http://repub.eur.nl/res/concept/jel-C15/ Recent publications classified by JEL Code C15 en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/39847/ 2014-04-15T00:00:00Z Accurate prediction of risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) requires precise estimation of the tail of the predictive distribution. Two novel concepts are introduced that offer a specific focus on this part of the predictive density: the censored posterior, a posterior in which the likelihood is replaced by the censored likelihood; and the censored predictive likelihood, which is used for Bayesian Model Averaging. We perform extensive experiments involving simulated and empirical data. Our results show the ability of these new approaches to outperform the standard posterior and traditional Bayesian Model Averaging techniques in applications of Value-at-Risk prediction in GARCH models. Gatarek, L.T. Hoogerheide, L.F. Honing, K. http://repub.eur.nl/res/pub/39840/ 2013-04-08T00:00:00Z This paper presents the Matlab package DeCo (Density Combination) which is based on the paper by Billio et al. (2013) where a constructive Bayesian approach is presented for combining predictive densities originating from different models or other sources of information. The combination weights are time-varying and may depend on past predictive forecasting performances and other learning mechanisms. The core algorithm is the function DeCo which applies banks of parallel Sequential Monte Carlo algorithms to filter the time-varying combination weights. The DeCo procedure has been implemented both for standard CPU computing and for Graphical Process Unit (GPU) parallel computing. For the GPU implementation we use the Matlab parallel computing toolbox and show how to use General Purposes GPU computing almost effortless. This GPU implementation comes with a speed up of the execution time up to seventy times compared to a standard CPU Matlab implementation on a multicore CPU. We show the use of the package and the computational gain of the GPU version, through some simulation experiments and empirical applications. Casarin, R. Grassi, S. Ravazzolo, F. Dijk, H.K. van http://repub.eur.nl/res/pub/38710/ 2012-12-01T00:00:00Z Regression analyses of cross-country economic growth data are complicated by two main forms of model uncertainty: the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function. Most discussions in the literature address these problems independently, yet a joint treatment is essential. We present a new framework that makes such a joint treatment possible, using flexible nonlinear models specified by Gaussian process priors and addressing the variable selection problem by means of Bayesian model averaging. Using this framework, we extend the linear model to allow for parameter heterogeneity of the type suggested by new growth theory, while taking into account the uncertainty in selecting explanatory variables. Controlling for variable selection uncertainty, we confirm the evidence in favor of parameter heterogeneity presented in several earlier studies. However, controlling for functional form uncertainty, we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections. Salimans, T. http://repub.eur.nl/res/pub/38198/ 2012-10-29T00:00:00Z We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models can be individually misspecified. A Sequential Monte Carlo method is proposed to approximate the filtering and predictive densities. The combination approach is assessed using statistical and utility-based performance measures for evaluating density forecasts. Simulation results indicate that, for a set of linear autoregressive models, the combination strategy is successful in selecting, with probability close to one, the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data. For the macro series we find that incompleteness of the models is relatively large in the 70's, the beginning of the 80's and during the recent financial crisis, and lower during the Great Moderation. With respect to returns of the S&P 500 series, we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 90's and switches to giving more weight to the professional forecasts over time. Billio, M. Casarin, R. Ravazzolo, F. Dijk, H.K. van http://repub.eur.nl/res/pub/37314/ 2012-09-21T00:00:00Z We discuss Bayesian inferential procedures within the family of instrumental variables regression models and focus on two issues: existence conditions for posterior moments of the parameters of interest under a flat prior and the potential of Direct Monte Carlo (DMC) approaches for efficient evaluation of such possibly highly onelliptical posteriors. We show that, for the general case of m endogenous variables under a flat prior, posterior moments of order r exist for the coefficients reflecting the endogenous regressors’ effect on the dependent variable, if the number of instruments is greater than m+r, even though there is an issue of local non-identification that causes non-elliptical shapes of the posterior. This stresses the need for efficient Monte Carlo integration methods. We introduce an extension of DMC that incorporates an acceptance-rejection sampling step within DMC. This Acceptance-Rejection within Direct Monte Carlo (ARDMC) method has the attractive property that the generated random drawings are independent, which greatly helps the fast convergence of simulation results, and which facilitates the evaluation of the numerical accuracy. The speed of ARDMC can be easily further improved by making use of parallelized computation using multiple core machines or computer clusters. We note that ARDMC is an analogue to the well-known 'Metropolis-Hastings within Gibbs' sampling in the sense that one 'more difficult' step is used within an 'easier' simulation method. We compare the ARDMC approach with the Gibbs sampler using simulated data and two empirical data sets, involving the settler mortality instrument of Acemoglu et al. (2001) and father's education's instrument used by Hoogerheide et al. (2012a). Even without making use of parallelized computation, an efficiency gain is observed both under strong and weak instruments, where the gain can be enormous in the latter case. Zellner, A. Ando, T. Basturk, N. Dijk, H.K. van http://repub.eur.nl/res/pub/37313/ 2012-09-20T00:00:00Z This paper presents the R package MitISEM, which provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. The package provides also an extended MitISEM algorithm, ‘sequential MitISEM’, which substantially decreases the computational time when the target density has to be approximated for increasing data samples. This occurs when the posterior distribution is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that the candidate distribution obtained by MitISEM outperforms those obtained by ‘naive’ approximations in terms of numerical efficiency. Further, the MitISEM approach can be used for Bayesian model comparison, using the predictive likelihoods. Basturk, N. Hoogerheide, L.F. Opschoor, A. Dijk, H.K. van http://repub.eur.nl/res/pub/30684/ 2011-11-30T00:00:00Z We propose a multivariate combination approach to prediction based on a distributional state space representation of the weights belonging to a set of Bayesian predictive densities which have been obtained from alternative models. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models are individually misspecified. The approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of US macroeconomic time series and surveys of stock market prices. For the macro series we find that incompleteness of the models is relatively large in the 70's, the beginning of the 80's and during the recent financial crisis; structural changes like the Great Moderation are empirically identified by our model combination and the predicted probabilities of recession accurately compare with the NBER business cycle dating. Model weights have substantial uncertainty attached and neglecting this may seriously affect results. With respect to returns of the S&P 500 series, we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 90's and switches to giving more weight to the left tail of the professional forecasts during the start of the financial crisis around 2008. Billio, M. Casarin, R. Ravazzolo, F. Dijk, H.K. van http://repub.eur.nl/res/pub/26507/ 2011-09-27T00:00:00Z A Direct Monte Carlo (DMC) approach is introduced for posterior simulation in the Instrumental Variables (IV) model with one possibly endogenous regressor, multiple instruments and Gaussian errors under a flat prior. This DMC method can also be applied in an IV model (with one or multiple instruments) under an informative prior for the endogenous regressor's effect. This DMC approach can not be applied to more complex IV models or Simultaneous Equations Models with multiple endogenous regressors. An Approximate DMC (ADMC) approach is introduced that makes use of the proposed Hybrid Mixture Sampling (HMS) method, which facilitates Metropolis-Hastings (MH) or Importance Sampling from a proper marginal posterior density with highly non-elliptical shapes that tend to infinity for a point of singularity. After one has simulated from the irregularly shaped marginal distri- bution using the HMS method, one easily samples the other parameters from their conditional Student-t and Inverse-Wishart posteriors. An example illustrates the close approximation and high MH acceptance rate. While using a simple candidate distribution such as the Student-t may lead to an infinite variance of Importance Sampling weights. The choice between the IV model and a simple linear model un- der the restriction of exogeneity may be based on predictive likelihoods, for which the efficient simulation of all model parameters may be quite useful. In future work the ADMC approach may be extended to more extensive IV models such as IV with non-Gaussian errors, panel IV, or probit/logit IV. Zellner, A. Ando, T. Basturk, N. Hoogerheide, L.F. Dijk, H.K. van http://repub.eur.nl/res/pub/23459/ 2011-05-02T00:00:00Z We summarize the general combination approach by Billio et al. [2010]. In the combination model the weights follow logistic autoregressive processes, change over time and their dynamics are possible driven by the past forecasting performances of the predictive densities. For illustrative purposes we apply it to combine White Noise and GARCH models to forecast the Amsterdam Exchange index and use the combined predictive forecasts in an investment asset allocation exercise. Billio, M. Casarin, R. Ravazzolo, F. Dijk, H.K. van http://repub.eur.nl/res/pub/22330/ 2011-01-04T00:00:00Z Using a Bayesian framework this paper provides a multivariate combination approach to prediction based on a distributional state space representation of predictive densities from alternative models. In the proposed approach the model set can be incomplete. Several multivariate time-varying combination strategies are introduced. In particular, a weight dynamics driven by the past performance of the predictive densities is considered and the use of learning mechanisms. The approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of US macroeconomic time series and of surveys of stock market prices. Billio, M. Casarin, R. Ravazzolo, F. Dijk, H.K. van http://repub.eur.nl/res/pub/22332/ 2011-01-01T00:00:00Z A class of adaptive sampling methods is introduced for efficient posterior and predictive simulation. The proposed methods are robust in the sense that they can handle target distributions that exhibit non-elliptical shapes such as multimodality and skewness. The basic method makes use of sequences of importance weighted Expectation Maximization steps in order to efficiently construct a mixture of Student-t densities that approximates accurately the target distribution -typically a posterior distribution, of which we only require a kernel - in the sense that the Kullback-Leibler divergence between target and mixture is minimized. We label this approach Mixture of t by Importance Sampling and Expectation Maximization (MitISEM). We also introduce three extensions of the basic MitISEM approach. First, we propose a method for applying MitISEM in a sequential manner, so that the candidate distribution for posterior simulation is cleverly updated when new data become available. Our results show that the computational effort reduces enormously. This sequential approach can be combined with a tempering approach, which facilitates the simulation from densities with multiple modes that are far apart. Second, we introduce a permutation-augmented MitISEM approach, for importance sampling from posterior distributions in mixture models without the requirement of imposing identification restrictions on the model's mixture regimes' parameters. Third, we propose a partial MitISEM approach, which aims at approximating the marginal and conditional posterior distributions of subsets of model parameters, rather than the joint. This division can substantially reduce the dimension of the approximation problem. Hoogerheide, L.F. Opschoor, A. Dijk, H.K. van http://repub.eur.nl/res/pub/22334/ 2011-01-01T00:00:00Z Divergent priors are improper when defined on unbounded supports. Bartlett's paradox has been taken to imply that using improper priors results in ill-defined Bayes factors, preventing model comparison by posterior probabilities. However many improper priors have attractive properties that econometricians may wish to access and at the same time conduct model comparison. We present a method of computing well defined Bayes factors with divergent priors by setting rules on the rate of diffusion of prior certainty. The method is exact; no approximations are used. As a further result, we demonstrate that exceptions to Bartlett's paradox exist. That is, we show it is possible to construct improper priors that result in well defined Bayes factors. One important improper prior, the Shrinkage prior due to Stein (1956), is one such example. This example highlights pathologies with the resulting Bayes factors in such cases, and a simple solution is presented to this problem. A simple Monte Carlo experiment demonstrates the applicability of the approach developed in this paper. Strachan, R.W. Dijk, H.K. van http://repub.eur.nl/res/pub/22337/ 2011-01-01T00:00:00Z Regression analyses of cross-country economic growth data are complicated by two main forms of model uncertainty: the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function. Most discussions in the literature address these problems independently, yet a joint treatment is essential. We perform this joint treatment by extending the linear model to allow for multiple-regime parameter heterogeneity of the type suggested by new growth theory, while addressing the variable selection problem by means of Bayesian model averaging. Controlling for variable selection uncertainty, we confirm the evidence in favor of new growth theory presented in several earlier studies. However, controlling for functional form uncertainty, we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections. Salimans, T. http://repub.eur.nl/res/pub/21723/ 2010-12-07T00:00:00Z This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero di®erences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statis- tic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties. Bian, G. McAleer, M.J. Wong, W-K. http://repub.eur.nl/res/pub/21727/ 2010-12-07T00:00:00Z This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero differences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statistic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties. Bian, G. McAleer, M.J. Wong, W-K. http://repub.eur.nl/res/pub/21593/ 2010-11-01T00:00:00Z This paper develops and tests a heterogeneous agents model for the option market. Our agents have different beliefs about the future level of volatility of the underlying stock index and trade accordingly. We consider two types of agents: fundamentalists and chartists, who are able to switch between groups according to a multinomial logit switching rule. The model simplifies to a GARCH-type specification with time-varying parameters. Estimation results for DAX30 index options reveal that different types of traders are actively involved in trading volatility. Our model improves frequently used standard GARCH-type models in terms of pricing performance. Frijns, B.P.M. Lehnert, T. Zwinkels, R.C.J. http://repub.eur.nl/res/pub/20281/ 2010-07-01T00:00:00Z The validity of family background variables instrumenting education in income regressions has been much criticized. In this paper, we use data of the 2004 German Socio-Economic Panel and Bayesian analysis in order to analyze to what degree violations of the strong validity assumption affect the estimation results. We show that, in case of moderate direct effects of the instrument on the dependent variable, the results do not deviate much from the benchmark case of no such effect (perfect validity of the instrument). The size of the bias is in many cases smaller than the standard error of education’s estimated coefficient. Thus, the violation of the strict validity assumption does not necessarily lead to strongly different results when compared to the strict validity case. This provides confidence in the use of family background variables as instruments in income regressions. Hoogerheide, L.F. Block, J.H. Thurik, A.R. http://repub.eur.nl/res/pub/19830/ 2010-06-01T00:00:00Z Strategic choices for efficient and accurate evaluation of marginal likelihoods by means of Monte Carlo simulation methods are studied for the case of highly non-elliptical posterior distributions. A comparative analysis is presented of possible advantages and limitations of different simulation techniques; of possible choices of candidate distributions and choices of target or warped target distributions; and finally of numerical standard errors. The importance of a robust and flexible estimation strategy is demonstrated where the complete posterior distribution is explored. Given an appropriately yet quickly tuned adaptive candidate, straightforward importance sampling provides a computationally efficient estimator of the marginal likelihood (and a reliable and easily computed corresponding numerical standard error) in the cases investigated in this paper, which include a non-linear regression model and a mixture GARCH model. Warping the posterior density can lead to a further gain in efficiency, but it is more important that the posterior kernel is appropriately wrapped by the candidate distribution than that is warped. Ardia, D. Basturk, N. Hoogerheide, L.F. Dijk, H.K. van http://repub.eur.nl/res/pub/19380/ 2010-04-27T00:00:00Z This paper proposes an up-to-date review of estimation strategies available for the Bayesian inference of GARCH-type models. The emphasis is put on a novel efficient procedure named AdMitIS. The methodology automatically constructs a mixture of Student-t distributions as an approximation to the posterior density of the model parameters. This density is then used in importance sampling for model estimation, model selection and model combination. The procedure is fully automatic which avoids difficult and time consuming tuning of MCMC strategies. The AdMitIS methodology is illustrated with an empirical application to S&P index log-returns. Several non-nested GARCH-type models are estimated and combined to predict the distribution of next-day ahead log-returns. Ardia, D. Hoogerheide, L.F. http://repub.eur.nl/res/pub/18574/ 2010-03-01T00:00:00Z Several Bayesian model combination schemes, including some novel approaches that simultaneously allow for parameter uncertainty, model uncertainty and robust time-varying model weights, are compared in terms of forecast accuracy and economic gains using financial and macroeconomic time series. The results indicate that the proposed time-varying model weight schemes outperform other combination schemes in terms of predictive and economic gains. In an empirical application using returns on the S&P 500 index, time-varying model weights provide improved forecasts with substantial economic gains in an investment strategy including transaction costs. Another empirical example refers to forecasting US economic growth over the business cycle. It suggests that time-varying combination schemes may be very useful in business cycle analysis and forecasting, as these may provide an early indicator for recessions. Hoogerheide, L.F. Kleijn, R.H. Ravazzolo, F. Dijk, H.K. van Verbeek, M.J.C.M.