H. K. van Dijk

Interactions between eurozone and US booms and busts: A Bayesian panel Markov-switching VAR model

Interactions between the eurozone and US booms and busts and among major eurozone economies are analyzed by introducing a panel Markov-switching VAR model well suitable for a multi-country cyclical analysis. The model accommodates changes in low and high data frequencies and endogenous time-varying transition matrices of the country-specific Markov chains. The transition matrix of each Markov chain depends on its own past history and on the history of the other chains, thus allowing for modelling of the interactions between cycles. An endogenous common eurozone cycle is derived by aggregating country-specific cycles. The model is estimated using a simulation based Bayesian approach in which an effi cient multi-move strategy algorithm is defined to draw common time-varying Markov-switching chains. Our results show that the US and eurozone cycles are not fully synchronized over the 1991-2013 sample period, with evidence of more recessions in the eurozone, in particular during the 90s when the monetary union was planned. Larger synchronization occurs at beginning of the Great Financial Crisis. Shocks affect the US 1-quarter in advance of the eurozone, but these spread very rapidly among economies. There exist reinforcement effects in the recession probabilities and in the probabilities of exiting recessions for both eurozone and US cycles, and substantial differences in the phase transitions within the eurozone. An increase in the number of eurozone countries in recession increases the probability of the US to stay within recession, while the US recession indicator has a negative impact on the probability to stay in recession for eurozone countries. Moreover, turning point analysis shows that the cycles of Germany, France and Italy are closer to the US cycle than other countries. Belgium, Spain, and Germany, provide more timely information on the aggregate recession than Netherlands and France.

Comment on Forecast Rationality Tests Based on Multi-Horizon Bounds

Forecast rationality under squared error loss implies various bounds on second moments of the forecasts across different horizons. For example, the mean squared forecast error should be nondecreasing in the horizon. Patton and Timmermann (2011) propose rationality tests based on such restrictions, including interesting new tests that can be conducted without having data on the target variable; that is, these tests can be performed by checking only the “internal consistency” of the “term structure” of forecasts. One of their novel tests that is easily implemented and that performs well in Monte Carlo simulations (in the sense that the actual size is equal to the nominal size and that the power is high) considers the hypothesis of optimal forecast revision in the context of a linear regression of the most recent forecast on the long-horizon forecast and the sequence of interim forecast revisions. That is, it considers the following regression:

Posterior-Predictive Evidence on US Inflation using Phillips Curve Models with Non-Filtered Time Series

Changing time series properties of US inflation and economic activity are analyzed within a class of extended Phillips Curve (PC) models. First, the misspecification effects of mechanical removal of low frequency movements of these series on posterior inference of a basic PC model are analyzed using a Bayesian simulation based approach. Next, structural time series models that describe changing patterns in low and high frequencies and backward as well as forward inflation expectation mechanisms are incorporated in the class of extended PC models. Empirical results indicate that the proposed models compare favorably with existing Bayesian Vector Autoregressive and Stochastic Volatility models in terms of fit and predictive performance. Weak identification and dynamic persistence appear less important when time varying dynamics of high and low frequencies are carefully modeled. Modeling inflation expectations using survey data and adding level shifts and stochastic volatility improves substantially in sample fit and out of sample predictions. No evidence is found of a long run stable cointegration relation between US inflation and marginal costs. Tails of the complete predictive distributions indicate an increase in the probability of disinflation in recent years.

Return and Risk of Pairs Trading Using a Simulation-Based Bayesian Procedure for Predicting Stable Ratios of Stock Prices

We investigate the direct connection between the uncertainty related to estimated stable ratios of stock prices and risk and return of two pairs trading strategies: a conditional statistical arbitrage method and an implicit arbitrage one. A simulation-based Bayesian procedure is introduced for predicting stable stock price ratios, defined in a cointegration model. Using this class of models and the proposed inferential technique, we are able to connect estimation and model uncertainty with risk and return of stock trading. In terms of methodology, we show the effect that using an encompassing prior, which is shown to be equivalent to a Jeffreys’ prior, has under an orthogonal normalization for the selection of pairs of cointegrated stock prices and further, its effect for the estimation and prediction of the spread between cointegrated stock prices. We distinguish between models with a normal and Student t distribution since the latter typically provides a better description of daily changes of prices on financial markets. As an empirical application, stocks are used that are ingredients of the Dow Jones Composite Average index. The results show that normalization has little effect on the selection of pairs of cointegrated stocks on the basis of Bayes factors. However, the results stress the importance of the orthogonal normalization for the estimation and prediction of the spread — the deviation from the equilibrium relationship — which leads to better results in terms of profit per capital engagement and risk than using a standard linear normalization.

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

Weak empirical evidence near and at the boundary of the parameter region is a predominant feature in econometric models. Examples are macroeconometric models with weak information on the number of stable relations, microeconometric models measuring connectivity between variables with weak instruments, financial econometric models like the random walk with weak evidence on the efficient market hypothesis and factor models for investment policies with weak information on the number of unobserved factors. A Bayesian analysis is presented of the common issue in these models, which refers to the topic of a reduced rank. We introduce a lasso type shrinkage prior combined with orthogonal normalization which restricts the range of the parameters in a plausible way. This can be combined with other shrinkage, smoothness and data based priors using training samples or dummy observations. Using such classes of priors, it is shown how conditional probabilities of evidence near and at the boundary can be evaluated effectively. These results allow for Bayesian inference using mixtures of posteriors under the boundary state and the near-boundary state. The approach is applied to the estimation of education-income effect in all states of the US economy. The empirical results indicate that there exist substantial differences of this effect between almost all states. This may affect important national and state-wise policies on required length of education. The use of the proposed approach may, in general, lead to more accurate forecasting and decision analysis in other problems in economics, finance and marketing.

Parallelization experience with four canonical econometric models using ParMitISEM

This paper presents the parallel computing implementation of the MitISEM algorithm, labeled Parallel MitISEM. The basic MitISEM algorithm, introduced by Hoogerheide, Opschoor and Van Dijk (2012), 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. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one.

Bayesian Forecasting of US Growth using Basic Time Varying Parameter Models and Expectations Data

Time varying patterns in US growth are analyzed using various univariate model structures, starting from a naive model structure where all features change every period to a model where the slow variation in the conditional mean and changes in the conditional variance are specified together with their interaction, including survey data on expected growth in order to strengthen the information in the model. Use is made of a simulation based Bayesian inferential method to determine the forecasting performance of the various model specifications. The extension of a basic growth model with a constant mean to models including time variation in the mean and variance requires careful investigation of possible identification issues of the parameters and existence conditions of the posterior under a diffuse prior. The use of diffuse priors leads to a focus on the likelihood fu nction and it enables a researcher and policy adviser to evaluate the scientific information contained in model and data. Empirical results indicate that incorporating time variation in mean growth rates as well as in volatility are important in order to improve for the predictive performances of growth models. Furthermore, using data information on growth expectations is important for forecasting growth in specific periods, such as the the recession periods around 2000s and around 2008.