Francesco Ravazzolo

Journal of applied econometrics Doi: https://doi.org/10.1002/jae.70018

ABSTRACT This paper provides a comprehensive analysis of the forecastability of the real price of natural gas in the United States at the monthly frequency considering a universe of models that differ in complexity and economic content. We find that considerable reductions in mean‐squared prediction error relative to a no‐change benchmark can be achieved in real time for horizons of up to 2 years. A particularly promising model is a vector autoregressive (VAR) model that includes the fundamental determinants of supply and demand for natural gas. To capture real‐time data constraints of these and other predictors, we assemble a rich database of historical vintages from multiple sources. We also compare our model‐based forecasts to model‐free forecasts provided by experts and futures markets. Given that no single forecasting method dominates, we show that combining forecasts from individual models selected in real time using the model confidence set as a novel criterion for dynamic model selection delivers the most accurate forecasts.

Waste and Biomass Valorization 16(8) s. 4009-4025 Doi: https://doi.org/10.1007/s12649-025-02948-3

Abstract International energy institutions project large shares of bioenergy as part of the decarbonization mix and small-scale generators in mountain regions can be interesting options in this space. In this study we assessed the techno-economics of small-scale (225 kW el ) biomass gasification-combined heat and power based on updated costs, under present and future energy market conditions. We found that, at 7,500 operating hours/year and a 70 €/t biomass cost, a 388 €/MWh levelized cost of energy is obtained, which is uncompetitive compared to alternative options like photovoltaic-storage or biogas. A loss in yearly operating hours and a reduction in unit capital cost have large impacts on unit cost, while heat valorization and remuneration, biomass cost and plant size represent secondary factors. An econometric forecast of consumer electricity prices in Italy to 2040 showed a subsidy requirement of 237 €/MWh and a total lifetime subsidy of 142 M€ with a carbon tax on conventional electricity growing by 11 €/t/y over twenty years, which represents a suboptimal generation infrastructure investment compared to the photovoltaic-storage or biogas alternatives. The results illustrate fundamental aspects of current bioenergy economics and deliver useful evidence for renewable energy planning in European mountain regions and beyond.

Annals of Applied Statistics 19(2) s. 1065-1085 Doi: https://doi.org/10.1214/25-AOAS2016

Since Russia’s invasion of Ukraine, many countries have pledged to end or restrict their oil and gas imports to curtail Moscow’s revenues and hinder its war effort. Thus, the European ministers agreed to trigger a cap on the gas price. To detect the importance of the price cap for gas, we provide a mixture representation for the gas price to detect the presence of outliers made by a truncated normal distribution and a uniform one. We focus our analysis on a unique dataset of different commodity prices for Germany and Italy, which are major Russian gas importers by exploiting the response of the different commodities to a gas shock through a Bayesian vector autoregressive (VAR) model. As a result, including a lower gas price cap smooths the impact of a gas shock on electricity prices, while not considering a price cap will increase exponentially this impact. Regarding the other commodities, gas shocks matter in the short and long run when a price cap is not considered.

Journal of business & economic statistics Doi: https://doi.org/10.1080/07350015.2024.2412011

Threshold autoregressive moving-average (TARMA) models extend the popular TAR model and are among the few parametric time series specifications to include a moving average in a nonlinear setting. The state dependent reactions to shocks is particularly appealing in Economics and Finance. However, no theory is currently available when the data present heavy tails or anomalous observations. Here we provide the first theoretical framework for robust M-estimation for TARMA models and study its practical relevance. Under mild conditions, we show that the robust estimator for the threshold parameter is super-consistent, while the estimators for autoregressive and moving-average parameters are strongly consistent and asymptotically normal. The Monte Carlo study shows that the M-estimator is superior, in terms of both bias and variance, to the least squares estimator, which can be heavily affected by outliers. The findings suggest that robust M-estimation should be generally preferred to the least squares method. We apply our methodology to a set of commodity price time series; the robust TARMA fit presents smaller standard errors and superior forecasting accuracy. The results support the hypothesis of a two-regime non-linearity characterized by slow expansions and fast contractions.

Studies in Nonlinear Dynamics & Econometrics Doi: https://doi.org/10.1515/snde-2024-0024

Journal of Econometrics 237(2) Doi: https://doi.org/10.1016/j.jeconom.2022.11.004

A flexible predictive density combination is introduced for large financial data sets which allows for model set incompleteness. Dimension reduction procedures that include learning allocate the large sets of predictive densities and combination weights to relatively small subsets. Given the representation of the probability model in extended nonlinear state-space form, efficient simulation-based Bayesian inference is proposed using parallel dynamic clustering as well as nonlinear filtering, implemented on graphics processing units. The approach is applied to combine predictive densities based on a large number of individual US stock returns of daily observations over a period that includes the Covid-19 crisis period. Evidence on dynamic cluster composition, weight patterns and model set incompleteness gives valuable signals for improved modelling. This enables higher predictive accuracy and better assessment of uncertainty and risk for investment fund management.

Review of economic dynamics 51 Doi: https://doi.org/10.1016/j.red.2023.09.006

We develop and estimate a DSGE model to evaluate the economic repercussions of cryptocurrency. In our model, cryptocurrency offers an alternative currency option to government currency, with endogenous supply and demand. We uncover a substitution effect between the real balances of government currency and cryptocurrency in response to technology, preferences and monetary policy shocks. We find that an increase in cryptocurrency productivity induces a rise in the relative price of government currency with respect to cryptocurrency. Since cryptocurrency and government currency are highly substitutable, the demand for the former increases whereas it drops for the latter. Our historical decomposition analysis shows that fluctuations in the cryptocurrency price are mainly driven by shocks in cryptocurrency demand, whereas changes in the real balances for government currency are mainly attributed to government currency and cryptocurrency demand shocks.

Energy 278 Doi: https://doi.org/10.1016/j.energy.2023.127831

One of the most controversial issues in the mid-term load forecasting literature is the treatment of weather. Because of the difficulty in obtaining precise weather forecasts for a few weeks ahead, researchers have, so far, implemented three approaches: a) excluding weather from load forecasting models altogether, b) assuming future weather to be perfectly known and c) including weather forecasts in their load forecasting models. This article provides the first systematic comparison of how the different treatments of weather affect load forecasting performance. We incorporate air temperature into short- and mid-term load forecasting models, comparing time-series methods and feed-forward neural networks. Our results indicate that models including future temperature always significantly outperform models excluding temperature, at all-time horizons. However, when future temperature is replaced with its prediction, these results become weaker.

Small Business Economics 62 Doi: https://doi.org/10.1007/s11187-023-00766-2

This study examines the impact of the COVID-19 pandemic on corporate financial performance using a unique, cross-country, and longitudinal sample of 3350 listed firms worldwide. We find that the financial performance of family firms has been significantly higher than that of nonfamily firms during the COVID-19 pandemic, accounting for pre-pandemic business conditions. This effect is pertinent to firms with strong family involvement in management or in both management and ownership. We also identify the role of firm-, industry-, and country-level contingencies for family business financial performance during the COVID-19 pandemic. This study offers a novel understanding of the financial resilience across different types of family business and sets an agenda for future research on the drivers of resilience of family firms to adverse events. It also provides important and novel evidence for policymakers, particularly for firms with different ownership and management structures.

Statistical Methods & Applications 33 Doi: https://doi.org/10.1007/s10260-023-00736-8

In the Italian electricity market, we analyze the Aggregate Zonal Imbalance, which is the algebraic sum, changed in sign, of the amount of energy procured by the Italian national Transmission and System Operator in the Dispatching Services Market at a given time in the northern Italian electricity macro-zone. Specifically, we determine possible relationships among the Aggregate Zonal Imbalances and other variables of interest in electricity markets, including renewable sources. From a methodological point of view, we use a multivariate model for time series that combines the marginal behavior with copula-type models. As a result, the flexibility of a copula approach will allow identifying the nature of non-linear linkages among the Aggregate Zonal Imbalance and other variables such as forecasted demand, forecasted wind and solar PV generation. In this respect, novel ways to measure dependence and association among random variates are adopted. Our results indicate a clear association between the Aggregate Zonal Imbalance and Forecasted Solar PV generation, and a weaker relationship with the other considered variables. We find this result both in terms of pairwise Spearman’s and Kendall’s correlations and in terms of upper and lower tail dependence. The analysis concludes with the proposal of new indicators to detect association among random vectors, which could identify the more important features driving imbalances.

Studies in Nonlinear Dynamics & Econometrics Doi: https://doi.org/10.1515/snde-2022-0106

This paper investigates the determinants of the European iTraxx corporate CDS index considering a large set of explanatory variables within a Markov switching model framework. The influence of financial and economic variables on CDS spreads are compared using linear, two, three, and four-regime models in a sample post-subprime financial crisis up to the COVID-19 pandemic. Results indicate that four regimes are necessary to model the CDS spreads. The fourth regime was activated during the COVID-19 pandemic and in high volatility periods. Further, the effect of the covariates differs significantly across regimes. Brent and term structure factors became relevant after the outbreak of the COVID-19 pandemic.

Economic Modelling 120 Doi: https://doi.org/10.1016/j.econmod.2022.106160

Recent research finds that forecasting electricity prices is very relevant. In many applications, it might be interesting to predict daily electricity prices by using their own lags or renewable energy sources. However, the recent turmoil of energy prices and the Russian–Ukrainian war increased attention in evaluating the relevance of industrial production and the Purchasing Managers’ Index output survey in forecasting the daily electricity prices. We develop a Bayesian reverse unrestricted MIDAS model which accounts for the mismatch in frequency between the daily prices and the monthly macro variables in Germany and Italy. We find that the inclusion of macroeconomic low frequency variables is more important for short than medium term horizons by means of point and density measures. In particular, accuracy increases by combining hard and soft information, while using only surveys gives less accurate forecasts than using only industrial production data.

Energy Economics 126 Doi: https://doi.org/10.1016/j.eneco.2023.107006

This article proposes different modelling approaches which exploit electricity market data to nowcast industrial production. Our models include linear, mixed-data sampling (MIDAS), Markov-Switching (MS) and MS-MIDAS regressions. Comparisons against autoregressive approaches and other commonly used macroeconomic predictors show that electricity market data combined with an MS model significantly improve nowcasting performance, especially during turbulent economic states, such as those generated by the recent COVID-19 pandemic. The most promising results are provided by an MS model which identifies two volatility regimes. These results confirm that electricity market data provide timely and easy-to-access information for nowcasting macroeconomic variables, especially when it is most valuable, i.e. during times of crisis and uncertainty.

Scientific Reports 13(1) Doi: https://doi.org/10.1038/s41598-023-38400-6

This research studies the impact of online news on social and economic consumer perceptions through semantic network analysis. Using over 1.8 million online articles on Italian media covering four years, we calculate the semantic importance of specific economic-related keywords to see if words appearing in the articles could anticipate consumers’ judgments about the economic situation and the Consumer Confidence Index. We use an innovative approach to analyze big textual data, combining methods and tools of text mining and social network analysis. Results show a strong predictive power for the judgments about the current households and national situation. Our indicator offers a complementary approach to estimating consumer confidence, lessening the limitations of traditional survey-based methods.

Spatial Economic Analysis 18(4) Doi: https://doi.org/10.1080/17421772.2023.2199034

The monitoring of the regional (provincial) economic situation is of particular importance due to the high level of heterogeneity and interdependences among different territories. Although econometric models allow for spatial and serial correlation of various kinds, the limited availability of territorial data restricts the set of relevant predictors at a more disaggregated level, especially for gross domestic product (GDP). Combining data from different sources at NUTS-3 level, this paper evaluates the predictive performance of a spatial dynamic panel data model with individual fixed effects and some relevant exogenous regressors, by using data on total gross value added (GVA) for 103 Italian provinces over the period 2000–2016. A comparison with nested panel sub-specifications as well as pure temporal autoregressive specifications has also been included. The main finding is that the spatial dynamic specification increases forecast accuracy more than its competitors throughout the out-of-sample, recognising an important role played by both space and time. However, when temporal cointegration is detected, the random-walk specification is still to be preferred in some cases even in the presence of short panels.

Journal of Forecasting Doi: https://doi.org/10.1002/for.2936

This paper uses a new textual data index for predicting stock market data. The index is applied to a large set of news to evaluate the importance of one or more general economic-related keywords appearing in the text. The index assesses the importance of the economic-related keywords, based on their frequency of use and semantic network position. We apply it to the Italian press and construct indices to predict Italian stock and bond market returns and volatilities in a recent sample period, including the COVID-19 crisis. The evidence shows that the index captures the different phases of financial time series well. Moreover, results indicate strong evidence of predictability for bond market data, both returns and volatilities, short and long maturities, and stock market volatility.

Journal of business & economic statistics Doi: https://doi.org/10.1080/07350015.2022.2035229

This article proposes a novel asymmetric continuous probabilistic score (ACPS) for evaluating and comparing density forecasts. It generalizes the proposed score and defines a weighted version, which emphasizes regions of interest, such as the tails or the center of a variable’s range. The (weighted) ACPS extends the symmetric (weighted) CRPS by allowing for asymmetries in the preferences underlying the scoring rule. A test is used to statistically compare the predictive ability of different forecasts. The ACPS is of general use in any situation where the decision-maker has asymmetric preferences in the evaluation of the forecasts. In an artificial experiment, the implications of varying the level of asymmetry in the ACPS are illustrated. Then, the proposed score and test are applied to assess and compare density forecasts of macroeconomic relevant datasets (U.S. employment growth) and of commodity prices (oil and electricity prices) with particular focus on the recent COVID-19 crisis period.

Oxford Bulletin of Economics and Statistics 85(3) Doi: https://doi.org/10.1111/obes.12532

We study the importance of time-varying volatility in modelling hourly electricity prices when fundamental drivers are included in the estimation. This allows us to contribute to the literature of large Bayesian VARs by using well-known time series models in a large dimension for the matrix of coefficients. Based on novel Bayesian techniques, we exploit the importance of both Gaussian and non-Gaussian error terms in stochastic volatility. We find that using regressors as fuel prices, forecasted demand and forecasted renewable energy is essential to properly capture the volatility of these prices. Moreover, we show that the time-varying volatility models outperform the constant volatility models in both the in-sample model-fit and the out-of-sample forecasting performance.

Information Sciences 590 s. 74-89 Doi: https://doi.org/10.1016/j.ins.2022.01.003

This paper examines the dependence between electricity prices, demand, and renewable energy sources by means of a multivariate copula model while studying Germany, the widest studied market in Europe. The inter-dependencies are investigated in-depth and monitored over time, with particular emphasis on the tail behavior. To this end, suitable tail dependence measures are introduced to take into account a multivariate extreme scenario appropriately identified through the Kendall’s distribution function. The empirical evidence demonstrates a strong association between electricity prices, renewable energy sources, and demand within a day and over the studied years. Hence, this analysis provides guidance for further and different incentives for promoting green energy generation while considering the time-varying dependencies of the involved variables.

International Journal of Forecasting 39(2) Doi: https://doi.org/10.1016/j.ijforecast.2022.01.003

This paper compares several models for forecasting regional hourly day-ahead electricity prices, while accounting for fundamental drivers. Forecasts of demand, in-feed from renewable energy sources, fossil fuel prices, and physical flows are all included in linear and nonlinear specifications, ranging in the class of ARFIMA-GARCH models—hence including parsimonious autoregressive specifications (known as expert-type models). The results support the adoption of a simple structure that is able to adapt to market conditions. Indeed, we include forecasted demand, wind and solar power, actual generation from hydro, biomass, and waste, weighted imports, and traditional fossil fuels. The inclusion of these exogenous regressors, in both the conditional mean and variance equations, outperforms in point and, especially, in density forecasting when the superior set of models is considered. Indeed, using the model confidence set and considering northern Italian prices, predictions indicate the strong predictive power of regressors, in particular in an expert model augmented for GARCH-type time-varying volatility. Finally, we find that using professional and more timely predictions of consumption and renewable energy sources improves the forecast accuracy of electricity prices more than using predictions publicly available to researchers.

Applied Energy 310 Doi: https://doi.org/10.1016/j.apenergy.2021.118510

The ongoing transformation of the electricity market has reshaped the hydropower production paradigm for storage reservoir systems, with a shift from strategies oriented towards maximizing regional energy production to strategies aimed at the revenue maximization of individual systems. Indeed, hydropower producers bid their energy production scheduling 1 day in advance, attempting to align the operational plan with hours where the expected electricity prices are higher. As a result, the accuracy of 1-day ahead prices forecasts has started to play a key role in the short-term optimization of storage reservoir systems. This paper aims to contribute to the topic by presenting a comparative assessment of revenues provided by short-term optimizations driven by two econometric models. Both models are autoregressive time-adapting hourly forecasting models, which exploit the information provided by past values of electricity prices, with one model, referred to as Autoarimax, additionally considering exogenous variables related to electricity demand and production. The benefit of using the innovative Autoarimax model is exemplified in two selected hydropower systems with different storage capacities. The enhanced accuracy of electricity prices forecasting is not constant across the year due to the large uncertainties characterizing the electricity market. Our results also show that the adoption of Autoarimax leads to larger revenues with respect to the use of a standard model, increases that depend strongly on the hydropower system characteristics. Our results may be beneficial for hydropower companies to enhance the expected revenues from storage hydropower systems, especially those characterized by large storage capacity.

The North American journal of economics and finance 55 s. 1-12 Doi: https://doi.org/10.1016/j.najef.2020.101347

We study contagion between Real Estate Investment Trusts (REITs) and the equity market in the U.S. over four sub-samples covering January, 2003 to December, 2017, by using Bayesian nonparametric quantile-on-quantile (QQ) regressions with heteroskedasticity. We find that the spillovers from the REITs on to the equity market has varied over time and quantiles defining the states of these two markets across the four sub-samples, thus providing evidence of shift-contagion. Further, contagion from REITs upon the stock market went up during the global financial crisis particularly, and also over the period corresponding to the European sovereign debt crisis, relative to the pre-crisis period. Our main findings are robust to alternative model specifications of the benchmark Bayesian QQ model, especially when we control for omitted variable bias using the heteroskedastic error structure. Our results have important implications for various agents in the economy namely, academics, investors and policymakers.

Energy Economics 98 Doi: https://doi.org/10.1016/j.eneco.2021.105268

This paper focuses on forecasting quarterly nominal global energy prices of commodities, such as oil, gas and coal,using the Global VAR dataset proposed by Mohaddes and Raissi (2018). This dataset includes a number of poten-tially informative quarterly macroeconomic variables for the 33 largest economies, overall accounting for morethan 80% of the global GDP. To deal with the information on this large database, we apply dynamic factor modelsbased on a penalized maximum likelihood approach that allows to shrink parameters to zero and to estimatesparse factor loadings. The estimated latent factors show considerable sparsity and heterogeneity in the selectedloadings across variables. When the model is extended to predict energy commodity prices up to four periodsahead, results indicate larger predictability relative to the benchmark random walk model for 1-quarter aheadfor all energy commodities and up to 4 quarters ahead for gas prices. Our model also provides superior forecaststhan machine learning techniques, such as elastic net, LASSO and random forest, applied to the same database.

Journal of Econometrics 230(2) s. 1-18 Doi: https://doi.org/10.1016/j.jeconom.2021.04.004

This paper introduces a new dynamic panel model with multi-layer network effects. Series-specific latent Markov chain processes drive the dynamics of the observable processes, and several types of interaction effects among the hidden chains allow for various degrees of endogenous synchronization of both latent and observable processes. The interaction is driven by a multi-layer network with exogenous and endogenous connectivity layers. We provide some theoretical properties of the model, develop a Bayesian inference framework and an efficient Markov Chain Monte Carlo algorithm for estimating parameters, latent states, and endogenous network layers. An application to the US-state coincident indicators shows that the synchronization in the US economy is generated by network effects among the states. The inclusion of a multi-layer network provides a new tool for measuring the effects of the public policies that impact the connectivity between the US states, such as mobility restrictions or job support schemes. The proposed new model and the related inference are general and may find application in a wide spectrum of datasets where the extraction of endogenous interaction effects is relevant and of interest.

Canadian Journal of Economics Doi: https://doi.org/10.1111/caje.12442

International Journal of Forecasting 36(3) s. 974-986 Doi: https://doi.org/10.1016/j.ijforecast.2019.11.002

We compare alternative univariate versus multivariate models and frequentist versus Bayesian autoregressive and vector autoregressive specifications for hourly day-ahead electricity prices, both with and without renewable energy sources. The accuracy of point and density forecasts is inspected in four main European markets (Germany, Denmark, Italy, and Spain) characterized by different levels of renewable energy power generation. Our results show that the Bayesian vector autoregressive specifications with exogenous variables dominate other multivariate and univariate specifications in terms of both point forecasting and density forecasting.

Journal of Risk and Financial Management 13(11) Doi: https://doi.org/10.3390/jrfm13110257

Advances in Decision Sciences 24(2) s. 1-38 Doi: https://doi.org/10.47654/v24y2020i2p66-103

Factor models (FM) are now widely used for forecasting with large set of time series. Another class of models, which can be easily estimated and used in a large dimensional setting, is multivariate autoregressive models (MAR), where independent autoregressive processes are assumed for the series in the panel. When applied to big data, the estimation, model selection and combination of both models can be time consuming. We assume both FM and MAR models are misspecified and provide a scoring rule which can be evaluated on an initial training sample to either select or combine the models in forecasting exercises on the whole sample. Some numerical illustrations are provided both on simulated data and on well known large economic datasets. The empirical results show that the frequency of the true positive signals is larger when FM and MAR forecasting performances differ substantially and it decreases as the horizon increases

Journal of Risk and Financial Management 12(2) Doi: https://doi.org/10.3390/jrfm12020085

International Journal of Forecasting 35(2) s. 485-501 Doi: https://doi.org/10.1016/j.ijforecast.2018.09.005

This paper studies the predictability of cryptocurrency time series. We compare several alternative univariate and multivariate models for point and density forecasting of four of the most capitalized series: Bitcoin, Litecoin, Ripple and Ethereum. We apply a set of crypto-predictors and rely on dynamic model averaging to combine a large set of univariate dynamic linear models and several multivariate vector autoregressive models with different forms of time variation. We find statistically significant improvements in point forecasting when using combinations of univariate models, and in density forecasting when relying on the selection of multivariate models. Both schemes deliver sizable directional predictability.

Journal of Empirical Finance 53(September) s. 181-196 Doi: https://doi.org/10.1016/j.jempfin.2019.07.001

We explore the interplay between sovereign and bank credit risk in a setting where Danish authorities first let two Danish banks default and then left the country’s largest bank, Danske Bank, to recapitalize privately. We find that the correlation between bank and sovereign credit default swap (CDS) rates changed with these events. Following the non-bailout events, the sensitivity to external shocks, proxied by CDS rates on the European banking sector, declined both for Danske Bank and for Danish sovereign debt. After Danske Bank’s recapitalization, its exposure to the European banking sector reappeared while that did not happen for Danish sovereign debt. The decoupling between CDS rates on sovereign and private bank debt indicates that the vicious feedback loop between bank and sovereign risk weakened after the non-bailout policies were introduced.

The Economic Journal 129(617) s. 311-337 Doi: https://doi.org/10.1111/ecoj.12520

We estimate demand, supply, monetary, investment and financial shocks in a VAR identified with a minimum set of sign restrictions on US data. We find that financial shocks are major drivers of fluctuations in output, stock prices and investment but have a limited effect on inflation. In a second step, we disentangle shocks originating in the housing sector, shocks originating in credit markets and uncertainty shocks. In the extended set‐up, financial shocks are even more important and a leading role is played by housing shocks that have large and persistent effects on output.

Annals of Applied Statistics 12(4) s. 2559-2586 Doi: https://doi.org/10.1214/18-AOAS1168

Journal of the American Statistical Association Doi: https://doi.org/10.1080/01621459.2016.1273117

Journal of International Money and Finance 81 s. 242-264 Doi: https://doi.org/10.1016/j.jimonfin.2017.12.001

Journal of Financial Econometrics 16(1) s. 34-62 Doi: https://doi.org/10.1093/jjfinec/nbx023

Statistical Science 32(1) s. 106-127 Doi: https://doi.org/10.1214/16-STS588

In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations has unexpected and undesired effects, and is bound to discredit skillful forecasts when the signal-to-noise ratio in the data generating process is low. Conditioning on outcomes is incompatible with the theoretical assumptions of established forecast evaluation methods, thereby confronting forecasters with what we refer to as the forecaster’s dilemma. For probabilistic forecasts, proper weighted scoring rules have been proposed as decision-theoretically justifiable alternatives for forecast evaluation with an emphasis on extreme events. Using theoretical arguments, simulation experiments and a real data study on probabilistic forecasts of U.S. inflation and gross domestic product (GDP) growth, we illustrate and discuss the forecaster’s dilemma along with potential remedies.

Journal of business & economic statistics 35(3) s. 470-485 Doi: https://doi.org/10.1080/07350015.2015.1087856

Journal of business & economic statistics 35(1) s. 110-129 Doi: https://doi.org/10.1080/07350015.2015.1061436

International Journal of Forecasting 33(1) s. 153-173 Doi: https://doi.org/10.1016/j.ijforecast.2016.02.004

Journal of applied econometrics 31(7) s. 1352-1370 Doi: https://doi.org/10.1002/jae.2501

International Journal of Forecasting 32(2) s. 283-292 Doi: https://doi.org/10.1016/j.ijforecast.2015.06.006

Journal of Commodity Markets 2(1) s. 45-57 Doi: https://doi.org/10.1016/j.jcomm.2016.07.005

Journal of applied econometrics 31(7) s. 1312-1332 Doi: https://doi.org/10.1002/jae.2502

Journal of Statistical Software 68 Doi: https://doi.org/10.18637/jss.v068.i03

Journal of applied econometrics 30(4) s. 551-575 Doi: https://doi.org/10.1002/jae.2379

Studies in Nonlinear Dynamics & Econometrics 18(4) s. 367-381 Doi: https://doi.org/10.1515/snde-2012-0088

Journal of Empirical Finance 29 s. 304-315 Doi: https://doi.org/10.1016/j.jempfin.2014.08.006

International Journal of Forecasting 30(1) s. 65-77 Doi: https://doi.org/10.1016/j.ijforecast.2013.02.003

Journal of Econometrics 177(2) s. 213-232 Doi: https://doi.org/10.1016/j.jeconom.2013.04.009

We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several speci cations 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 misspeci ed. A Sequential Monte Carlo method is proposed to approximate the ltering and predictive densities. The combination approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of simulated data, US macroeconomic time series and surveys of stock market prices. 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. Also, substantial uncertainty appears in the weights when predictors are similar; residual uncertainty reduces when the model set is complete; and learning reduces this uncertainty. For the macro series we nd that incompleteness of the models is relatively large in the 70's, the beginning of the 80's and during the recent nancial crisis, and lower during the Great Moderation; the predicted probabilities of recession accurately compare with the NBER business cycle dating; model weights have substantial uncertainty attached. With respect to returns of the S&P 500 series, we nd 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. Information on the complete predictive distribution and not just on some moments turns out to be very important, above all during turbulent times such as the recent nancial crisis. More generally, the proposed distributional state space representation o ers a great exibility in combining densities.

Journal of Money, Credit and Banking 45(2-3) s. 449-463 Doi: https://doi.org/10.1111/jmcb.12009