the Smets and Wouters (2007) model of the US economy. The estimation of the model and forecasting are carried out in a Bayesian way on data covering the period 1959Q12016Q1. 
Keywords:  Bayesian estimation, direct forecasting, iterated forecasting, multistep forecasts, VAR 
JEL:  C11 C32 C53 
Date:  2016–06 
URL:  http://d.repec.org/n?u=RePEc:cnb:wpaper:2016/05&r=ets 
By:  Jianbin Wu; Geert Dhaene 
Abstract:  We propose sparse versions of multivariate GARCH models that allow for volatility and correlation spillover effects across assets. The proposed models are generalizations of existing diagonal DCC and BEKK models, yet they remain estimable for highdimensional systems of asset returns. To cope with the high dimensionality of the model parameter spaces, we employ the L1 regularization technique to penalize the offdiagonal elements of the coefficient matrices. A simulation experiment for the sparse DCC model shows that the true underlying sparse parameter structure can be uncovered reasonably well. In an application to weekly and daily market returns for 24 countries using data from 1994 to 2014, we find that the sparse DCC model outperforms the standard DCC and the diagonal DCC models in and out of sample. Likewise, the sparse BEKK model outperforms the diagonal BEKK model. 
Date:  2016–06 
URL:  http://d.repec.org/n?u=RePEc:ete:ceswps:544324&r=ets 
By:  Geert Dhaene; Jianbin Wu 
Abstract:  We introduce and evaluate mixedfrequency multivariate GARCH models for forecasting lowfrequency (weekly or monthly) multivariate volatility based on highfrequency intraday returns (at fiveminute intervals) and on the overnight returns. The lowfrequency conditional volatility matrix is modelled as a weighted sum of an intraday and an overnight component, driven by the intraday and the overnight returns, respectively. The components are specified as multivariate GARCH (1,1) models of the BEKK type, adapted to the mixedfrequency data setting. For the intraday component, the squared highfrequency returns enter the GARCH model through a parametrically specified mixeddata sampling (MIDAS) weight function or through the sum of the intraday realized volatilities. For the overnight component, the squared overnight returns enter the model with equal weights. Alternatively, the lowfrequency conditional volatility matrix may be modelled as a singlecomponent BEKKGARCH model where the overnight returns and the highfrequency returns enter through the weekly realized volatility (defined as the unweighted sum of squares of overnight and highfrequency returns), or where the overnight returns are simply ignored. All model variants may further be extended by allowing for a nonparametrically estimated slowlyvarying longrun volatility matrix. The proposed models are evaluated using fiveminute and overnight return data on four DJIA stocks (AXP, GE, HD, and IBM) from January 1988 to November 2014. The focus is on forecasting weekly volatilities (defined as the low frequency). The mixedfrequency GARCH models are found to systematically dominate the lowfrequency GARCH model in terms of insample fit and outofsample forecasting accuracy. They also exhibit much lower lowfrequency volatility persistence than the lowfrequency GARCH model. Among the mixedfrequency models, the lowfrequency persistence estimates decrease as the data frequency increases from daily to fiveminute frequency, and as overnight returns are included. That is, ignoring the available highfrequency information leads to spuriously high volatility persistence. Among the other findings are that the singlecomponent model variants perform worse than the twocomponent variants; that the overnight volatility component exhibits more persistence than the intraday component; and that MIDAS weighting performs better than not weighting at all (i.e., than realized volatility). 
Date:  2016–06 
URL:  http://d.repec.org/n?u=RePEc:ete:ceswps:544330&r=ets 
By:  Geert Dhaene; Piet Sercu; Jianbin Wu 
Abstract:  We study international asset pricing in a largedimensional multivariate GARCHinmean framework. We examine different estimation methods and find that the twostep estimation method proposed by Bali and Engle (2010) tends to underestimate the riskreturn coefficient and the corresponding standard error. We also show that the estimate is improved by onestep estimation and by increasing the crosssectional dimension. Using stock index returns for up to 24 countries and 4 major currencies in the period 20012015, onestep estimation gives a market riskreturn coefficient of around 6. The estimate is robust to variations in model specification, data frequency, and the number of stock markets considered. 
Date:  2016–06 
URL:  http://d.repec.org/n?u=RePEc:ete:ceswps:544332&r=ets 
By:  Brave, Scott (Federal Reserve Bank of Chicago); Butters, R. Andrew (Indiana University); Justiniano, Alejandro (Federal Reserve Bank of Chicago) 
Abstract:  Mixed frequency Bayesian vector autoregressions (MFBVARs) allow forecasters to incorporate a large number of mixed frequency indicators into forecasts of economic activity. This paper evaluates the forecast performance of MFBVARs relative to surveys of professional forecasters and investigates the influence of certain specification choices on this performance. We leverage a novel realtime dataset to conduct an outofsample forecasting exercise for U.S. real gross domestic product (GDP). MFBVARs are shown to provide an attractive alternative to surveys of professional forecasters for forecasting GDP growth. However, certain specification choices such as model size and prior selection can affect their relative performance. 
Keywords:  Mixed frequency; Bayesian VAR; Realtime data; Nowcasting 
JEL:  C32 C53 E37 
Date:  2016–05–20 
URL:  http://d.repec.org/n?u=RePEc:fip:fedhwp:wp201605&r=ets 
By:  Fengler, Matthias R.; Herwartz, Helmut 
Abstract:  We propose global and disaggregated spillover indices that allow us to assess variance and covariance spillovers, locally in time and conditionally on timet information. Key to our approach is the vector moving average representation of the halfvectorized `squared' multivariate GARCH process of the popular BEKK model. In an empirical application to a fourdimensional system of broad asset classes (equity, fixed income, foreign exchange and commodities), we illustrate the new spillover indices at various levels of (dis)aggregation. Moreover, we demonstrate that they are informative of the valueatrisk violations of portfolios composed of the considered asset classes. 
Keywords:  BEKK model, forecast error variance decomposition, multivariate GARCH, spillover index, valueatrisk, variance spillovers 
JEL:  C32 C58 F3 G1 
Date:  2015–03–17 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:72197&r=ets 
By:  Jack Fosten (University of East Anglia) 
Abstract:  This paper provides an extension of DieboldMarianoWest (DMW) forecast accuracy tests to allow for factoraugmented models to be compared with nonnested benchmarks. The outof sample approach to forecast evaluation requires that both the factors and the forecasting model parameters are estimated in a rolling fashion, which poses several new challenges which we address in this paper. Firstly, we show the convergence rates of factors estimated in different rolling windows, and then give conditions under which the asymptotic distribution of the DMW test statistic is not affected by factor estimation error. Secondly, we draw attention to the issue of "signchanging" across rolling windows of factor estimates and factoraugmented model coefficients, caused by the lack of sign identification when using Principal Components Analysis to estimate the factors. We show that arbitrary signchanging does not affect the distribution of the DMW test statistic, but it does prohibit the construction of valid bootstrap critical values using existing procedures. We solve this problem by proposing a novel new normalization for rolling factor estimates, which has the effect of matching the sign of factors estimated in different rolling windows. We establish the firstorder validity of a simpletoimplement block bootstrap procedure and illustrate its properties using Monte Carlo simulations and an empirical application to forecasting U.S. CPI inflation. 
Keywords:  boostrap, diffusion index, factor model, predictive ability 
JEL:  C12 C22 C38 C53 
Date:  2016–01–28 
URL:  http://d.repec.org/n?u=RePEc:uea:ueaeco:2016_05&r=ets 
By:  Jack Fosten (University of East Anglia) 
Abstract:  This paper provides consistent information criteria for the selection of forecasting models which use a subset of both the idiosyncratic and common factor components of a big dataset. This hybrid model approach has been explored by recent empirical studies to relax the strictness of pure factoraugmented model approximations, but no formal model selection procedures have been developed. The main difference to previous factoraugmented model selection procedures is that we must account for estimation error in the idiosyncratic component as well as the factors. Our first contribution shows that this combined estimation error vanishes at a slower rate than in the case of pure factoraugmented models in circumstances in which N is of larger order than sqrt(T), where N and T are the crosssection and time series dimensions respectively. Under these circumstances we show that existing factoraugmented model selection criteria are inconsistent, and the standard BIC is inconsistent regardless of the relationship between N and T. Our main contribution solves this issue by proposing new information criteria which account for the additional source of estimation error, whose properties are explored through a Monte Carlo simulation study. We conclude with an empirical application to longhorizon exchange rate forecasting using a recently proposed model with countryspecific idiosyncratic components from a panel of global exchange rates. 
Keywords:  forecasting, factor model, model selection, information criteria, idiosyncratic 
JEL:  C13 C22 C38 C52 C53 
Date:  2016–03–14 
URL:  http://d.repec.org/n?u=RePEc:uea:ueaeco:2016_07&r=ets 
By:  Adams, Zeno; Fuess, Roland; Glueck, Thorsten 
Abstract:  Multivariate GARCH models have been designed as an extension of their univariate counterparts. Such a view is appealing from a modeling perspective but imposes correlation dynamics that are similar to timevarying volatility. In this paper, we argue that correlations are quite different in nature. We demonstrate that the highly unstable and erratic behavior that is typically observed for the correlation among financial assets is to a large extent a statistical artefact. We provide evidence that spurious correlation dynamics occur in response to financial events that are sufficiently large to cause a structural break in the timeseries of correlations. A measure for the autocovariance structure of conditional correlations allows us to formally demonstrate that the volatility and the persistence of daily correlations are not primarily driven by financial news but by the level of the underlying true correlation. Our results indicate that a rollingwindow sample correlation is often a better choice for empirical applications in finance. 
Keywords:  Changepoint tests; correlation breaks; dynamic conditional correlation (DCC); multivariate GARCH models; spurious conditional correlation 
JEL:  C12 C52 G01 G11 
Date:  2016–06 
URL:  http://d.repec.org/n?u=RePEc:usg:sfwpfi:2016:13&r=ets 