
on Econometric Time Series 
By:  Joshua C.C. Chan; Eric Eisenstat; Chenghan Hou; Gary Koop 
Abstract:  Adding multivariate stochastic volatility of a flexible form to large Vector Autoregressions (VARs) involving over a hundred variables has proved challenging due to computational considerations and overparameterization concerns. The existing literature either works with homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility. These involve estimating large numbers of parsimonious models and then taking a weighted average across these models. We discuss various schemes for choosing the weights. In our empirical work involving VARs of up to 196 variables, we show that composite likelihood methods have similar properties to existing alternatives used with small data sets in that they estimate the multivariate stochastic volatility in a flexible and realistic manner and they forecast comparably. In very high dimensional VARs, they are computationally feasible where other approaches involving stochastic volatility are not and produce superior forecasts than natural conjugate prior homoscedastic VARs. 
Keywords:  Bayesian, large VAR, composite likelihood, prediction pools, stochastic volatility 
JEL:  C11 C32 C53 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:een:camaaa:201826&r=ets 
By:  Jonas Dovern; Hans Manner 
Abstract:  Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate GARCHbased multivariate density forecasts for a vector of stock market returns. 
Keywords:  density calibration, goodnessoffit test, predictive density, Rosenblatt transformation 
JEL:  C12 C32 C52 C53 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_7023&r=ets 
By:  Joshua C.C. Chan; Liana Jacobi; Dan Zhu 
Abstract:  Vector autoregressions combined with Minnesotatype priors are widely used for macroeconomic forecasting. The fact that strong but sensible priors can substantially improve forecast performance implies VAR forecasts are sensitive to prior hyperparameters. But the nature of this sensitivity is seldom investigated. We develop a general method based on Automatic Differentiation to systematically compute the sensitivities of forecasts—both points and intervals—with respect to any prior hyperparameters. In a forecasting exercise using US data, we find that forecasts are relatively sensitive to the strength of shrinkage for the VAR coefficients, but they are not much affected by the prior mean of the error covariance matrix or the strength of shrinkage for the intercepts. 
Keywords:  vector autoregression, automatic differentiation, interval forecasts 
JEL:  C11 C53 E37 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:een:camaaa:201825&r=ets 
By:  Christiane Baumeister; James D. Hamilton 
Abstract:  Reporting point estimates and error bands for structural vector autoregressions that are only set identified is a very common practice. However, unless the researcher is persuaded on the basis of prior information that some parameter values are more plausible than others, this common practice has no formal justification. When the role and reliability of prior information is defended, Bayesian posterior probabilities can be used to form an inference that incorporates doubts about the identifying assumptions. We illustrate how prior information can be used about both structural coefficients and the impacts of shocks, and propose a new distribution, which we call the asymmetric t distribution, for incorporating prior beliefs about the signs of equilibrium impacts in a nondogmatic way. We apply these methods to a threevariable macroeconomic model and conclude that monetary policy shocks were not the major driver of output, inflation, or interest rates during the Great Moderation. 
Keywords:  structural vector autoregressions, set identification, monetary policy, impulseresponse functions, historical decompositions, model uncertainty, informative priors 
JEL:  C11 C32 E52 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_7048&r=ets 
By:  Claudio, Morana 
Abstract:  This paper proposes a threestep estimation strategy for dynamic conditional correlation models. In the first step, conditional variances for individual and aggregate series are estimated by means of QML equation by equation. In the second step, conditional covariances are estimated by means of the polarization identity, and conditional correlations are estimated by their usual normalization. In the third step, the twostep conditional covariance and correlation matrices are regularized by means of a new nonlinear shrinkage procedure and used as starting value for the maximization of the joint likelihood of the model. This yields the final, third step smoothed estimate of the conditional covariance and correlation matrices. Due to its scant computational burden, the proposed strategy allows to estimate high dimensional conditional covariance and correlation matrices. An application to global minimum variance portfolio is also provided, confirming that SPDCC is a simple and viable alternative to existing DCC models. 
Keywords:  Conditional covariance, Dynamic conditional correlation model, Semiparametric dynamic conditional correlation model, Multivariate GARCH. 
JEL:  C32 C58 
Date:  2018–06–04 
URL:  http://d.repec.org/n?u=RePEc:mib:wpaper:382&r=ets 
By:  G. Angelini; L. Fanelli 
Abstract:  In this paper we discuss general identification results for Structural Vector Autoregressions (SVARs) with external instruments, considering the case in which r valid instruments are used to identify g ≥ 1 structural shocks, where r ≥ g. We endow the SVAR with an auxiliary statistical model for the external instruments which is a system of reduced form equations. The SVAR and the auxiliary model for the external instruments jointly form a `larger' SVAR characterized by a particularly restricted parametric structure, and are connected by the covariance matrix of their disturbances which incorporates the `relevance' and `exogeneity' conditions. We discuss identification results and likelihoodbased estimation methods both in the `multiple shocks' approach, where all structural shocks are of interest, and in the `partial shock' approach, where only a subset of the structural shocks is of interest. Overidentified SVARs with external instruments can be easily tested in our setup. The suggested method is applied to investigate empirically whether commonly employed measures of macroeconomic and financial uncertainty respond onimpact, other than with lags, to business cycle uctuations in the U.S. in the period after the Global Financial Crisis. To do so, we employ two external instruments to identify the real economic activity shock in a partial shock approach. 
JEL:  C32 C51 E44 G10 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp1122&r=ets 
By:  Cassim, Lucius 
Abstract:  The main objective of this study is to derive semi parametric GARCH (1, 1) estimator under serially dependent innovations. The specific objectives are to show that the derived estimator is not only consistent but also asymptotically normal. Normally, the GARCH (1, 1) estimator is derived through quasimaximum likelihood estimation technique and then consistency and asymptotic normality are proved using the weak law of large numbers and Lindeberg central limit theorem respectively. In this study, we apply the quasimaximum likelihood estimation technique to derive the GARCH (1, 1) estimator under the assumption that the innovations are serially dependent. Allowing serial dependence of the innovations has however brought problems in terms of methodology. Firstly, we cannot split the joint probability distribution into a product of marginal distributions as is normally done. Rather, the study splits the joint distribution into a product of conditional densities to get around this problem. Secondly, we cannot use the weak laws of large numbers or/and the Lindeberg central limit theorem. We therefore employ the martingale techniques to achieve the specific objectives. Having derived the semi parametric GARCH (1, 1) estimator, we have therefore shown that the derived estimator not only converges almost surely to the true population parameter but also converges in distribution to the normal distribution with the highest possible convergence rate similar to that of parametric estimators 
Keywords:  GARCH(1,1), semi parametric , Quasi Maximum Likelihood Estimation, Martingale 
JEL:  C4 C58 
Date:  2018–05–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:86572&r=ets 
By:  Shota Gugushvili; Frank van der Meulen; Moritz Schauer; Peter Spreij 
Abstract:  Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogramtype prior on the volatility with piecewise constant realisations on bins forming a partition of the time interval. The values on the bins are assigned an inverse Gamma Markov chain (IGMC) prior. Posterior inference is straightforward to implement via Gibbs sampling, as the full conditional distributions are available explicitly and turn out to be inverse Gamma. We also discuss in detail the hyperparameter selection for our method. Our nonparametric Bayesian approach leads to good practical results in representative simulation examples. Finally, we apply it on a classical data set in changepoint analysis: weekly closings of the DowJones industrial averages. 
Date:  2018–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1801.09956&r=ets 
By:  Sylvain Barde (Sciences Po) 
Abstract:  There centincreasein the breath of computational methodologies has been matched with a corresponding increase in the difﬁculty of comparing the relative explanatory power of models from different methodological lineages.In order to help address this problem a Markovian information criterion (MIC) is developed that is analogous to the Akaike information criterion (AIC) in its theoretical derivation and yet can be applied to any model able to generate simulated or predicted data,regardless of its methodology. Both the AIC and proposed MIC rely on the Kullback–Leibler (KL) distance between model predictions and real data as a measure of prediction accuracy. Instead of using the maximum likelihood approach like the AIC, the proposed MIC relies instead on the literal interpretation of the KL distance as the inefﬁciency of compressing real data using modelled probabilities, and therefore uses the output of a universal compression algorithm to obtain an estimate of the KL distance. Several Monte Carlo tests are carried out in order to (a) conﬁrm the performance of the algorithm and (b) evaluate the ability of the MIC to identify the true datagenerating process from a set of alternative models. 
Keywords:  AIC; Description length; Markov process; Market selection 
JEL:  B41 C15 C52 C63 
Date:  2017–03 
URL:  http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/5fafm6me7k8omq5jbo61urqq27&r=ets 
By:  Russell Davidson; Andrea Monticini (Università Cattolica del Sacro Cuore; Dipartimento di Economia e Finanza, Università Cattolica del Sacro Cuore) 
Abstract:  The fast double bootstrap can improve considerably on the single bootstrap when the bootstrapped statistic is approximately independent of the bootstrap DGP. This is because, among the approximations that underlie the fast double bootstrap (FDB), is the assumption of such independence. In this paper, use is made of a discrete formu lation of bootstrapping in order to develop a conditional version of the FDB, which makes use of the joint distribution of a statistic and its bootstrap counterpart, rather than the joint distribution of the statistic and the full distribution of its bootstrap counterpart, which is available only by means of a simulation as costly as the full double bootstrap. Simulation evidence shows that the conditional FDB can greatly improve on the performance of the FDB when the statistic and the bootstrap DGP are far from independent, while giving similar results in cases of near independence. 
Keywords:  Bootstrap inference, fast double bootstrap, discrete model, conditional fast double bootstrap. 
JEL:  C12 C22 C32 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:ctc:serie1:def070&r=ets 
By:  ChiaLin Chang (National Chung Hsing University, Taiwan); ShuHan Hsu (National Chung Hsing University, Taiwan); Michael McAleer (Asia University, Taiwan) 
Abstract:  Since 2008, when Taiwan’s President Ma YingJeou relaxed the CrossStrait policy, China has become Taiwan’s largest source of international tourism. In order to understand the risk persistence of Chinese tourists, the paper investigates the shortrun and longrun persistence of shocks to the change rate of Chinese tourists to Taiwan. The daily data used for the empirical analysis is from 1 January 2013 to 28 February 2018. McAleer’s (2015) fundamental equation in tourism finance is used to link the change rate of tourist arrivals and the change in tourist revenues. Three widelyused univariate conditional volatility models, namely GARCH(1,1), GJR(1,1) and EGARCH(1,1), are used to measure the shortrun and longrun persistence of shocks, as well as symmetric, asymmetric and leverage effects. Three different Heterogeneous AutoRegressive (HAR) models, HAR(1), HAR(1,7) HAR(1,7,28), are considered as alternative mean equations for capturing a variety of long memory effects. The mean equations associated with GARCH(1,1), GJR(1,1) and EGARCH(1,1) are used to analyse the risk persistence of the change in Chinese tourists. The exponential smoothing process is used to adjust the seasonality around the trend in Chinese tourists. The empirical results show asymmetric impacts of positive and negative shocks on the volatility of the change in the number of Grouptype and Medicaltype tourists, while Individualtype tourists display a symmetric volatility pattern. Somewhat unusually, leverage effects are observed in EGARCH for Medicaltype tourists, which shows a negative correlation between shocks in tourist numbers and the subsequent shocks to volatility. For both Grouptype and Medicaltype tourists, the asymmetric impacts on volatility show that negative shocks have larger effects than do positive shocks. The leverage effect in EGARCH for Medicaltype tourists implies that larger shocks would decrease volatility in the change in the numbers of Medicaltype tourists. These results suggest that Taiwan tourism authorities should act to prevent the negative shocks for the Grouptype and Medicaltype Chinese tourists to dampen the shocks that arise from having fewer Chinese tourists to Taiwan. 
Keywords:  Asymmetric risk; leverage; risk persistence; tourist revenues; conditional volatility models; Heterogeneous AutoRegressive (HAR) models 
JEL:  G32 C22 C58 
Date:  2018–05–18 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20180047&r=ets 
By:  Yanele Nyamela (Department of Economics, University of Pretoria, Pretoria, South Africa); Vasilios Plakandaras (Department of Economics, Democritus University of Thrace, Greece); Rangan Gupta (Department of Economics, University of Pretoria, Pretoria, South Africa) 
Abstract:  In this paper, we analyze the impact of uncertainty shocks at the dailyfrequency on key macroeconomic variables for the United States. In doing so, we use a vector autoregressive (VAR) model, including the inflation rate, a realtime measure of economic activity and a measure of monetary policy as endogenous variables and decompose uncertainty effects into short, medium and longterm based on a discretetime Fourier transformation. Aggregate results (prior to decomposition) show that an increase in economic uncertainty has a significant expansionary impact on monetary policy. However, when we decompose uncertainty into its short, medium and longrun components, we find that economic activity is affected negatively in a statistically significant manner to shocks in lowfrequency uncertainty, while, statistically significant monetary expansion is observed under shocks to relatively high frequencies of uncertainty. 
Keywords:  Uncertainty, FrequencyDependence, Daily Data 
JEL:  C32 E31 E32 E52 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:pre:wpaper:201833&r=ets 
By:  Tan T. M. Le (Univ Rennes, CREM, CNRS, UMR 6211, F35000 Rennes, France, and Hue University, Vietnam); Franck Martin (Univ Rennes, CREM, CNRS, UMR 6211, F35000 Rennes, France,); Duc K. Nguyenc (Ipag Business School, Paris, France) 
Abstract:  Conditional granger causality framework in Barnett and Seth (2014) is employed to measure the connectedness among the most globally traded currencies. The connectedness exhibits dynamics through time on both breadth and depth dimensions at three levels: nodewise, groupwise and systemwise. Overall, rolling connectedness series could capture major systemic events like Lehman Brothers'collapse and the getthrough of Outright Monetary Transactions in Europe in September 2012. The rolling total breath connectedness series spike during highrisk episodes, becomes more stable in lower risk environment and is positively correlated with volatility index and Ted spread, thus, can be considered as a systemic risk indicator in light of Billio et al. (2012). Global currencies tend structure into communities based on connection strength and density. While more links are found related to currencies from emerging markets, G11 currencies are net spreaders of foreign exchange rate returns. Finally, hard currencies including Canadian dollar, Norwegian Krone and Japanese Yen frequently present among the top most connected, though the centrality positions vary over time. 
Keywords:  conditional granger causality, exchange rates, connectedness, systemic risk 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:tut:cremwp:201804&r=ets 
By:  Takuji Fueki; Hiroka Higashi; Naoto Higashio; Jouchi Nakajima; Shinsuke Ohyama; Yoichiro Tamanyu 
Abstract:  This paper proposes a simple but comprehensive structural vector autoregressive (SVAR) model to examine the underlying factors of oil price dynamics. The distinguishing feature is to explicitly assess the role of expectations on future aggregate demand and oil supply in addition to the traditional realized aggregate demand and supply factors. Our empirical analysis shows that identified future demand and supply shocks explain about 3035 percent of historical oil price fluctuations. In particular, future oil supply shocks are more than twice as important as realized and future demand shocks in accounting for oil price developments. The empirical result indicates that the influence of oil price shocks on global output varies according to the nature of each shock. We also show that the financial factors and the development of shaleoil technology are additional relevant sources of oil price fluctuations. 
Keywords:  oil demand and supply, oil price, structural vector autoregressive model 
JEL:  C32 E44 G12 G15 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:bis:biswps:725&r=ets 
By:  Sahu, Priyanka 
Abstract:  This paper attempts to investigate the impact of demand and supply shocks on core inflation in India. Firstly, it calculates core inflation through asymmetric trim mean approach and secondly autoregressive distributed model is used to explain the dynamic effects of shocks on core inflation. Empirical findings based on ARDL bound test confirms the existence of long run relationship between core inflation with other macroeconomic variables and CUSUM and CUSUMSQ test show stability of coefficients in the model. Overall, the response of core inflation to demand shock is high in case of real variables as compared to monetary variables and its response to skewnessbased supply shock is high as compared to food and fuel inflation. 
Keywords:  Headline Inflation, Core Inflation, Demand Shocks, Supply Shocks, Asymmetric trimmed Mean, Autoregressive Model, Bound Test. 
JEL:  C22 E31 E51 E52 
Date:  2018–03–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:86588&r=ets 