Density Forecasts Research Articles

Intelligent crude oil price probability forecasting: Deep learning models and industry applications

The crude oil price has been subject to periodic fluctuations because of seasonal changes in industrial demand and supply, weather, natural disasters and global political unrest. An accurate forecast of crude oil prices is of utmost importance for decision makers and industry players in the energy sector. Despite this, the volatility of crude oil prices contributes to the uncertainty of the energy industry, which was particularly challenging following the recent global spread of the COVID-19 epidemic and the Russia–Ukraine conflict. This paper proposes a hybrid deep learning (DL) modelling framework to deal with the volatility of crude oil prices, applying ensemble empirical mode decomposition (EEMD), convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) integrated with quantile regression (QR); named EEMD-CNN-BiLSTM-QR. Two real-world datasets on crude oil prices from the West Texas Intermediate and Brent Crude Oil markets were employed to validate the EEMD-CNN-BiLSTM-QR hybrid modelling framework. Given that the probability density forecast can capture uncertainty, an in-depth analysis was carried out and prediction accuracy calculated. The findings of this study demonstrate that the proposed EEMD-CNN-BiLSTM-QR DL modelling framework, which uses the probability density forecast method, is superior to other tested models in terms of its ability to forecast crude oil prices. The novelty of this study stems mainly from its use of QR, which allows for the description of the conditional distribution of predicted variables and the extraction of more uncertain information for probability density forecasts.

Species discrimination of β-phenylethylamine, NaCl and NaOH based on Ultraviolet spectroscopy and principal component analysis combined with improved clustering by fast search and find of density peaks algorithm

This paper aimed at putting forward an approach integrating the improved clustering by fast search and find of density peaks (I-CFSFDP) algorithm with Ultraviolet (UV) spectroscopy for identifying the species of NaCl, NaOH, β-phenylethylamine(PEA) and their mixtures. For solving the issue that the clustering precision of the CFSFDP algorithm relies on the density forecast of the dataset and the manually selection of the truncated distance dc. The idea of kernel density forecast was adopted to the I-CFSFDP algorithm. The I-CFSFDP algorithm can observe the clusters of arbitrary shapes and use an adaptive method to evaluate the truncated distance dc, thereby generating more accurate clusters and identifying the core points in the clusters effectively. The dimensions of the UV spectra was reduced with principal component analysis (PCA), and the results of PCA were invoked as the input of the I-CFSFDP algorithm. Meanwhile, the effect of PCA-I-CFSFDP was evaluated by recall, accuracy, F-Score and precision. Besides, the DBSCAN and PCA-CFSFDP algorithms were used to compare with the PCA-I-CFSFDP algorithm. All of the classification outcomes displayed that the PCA-I-CFSFDP algorithm has better performance than the DBSCAN and PCA-CFSFDP algorithms. Therefore, the PCA-I-CFSFDP algorithm integrated with UV spectroscopy is a simple, quick and credible identification approach for detecting PEA, NaCl, NaOH and the mixtures.

Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?

Extensions of the stochastic volatility (SV) model focus on improving volatility inference or modeling higher moments of the return distribution. This study investigates which extension can better improve return density forecasts. By examining various specifications with S&P 500 daily returns for nearly 20 years, we find that a more accurate capture of volatility dynamics with realized volatility and implied volatility is more important than modeling higher moments for a conventional SV model in terms of both density and tail forecasts. The accuracy of volatility estimation and forecasts should be the precondition for higher moment extensions.

On the forecasting performance of small-scale DGSE models: a Monte Carlo evaluation and an application to UK

This article investigates the forecasting performance of a new small-scale dynamic stochastic general equilibrium (DSGE) model. To this end, this article first conducts a Monte Carlo study for the evaluation of the new model against another DSGE model , a standard vector autoregression (VAR), and a Bayesian VAR, using root mean square error and directional accuracy measures. An empirical application to UK quarterly data of output gap, inflation, and interest rates over the period 1986–2019 is also carried out for point and density forecasts. The empirical findings unveil a better performance of the new model for directional accuracy than for root mean square error, while density forecasts indicate no statistical differences among the new model and the VAR models.

Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

Abstract The COVID-19 pandemic has led to enormous data movements that strongly affect parameters and forecasts from standard Bayesian vector autoregressions (BVARs). To address these issues, we propose BVAR models with outlier-augmented stochastic volatility (SV) that combine transitory and persistent changes in volatility. The resulting density forecasts are much less sensitive to outliers in the data than standard BVARs. Predictive Bayes factors indicate that our outlier-augmented SV model provides the best fit for the pandemic period, as well as for earlier subsamples of high volatility. In historical forecasting, outlier-augmented SV schemes fare at least as well as a conventional SV model.

Testing for differences in survey‐based density expectations: A compositional data approach

SummaryWe propose to treat survey‐based density expectations as compositional data when testing either for heterogeneity in density forecasts across different groups of agents or for changes over time. Monte Carlo simulations show that the proposed test has more power relative to both a bootstrap approach based on the KLIC and an approach that involves multiple testing for differences of individual parts of the density. In addition, the test is computationally much faster than the KLIC‐based one, which relies on simulations, and allows for comparisons across multiple groups. Using density expectations from the ECB Survey of Professional Forecasters and the US Survey of Consumer Expectations, we show the usefulness of the test in detecting possible changes in density expectations over time and across different types of forecasters.

Distribution‐Based Model Evaluation and Diagnostics: Elicitability, Propriety, and Scoring Rules for Hydrograph Functionals

AbstractDistribution forecasts P over future quantities or events are routinely made in hydrology but usually traded for a (likelihood‐weighted) mean or median prediction to accommodate error measures or scoring functions such as the mean absolute error or mean squared error. Case in point is the so‐called KG efficiency (KGE) of Gupta et al. (2009, https://doi.org/10.1016/j.jhydrol.2009.08.003) and improvements thereof (Lamontagne et al., 2020, https://doi.org/10.1029/2020wr027101), which have rapidly gained popularity among hydrologists as alternative scoring functions to the commonly used Nash and Sutcliffe (1970, https://doi.org/10.1016/0022‐1694(70)90255‐6) efficiency, but are equally exclusive in how they quantify model performance using only single‐valued output of the quantities of interest. This point‐valued mapping necessarily implies a loss of information about model performance. This paper advocates the use of probabilistic watershed model training, evaluation and diagnostics. Distribution evaluation opens a mature literature on scoring rules whose strong statistical underpinning provides, as we will demonstrate, the theory, context and guidelines necessary for the development of robust information‐theoretically principled metrics for watershed signatures. These so‐called hydrograph functionals are scalar‐valued mappings of major behavioral watershed functions embodied in a strictly proper scoring rule. We discuss past developments that led to the current state‐of‐the‐art of distribution evaluation in hydrology and review scoring rules for dichotomous and categorical events, quantiles (intervals) and density forecasts. We are particularly concerned with elicitable functionals and scoring rule propriety, discuss the decomposition of scoring rules into a sharpness, reliability and entropy term and present diagnostically appealing strictly proper divergence scores of hydrograph functionals for flood frequency analysis, flow duration and recession curves. The usefulness and power of distribution‐based model evaluation and diagnostics by means of scoring rules is demonstrated on simple illustrative problems and discharge distributions simulated with watershed models using random sampling and Bayesian model averaging. The presented theory (a) enables a more complete evaluation of distribution forecasts, (b) offers a statistically principled means for watershed model training, evaluation, diagnostics and selection using hydrograph functionals and/or extreme events and (c) provides a universal framework for metric development of watershed signatures, promoting metric standardization and reproducibility.

The tail risk of crude oil Price_Based on EPU and geopolitical risk perspective

This study investigates the conditional prediction of crude oil price growth rates as a function of geopolitical risk (GPR) and economic policy uncertainty (EPU), characterizing the extreme tail risk characteristics. Utilizing monthly data on crude oil futures price growth rates from 1997 Jan to 2022 Dec, we employ Quantile Regression and Growth at Risk models to capture the heterogeneous and asymmetric effects of GPR and EPU across different quantiles of the oil price distribution. The sample period covers major geopolitical events, economic recessions, and the emergence of new energy sources, providing a comprehensive view of the factors influencing crude oil market dynamics.The empirical findings reveal significant asymmetries in the forecast density function of crude oil price growth rates, with periodic right-skewed deviations during financial crises and epidemic situations, and prevalent left-skewed deviations during the remaining sample periods. The impact of EPU on crude oil prices is found to be more pronounced in the short to medium term, while the influence of GPR persists over a longer duration, exacerbating the upside risk of price growth. The study highlights the effectiveness of EPU and GPR in capturing the tail characteristics of crude oil price growth, offering valuable risk identification indicators for policymakers and market participants.Furthermore, the analysis uncovers the heterogeneous effects of EPU and GPR across different quantiles of the oil price distribution. The results indicate that the relationship between these uncertainty measures and crude oil prices varies depending on the market conditions and the specific quantile examined. This finding underscores the importance of considering the entire distribution of crude oil prices rather than focusing solely on the conditional mean.The study contributes to the existing literature by providing a comprehensive examination of the role of geopolitical risk and economic policy uncertainty in driving crude oil price dynamics, with a particular focus on tail risks. The findings have important implications for risk management strategies in the energy sector.By employing advanced econometric techniques and considering a wide range of geopolitical and economic factors, this study offers new insights into the complex and evolving nature of crude oil price dynamics. The results highlight the need for policymakers and market participants to consider the asymmetric and heterogeneous effects of uncertainty measures when assessing the risks and opportunities in the crude oil market.

Seasonal forecasting of Bactrocera dorsalis Hendel, 1912 (Diptera: Tephritidae) in bioclimatic zones of Sri Lanka using the SARIMA model

Bactrocera dorsalis Hendel is a severe fruit pest that causes significant economic losses globally. Despite B. dorsalis having been distributed mostly across Asia, studies on its current and future density variation in Sri Lanka are sparse to date. The present study was thus carried out to assess the contemporary density variation (2020–2022) and future density fluctuation (2023–2025) of B. dorsalis in bioclimatic zones of Sri Lanka. The density was assessed using the monthly-based fruit fly trap collection method from randomly selected 40 locations in all bioclimatic zones (wet, intermediate, dry, and arid). The SARIMA modelling technique was applied for delineating the best-fit model and for density forecasting in each bioclimatic zone. The density variations were depicted for the year and for the bioclimatic zone (2020–2025) by colour intensity maps using QGIS. According to the findings, B. dorsalis shows a seasonal component to its year-round density variation and an ascending trend in its density from 2020 to 2025. Density forecasting records a 20%, 30%, 26%, and 37% density increase in the wet, intermediate, dry, and arid zones, respectively, in 2025. In 2025, the highest predicted B. dorsalis density from the arid zone and the lowest predicted density from the wet zone were recorded. This study contains the first forecasting attempt for B. dorsalis density using the SARIMA approach as well as the application of colour-intensity depiction for its density variation in Sri Lanka, which leads decision makers and stakeholders in economic agriculture to plan the scientific management of B. dorsalis to avoid its current and potential future threat to the country’s fruit industry.

Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics

SummaryQuantile regression methods are increasingly used to forecast tail risks and uncertainties in macroeconomic outcomes. This paper reconsiders how to construct predictive densities from quantile regressions. We compare a popular two‐step approach that fits a specific parametric density to the quantile forecasts with a nonparametric alternative that lets the “data speak.” Simulation evidence and an application revisiting GDP growth uncertainties in the United States demonstrate the flexibility of the nonparametric approach when constructing density forecasts from both frequentist and Bayesian quantile regressions. They identify its ability to unmask deviations from symmetrical and unimodal densities. The dominant macroeconomic narrative becomes one of the evolution, over the business cycle, of multimodalities rather than asymmetries in the predictive distribution of GDP growth when conditioned on financial conditions.

Spanish GDP short-term point and density forecasting using a mixed-frequency dynamic factor model

AbstractWe have assessed the effect of data releases when constructing short-term point and density forecasts of the Spanish gross domestic product growth. For this purpose, we considered a real-forecasting exercise in which we defined several pseudo-data vintages that had a mixture of monthly and quarterly frequencies and were unbalanced towards the end of the sample. We implemented a mixed-frequency dynamic factor model to deal with data features and to produce gross domestic product forecasts. We evaluated the predictive content of data releases from point and density forecast perspectives, the latter aspect of the analysis being previously unexplored in the literature producing Spanish gross domestic product short-term forecasts. We observed significant improvements in point forecasts as information is released throughout the quarter, confirming existing results. Additionally, our findings indicated substantial enhancements in the accuracy of density forecasts as new data releases materialized.

Evaluating Density Forecasts Using Weighted Multivariate Scores in a Risk Management Context

AbstractScoring rules are commonly applied to assess the accuracy of density forecasts in both univariate and multivariate settings. In a financial risk management context, we are mostly interested in a particular region of the density: the (left) tail of a portfolio’s return distribution. The dependence structure between returns on different assets (associated with a given portfolio) is usually time-varying and asymmetric. In this paper, we conduct a simulation study to compare the discrimination ability between the well-established scores and their threshold-weighted versions with selected regions. This facilitates a comprehensive comparison of the performance of scoring rules in different settings. Our empirical applications also confirm the importance of weighted-threshold scores for accurate estimates of Value-at-risk and related measures of downside risk.

Expectation formation and the Phillips curve revisited

Abstract This paper studies expectation formation of professional forecasters in the context of the Phillips curve. We assess whether professionals form their expectations regarding inflation and unemployment consistent with the Phillips curve based on individual forecast data taken from the ECB Survey of Professional Forecasters. We consider expectations over different horizons and do not restrict the analysis to point forecasts but we also take the information inherent in density forecasts into account. We explicitly consider the role of anchoring of inflation expectations as potential source of nonlinearity, and we also assess whether the Phillips curve relation translates to a link between uncertainty regarding inflation and unemployment. Our findings show that professionals tend to build their expectations in line with the Phillips curve but this is only observed for expectations made for shorter horizons. For longer horizons, the Phillips curve connection is much weaker. This relationship also depends on the degree of anchoring and results in a connection between uncertainty regarding future inflation and unemployment.

Penalized Bayesian Approach-Based Variable Selection for Economic Forecasting

This paper proposes a penalized Bayesian computational algorithm as an improvement to the LASSO approach for economic forecasting in multivariate time series. Methodologically, a weighted variable selection procedure is involved in handling high-dimensional and highly correlated data, reduce the dimensionality of the model and parameter space, and then select a promising subset of predictors affecting the outcomes. It is weighted because of two auxiliary penalty terms involved in prior specifications and posterior distributions. The empirical example addresses the issue of pandemic disease prediction and the effects on economic development. It builds on a large set of European and non-European regions to also investigate cross-unit heterogeneity and interdependency. According to the estimation results, density forecasts are conducted to highlight how the promising subset of covariates would help to predict potential contagion due to pandemic diseases. Policy issues are also discussed.

Density forecast combinations: The real‐time dimension

AbstractEuro area real‐time density forecasts from three dynamic stochastic general equilibrium (DSGE) and three Bayesian vector autoregression (BVAR) models are compared with six combination methods over the sample 2001Q1–2019Q4. The terms information and observation lag are introduced to distinguish time shifts between data vintages and actuals used to compute model weights and compare the forecast, respectively. Bounds for finite mixture combinations are presented, allowing for benchmarking them given the models. Empirically, combinations with limited weight variation often improve upon the individual models for the output and the joint forecasts with inflation. This reflects overconfident BVAR forecasts before the Great Recession. For inflation, a BVAR model typically performs best.

Reprint of: When will Arctic sea ice disappear? Projections of area, extent, thickness, and volume

Rapidly diminishing Arctic summer sea ice is a strong signal of the pace of global climate change. We provide point, interval, and density forecasts for four measures of Arctic sea ice: area, extent, thickness, and volume. Importantly, we enforce the joint constraint that these measures must simultaneously arrive at an ice-free Arctic. We apply this constrained joint forecast procedure to models relating sea ice to atmospheric carbon dioxide concentration and models relating sea ice directly to time. The resulting “carbon-trend” and “time-trend” projections are mutually consistent and predict a nearly ice-free summer Arctic Ocean by the mid-2030s with an 80% probability. Moreover, the carbon-trend projections show that global adoption of a lower carbon path would likely delay the arrival of a seasonally ice-free Arctic by only a few years.

Using Density Forecast for Growth-at-Risk to Improve Mean Forecast of GDP Growth in Korea

Using Density Forecast for Growth-at-Risk to Improve Mean Forecast of GDP Growth in Korea

Forecasts with Bayesian vector autoregressions under real time conditions

AbstractThis paper investigates the sensitivity of forecast performance metrics to taking a real time versus pseudo out‐of‐sample perspective. I use monthly vintages of two popular datasets for the United States and the euro area. Variants of vector autoregressions, varying the size of the information sets and the conditional mean and variance specification, are considered. The results suggest differences in the relative ordering of model performance for point and density forecasts depending on the forecast simulation design used to evaluate predictive accuracy. Differentials are more pronounced for the European dataset, and stochastic volatility is a particularly attractive model feature to obtain accurate forecasts in real time.

Uncertainty of household inflation expectations: Reconciling point and density forecasts

We examine measures of uncertainty of household inflation expectations derived from matched point and density forecasts that are “reconciled”, where the mean (or the median) of the densities are matched to the point forecasts using exponential tilting.

From Fixed‐Event to Fixed‐Horizon Density Forecasts: Obtaining Measures of Multihorizon Uncertainty from Survey Density Forecasts

AbstractThe U.S. Survey of Professional Forecasters produces precise and timely point forecasts for key macro‐economic variables. However, the accompanying density forecasts are mostly conducted for “fixed events.” For example, in each quarter, panelists predict output growth and inflation for the current calendar year and the next, hence the forecast horizon changes with each survey round. This limits the forecasts' usefulness to policymakers, researchers, and market participants. We propose a density combination approach that weights fixed‐event density forecasts, aiming at obtaining a correctly calibrated fixed‐horizon density forecast. We show that our method produces competitive density forecasts relative to widely used alternatives.