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on Econometric Time Series |
| By: | Filippeli, Thomai (Bank of England); Harrison, Richard (Bank of England); Theodoridis, Konstantinos (Cardiff Business School) |
| Abstract: | We present a new method for estimating Bayesian vector auto-regression (VAR) models using priors from a dynamic stochastic general equilibrium (DSGE) model. We use the DSGE model priors to determine the moments of an independent Normal-Wishart prior for the VAR parameters. Two hyper-parameters control the tightness of the DSGE-implied priors on the autoregressive coefficients and the residual covariance matrix respectively. Determining these hyper-parameters by selecting the values that maximize the marginal likelihood of the Bayesian VAR provides a method for isolating subsets of DSGE parameter priors that are at odds with the data. We illustrate the ability of our approach to correctly detect incorrect DSGE priors for the variance of structural shocks using a Monte Carlo experiment. We also demonstrate how posterior estimates of the DSGE parameter vector can be recovered from the BVAR posterior estimates: a new ‘quasi-Bayesian’ DSGE estimation. An empirical application on US data reveals economically meaningful differences in posterior parameter estimates when comparing our quasi-Bayesian estimator with Bayesian maximum likelihood. Our method also indicates that the DSGE prior implications for the residual covariance matrix are at odds with the data. |
| Keywords: | BVAR; DSGE; DSGE-VAR; Gibbs sampling; marginal likelihood evaluation; predictive likelihood evaluation; quasi-Bayesian DSGE estimation |
| JEL: | C11 C13 C32 C52 |
| Date: | 2018–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0716&r=ets |
| By: | Luis Uzeda |
| Abstract: | Implications for signal extraction from specifying unobserved components (UC) models with correlated or orthogonal innovations have been well investigated. In contrast, the forecasting implications of specifying UC models with different state correlation structures are less well understood. This paper attempts to address this gap in light of the recent resurgence of studies adopting UC models for forecasting purposes. Four correlation structures for errors are entertained: orthogonal, correlated, perfectly correlated innovations, and a new approach that combines features from two contrasting cases, namely, orthogonal and perfectly correlated innovations. Parameter space restrictions associated with different correlation structures and their connection with forecasting are discussed within a Bayesian framework. As perfectly correlated innovations reduce the covariance matrix rank, a Markov Chain Monte Carlo sampler, which builds upon properties of Toeplitz matrices and recent advances in precision-based algorithms, is developed. Our results for several measures of U.S. inflation indicate that the correlation structure between state variables has important implications for forecasting performance as well as estimates of trend inflation. |
| Keywords: | Econometric and statistical methods, Inflation and prices |
| JEL: | C C1 C11 C15 C5 C51 C53 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:18-14&r=ets |
| By: | Miranda-Agrippino, Silvia (Bank of England and CFM); Ricco, Giovanni (University of Warwick and OFCE - SciencesPo) |
| Abstract: | This article reviews Bayesian inference methods for Vector Autoregression models, commonly used priors for economic and financial variables, and applications to structural analysis and forecasting. |
| Keywords: | Bayesian inference ; Vector Autoregression Models ; BVAR ; SVAR ; forecasting |
| JEL: | C30 C32 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1159&r=ets |
| By: | Daniel Grabowski (Department of Economics, University of Giessen); Anna Staszewska-Bystrova (Faculty of Economics and Sociology, University of Lodz); Peter Winker (Department of Economics, University of Giessen) |
| Abstract: | This article investigates the construction of skewness-adjusted confidence intervals and joint confidence bands for impulse response functions from vector autoregressive models. Three different implementations of the skewness adjustment are investigated. The methods are based on a bootstrap algorithm that adjusts mean and skewness of the bootstrap distribution of the autoregressive coefficients before the impulse response functions are computed. Using extensive Monte Carlo simulations, the methods are shown to improve the coverage accuracy in small and medium sized samples and for unit root processes for both known and unknown lag orders. |
| Keywords: | Bootstrap, confidence intervals, joint confidence bands, vector autoregression |
| JEL: | C15 C32 |
| Date: | 2018–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:ann:wpaper:1/2018&r=ets |
| By: | Rothfelder, Mario (Tilburg University, School of Economics and Management) |
| Abstract: | This thesis is composed of three essays on time-varying parameters and time series networks where each essay deals with specific aspects thereof. The thesis starts with proposing a 2SLS based test for a threshold in models with endogenous regressors in Chapter 2. Many economic models are formulated in this way, for example output growth or unemployment rates in different states of the economy. Therefore, it is necessary to have tools available which are capable of indicating whether such effects exist in the data or not. Chapter 3 proposes, to my best knowledge, the first estimator for the inverse of the long-run covariance matrix of a linear, potentially heteroskedastic stochastic process under unknown sparsity constraints. That is, the econometrician does not know which entries of the inverse are equal to zero and which not. Such situations naturally arise, for example, when modelling partial correlation networks based on time series data. Finally, in Chapter 4 this thesis empirically investigates how robust two commonly applied network measures, the From- and the To-degree, are to the exclusion of central nodes in financial volatility networks. This question is motivated by the current empirical literature which excludes certain nodes such as Lehman Brothers from their analysis. |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiutis:fc7a10c0-7eee-479a-ac22-b36ce45f2037&r=ets |
| By: | Naoki Awaya (Graduate School of Economics, The University of Tokyo); Yasuhiro Omori (Faculty of Economics, The University of Tokyo) |
| Abstract: | An efficient simulation-based methodology is proposed for the rolling window esti- mation of state space models. Using the framework of the conditional sequential Monte Carlo update in the particle Markov chain Monte Carlo estimation, weighted particles are updated to learn and forget the information of new and old observations by the forward and backward block sampling with the particle simulation smoother. These particles are also propagated by the MCMC update step. Theoretical justifications are provided for the proposed estimation methodology. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of model parameters and marginal likelihoods are estimated with accuracy. Finally, as a special case, our proposed method can be used as a new sequential MCMC based on Particle Gibbs, which is shown to outperform SMC2 that is the promising alternative method based on Particle MH in the simulation experiments. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2018cf1080&r=ets |
| By: | Paolo Gorgi (VU Amsterdam); Siem Jan (S.J.) Koopman (VU Amsterdam; Tinbergen Institute, The Netherlands); Mengheng Li (VU Amsterdam) |
| Abstract: | We introduce a mixed-frequency score-driven dynamic model for multiple time series where the score contributions from high-frequency variables are transformed by means of a mixed-data sampling weighting scheme. The resulting dynamic model delivers a flexible and easy-to-implement framework for the forecasting of a low-frequency time series variable through the use of timely information from high-frequency variables. We aim to verify in-sample and out-of-sample performances of the model in an empirical study on the forecasting of U.S.~headline inflation. In particular, we forecast monthly inflation using daily oil prices and quarterly inflation using effective federal funds rates. The forecasting results and other findings are promising. Our proposed score-driven dynamic model with mixed-data sampling weighting outperforms competing models in terms of point and density forecasts. |
| Keywords: | Factor model; GAS model; Inflation forecasting; MIDAS; Score-driven model; Weighted maximum likelihood |
| JEL: | C42 |
| Date: | 2018–03–21 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20180026&r=ets |
| By: | Mengheng Li (VU Amsterdam); Siem Jan (S.J.) Koopman (VU Amsterdam; Tinbergen Institute, The Netherlands) |
| Abstract: | We consider unobserved components time series models where the components are stochastically evolving over time and are subject to stochastic volatility. It enables the disentanglement of dynamic structures in both the mean and the variance of the observed time series. We develop a simulated maximum likelihood estimation method based on importance sampling and assess its performance in a Monte Carlo study. This modelling framework with trend, seasonal and irregular components is applied to quarterly and monthly US inflation in an empirical study. We find that the persistence of quarterly inflation has increased during the 2008 financial crisis while it has recently returned to its pre-crisis level. The extracted volatility pattern for the trend component can be associated with the energy shocks in the 1970s while that for the irregular component responds to the monetary regime changes from the 1980s. The scale of the changes in the seasonal component has been largest during the beginning of the 1990s. We finally present empirical evidence of relative improvements in the accuracies of point and density forecasts for monthly US inflation. |
| Keywords: | Importance Sampling; Kalman Filter; Monte Carlo Simulation; Stochastic Volatility; Unobserved Components Time Series Model; Inflation |
| JEL: | C32 C53 E31 E37 |
| Date: | 2018–03–21 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20180027&r=ets |
| By: | Marta Banbura (European Central Bank, Germany); Andries van Vlodrop (VU Amsterdam, the Netherlands) |
| Abstract: | We develop a vector autoregressive model with time variation in the mean and the variance. The unobserved time-varying mean is assumed to follow a random walk and we also link it to long-term Consensus forecasts, similar in spirit to so called democratic priors. The changes in variance are modelled via stochastic volatility. The proposed Gibbs sampler allows the researcher to use a large cross-sectional dimension in a feasible amount of computational time. The slowly changing mean can account for a number of secular developments such as changing inflation expectations, slowing productivity growth or demographics. We show the good forecasting performance of the model relative to popular alternatives, including standard Bayesian VARs with Minnesota priors, VARs with democratic priors and standard time-varying parameter VARs for the euro area, the United States and Japan. In particular, incorporating survey forecast information helps to reduce the uncertainty about the unconditional mean and along with the time variation improves the long-run forecasting performance of the VAR models. |
| Keywords: | Consensus forecasts; forecast evaluation; large cross-sections; state space models. |
| JEL: | C11 C32 C53 E37 |
| Date: | 2018–03–21 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20180025&r=ets |
| By: | Elhorst, J. Paul; Gross, Marco; Tereanu, Eugen |
| Abstract: | We bring together the spatial and global vector autoregressive (GVAR) classes of econometric models by providing a detailed methodological review of where they meet in terms of structure, interpretation, and estimation methods. We discuss the structure of cross-section connectivity (weight) matrices used by these models and its implications for estimation. Primarily motivated by the continuously expanding literature on spillovers, we define a broad and measurable concept of spillovers. We formalize it analytically through the indirect effects used in the spatial literature and impulse responses used in the GVAR literature. Finally, we propose a practical step-by-step approach for applied researchers who need to account for the existence and strength of cross-sectional dependence in the data. This approach aims to support the selection of the appropriate modeling and estimation method and of choices that represent empirical spillovers in a clear and interpretable form. JEL Classification: C33, C38, C51 |
| Keywords: | GVARs, spatial models, spillovers, weak and strong cross-sectional dependence |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20182134&r=ets |