Forecasting from others’ experience: Bayesian estimation of the generalized Bass model

We propose a Bayesian estimation procedure for the generalized Bass model that is used in product diffusion models. Our method forecasts product sales early based on previous similar markets; that is, we obtain pre-launch forecasts by analogy. We compare our forecasting proposal to traditional estimation approaches, and alternative new product diffusion specifications. We perform several simulation exercises, and use our method to forecast the sales of room air conditioners, BlackBerry handheld devices, and compressed natural gas. The results show that our Bayesian proposal provides better predictive performances than competing alternatives when little or no historical data are available, which is when sales projections are the most useful.     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

Open economy forecasting with a DSGE-VAR: Head to head with the RBNZ published forecasts

We construct a DSGE-VAR model for competing head to head with the long history of published forecasts of the Reserve Bank of New Zealand. We also construct a Bayesian VAR model with a Minnesota prior for forecast comparison. The DSGE-VAR model combines a structural DSGE model with a statistical VAR model based on the in-sample fit over the majority of New Zealand’s inflation-targeting period. We evaluate the real-time out-of-sample forecasting performance of the DSGE-VAR model, and show that the forecasts from the DSGE-VAR are competitive with the Reserve Bank of New Zealand’s published, judgmentally-adjusted forecasts. The Bayesian VAR model with a Minnesota prior also provides a competitive forecasting performance, and generally, with a few exceptions, out-performs both the DSGE-VAR and the Reserve Bank’s own forecasts.     

Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage

We develop a novel Bayesian doubly adaptive elastic-net Lasso (DAELasso) approach for VAR shrinkage. DAELasso achieves variable selection and coefficient shrinkage in a data-based manner. It deals constructively with explanatory variables which tend to be highly collinear by encouraging the grouping effect. In addition, it also allows for different degrees of shrinkage for different coefficients. Rewriting the multivariate Laplace distribution as a scale mixture, we establish closed-form conditional posteriors that can be drawn from a Gibbs sampler. An empirical analysis shows that the forecast results produced by DAELasso and its variants are comparable to those from other popular Bayesian methods, which provides further evidence that the forecast performances of large and medium sized Bayesian VARs are relatively robust to prior choices, and, in practice, simple Minnesota types of priors can be more attractive than their complex and well-designed alternatives.     

Bayesian model averaging for mortality forecasting using leave-future-out validation

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to some well-documented drawbacks, including model misspecification, parameter uncertainty, and overfitting. To address these issues we first consider mortality modeling in a Bayesian negative-binomial framework to account for overdispersion and the uncertainty about the parameter estimates in a natural and coherent way. Model averaging techniques are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation and compare them to standard Bayesian model averaging (BMA) based on marginal likelihood. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets, along with a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on an out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.     

Forecasting China's foreign exchange reserves using dynamic model averaging: The roles of macroeconomic fundamentals,financial stress and economic uncertainty

We develop models for examining possible predictors of growth of China's foreign exchange reserves that embrace Chinese and global trade, financial and risk (uncertainty) factors. Specifically, by comparing with other alternative models, we show that the dynamic model averaging (DMA) and dynamic model selection (DMS) models outperform not only linear models (such as random walk, recursive OLS-AR(1) models, recursive OLS with all predictive variables models) but also the Bayesian model averaging (BMA) model for examining possible predictors of growth of those reserves. The DMS is the best overall across all forecast horizons. While some predictors matter more than others over the forecast horizons, there are few that stand the test of time. The US–China interest rate differential has a superior predictive power among the 13 predictors considered, followed by the nominal effective exchange rate and the interest rate spread for most of the forecast horizons. The relative predictive prowess of the oil and copper prices alternates, depending on the commodity cycles. Policy implications are also provided.     

高速公路交通事故概率预测方法研究

准确的高速公路交通事故概率预测可提高高速公路行车安全。通过分析高速公路交通事故的影响因素,建立高速公路交通事故影响因素体系,构造贝叶斯网络,提出基于贝叶斯网络的高速公路交通事故概率预测方法。此方法利用数据库先验概率信息及贝叶斯预测模型,得出高速公路交通事故概率值,以此判断事故危险等级。     

Realized volatility forecast with the Bayesian random compressed multivariate HAR model

We develop a Bayesian random compressed multivariate heterogeneous autoregressive (BRC-MHAR) model to forecast the realized covariance matrices of stock returns. The proposed model randomly compresses the predictors and reduces the number of parameters. We also construct several competing multivariate volatility models with the alternative shrinkage methods to compress the parameter’s dimensions. We compare the forecast performances of the proposed models with the competing models based on both statistical and economic evaluations. The results of statistical evaluation suggest that the BRC-MHAR models have the better forecast precision than the competing models for the short-term horizon. The results of economic evaluation suggest that the BRC-MHAR models are superior to the competing models in terms of the average return, the Shape ratio and the economic value.     

Forecasting week-to-week television ratings using reduced-form and structural dynamic models

Rather than being sold several months before a program is aired, more than 20% of TV advertising slots are retained for sale weekly near the program’s broadcast time. Distinct from the literature that mainly focuses on the forecasting of program ratings for advanced sales of advertising slots, we explore approaches that can provide more accurate forecasts for near real-time ratings. We propose two dynamic models that mainly employ individual viewing records for past episodes to forecast viewers’ decisions on episodes in the coming week, and therefore the ratings for these episodes. One is a reduced-form dynamic model that measures the influence of past watching experience by the weighted average of the viewers’ choices of past episodes. The other is a structural dynamic model that goes deeper in its use of previous viewing information by modeling the underlying process of this influence based on the Bayesian updating theory. Using data from the Hong Kong TV industry, we test and compare the two models. Results show that the reduced-form model generally performs better when the variance of ratings across episodes is small, while the structural model generates more accurate forecasts in other cases.     

三层供应链协同预测博弈研究

运用纳什均衡和贝叶斯更新模型,得到了在一个三层供应链中联合预测的实现条件。模型中,供应商、运输商、零售商均需决定在预测技术上的投资水平,三方的需求预测将会被汇总成一个统一的预测。结果表明,各方预测能力越接近中等水平,会有更多成员倾向于在预测上进行投资。预测能力偏离中等水平越远,越容易出现搭便车行为,即至少有一方不进行预测。     

Forecasting inflation using time‐varying Bayesian model averaging

This paper presents a Bayesian model averaging regression framework for forecasting US inflation, in which the set of predictors included in the model is automatically selected from a large pool of potential predictors and the set of regressors is allowed to change over time. Using real‐time data on the 1960–2011 period, this model is applied to forecast personal consumption expenditures and gross domestic product deflator inflation. The results of this forecasting exercise show that, although it is not able to beat a simple random‐walk model in terms of point forecasts, it does produce superior density forecasts compared with a range of alternative forecasting models. Moreover, a sensitivity analysis shows that the forecasting results are relatively insensitive to prior choices and the forecasting performance is not affected by the inclusion of a very large set of potential predictors.     

Learning,forecasting and structural breaks

We provide a general methodology for forecasting in the presence of structural breaks induced by unpredictable changes to model parameters. Bayesian methods of learning and model comparison are used to derive a predictive density that takes into account the possibility that a break will occur before the next observation. Estimates for the posterior distribution of the most recent break are generated as a by‐product of our procedure. We discuss the importance of using priors that accurately reflect the econometrician's opinions as to what constitutes a plausible forecast. Several applications to macroeconomic time‐series data demonstrate the usefulness of our procedure. Copyright © 2008 John Wiley & Sons, Ltd.     

Bayesian forecast combination using time-varying features

In this work, we propose a novel framework for density forecast combination by constructing time-varying weights based on time-varying features. Our framework estimates weights in the forecast combination via Bayesian log predictive scores, in which the optimal forecast combination is determined by time series features from historical information. In particular, we use an automatic Bayesian variable selection method to identify the importance of different features. To this end, our approach has better interpretability compared to other black-box forecasting combination schemes. We apply our framework to stock market data and M3 competition data. Based on our structure, a simple maximum-a-posteriori scheme outperforms benchmark methods, and Bayesian variable selection can further enhance the accuracy for both point forecasts and density forecasts.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Evaluating Point and Density Forecasts of DSGE Models

This paper investigates the accuracy of forecasts from four dynamic stochastic general equilibrium (DSGE) models for inflation, output growth and the federal funds rate using a real‐time dataset synchronized with the Fed's Greenbook projections. Conditioning the model forecasts on the Greenbook nowcasts leads to forecasts that are as accurate as the Greenbook projections for output growth and the federal funds rate. Only for inflation are the model forecasts dominated by the Greenbook projections. A comparison with forecasts from Bayesian vector autoregressions shows that the economic structure of the DSGE models which is useful for the interpretation of forecasts does not lower the accuracy of forecasts. Combining forecasts of several DSGE models increases precision in comparison to individual model forecasts. Comparing density forecasts with the actual distribution of observations shows that DSGE models overestimate uncertainty around point forecasts. Copyright © 2013 John Wiley & Sons, Ltd.     

A Geo-Additive Bayesian Discrete-Time Survival Model and its Application to Spatial Analysis of Childhood Mortality in Malawi

We describe a flexible geo-additive Bayesian survival model that controls, simultaneously, for spatial dependence and possible nonlinear or time-varying effects of other variables. Inference is fully Bayesian and is based on recently developed Markov Chain Monte Carlo techniques. In illustrating the model we introduce a spatial dimension in modelling under-five mortality among Malawian children using data from Malawi Demographic and Health Survey of 2000. The results show that district-level socioeconomic characteristics are important determinants of childhood mortality. More importantly, a separate spatial process produces district clustering of childhood mortality indicating the importance of spatial effects. The visual nature of the maps presented in this paper highlights relationships that would, otherwise, be overlooked in standard methods.     

具有任意投资水平的供应链协同预测博弈研究

运用纳什均衡和贝叶斯更新模型,得到了供应链联合预测均衡的存在条件。模型中,供应商和零售商均需决定在预测技术上的投资水平,双方的需求预测将会被汇总成一个统一的预测。结果表明,双方预测能力越接近中等水平,越容易实现联合预测。预测能力偏离中等水平越远,越容易出现搭便车行为,即至少有一方不进行预测。     

Projecting the future size and health status of the U.S. elderly population

"A projection model based on a multivariate continuous state, stochastic process is presented. The model allows multiple time-varying covariates to be used so parameters can be estimated from time series information on health changes and mortality, and their interaction. Health changes are simulated by altering parameters controlling the age trajectory and diffusion of risk factor means, variances, and covariances....By increasing the information used in projections it may be possible to better (a) anticipate the state of health at extreme ages, (b) forecast changes in health at specific ages over time, (c) stimulate the effects of specific interventions, and (d) determine the sensitivity of outcomes to a range of interventions."     

中国经济增长的周期性波动研究及其产业结构特征(1992～2010年)

本文使用基于贝叶斯方法的结构突变模型,研究了1992～2010年我国经济增长的周期性波动特征。研究发现,该阶段我国经济增长分别经历了一次六阶段的U形中长周期和一次三阶段的V形短周期,国际经济环境的变化对我国经济的影响日益显著,同时经济增长的波动存在季度性。通过对三次产业GDP增长率的分析,我们还发现三者之间存在着较大偏离,第二产业对我国经济增长的周期性波动起着决定性的影响,同时第二、第三产业之间的关联性在不断增强。     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.