Forecasting http://lists.repec.org/mailman/listinfo/nep-for Forecasting 2026-09-28 Entropic tilting of forecasts to SPF histograms: analytics & applications https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263284&r=&r=for We develop a direct approach to incorporating survey density forecasts into model-based predictive distributions. Histogram forecasts from the U.S. Survey of Professional Forecasters (SPF) carry rich nonparametric information about expected outcomes, but existing methods rely on moment-based approximations that discard part of it. We instead tilt entropically to the histogram probabilities themselves, matching them exactly. After reformulating the single-histogram problem, we derive a new analytic characterization of the multiple-histogram case, solved by Iterative Proportional Fitting and applicable to simulated densities from essentially any model. Applying the method to real-time forecasts from a Bayesian VAR with time-varying volatility, we find that tilting to SPF histograms substantially improves accuracy relative to the model’s baseline forecasts, especially during the Great Recession and the COVID-19 pandemic. The gains extend beyond the variables the SPF targets, improving forecasts for other variables in the system as well. JEL Classification: C11, C53, E37 Mertens, Elmar Clark, Todd E. Bayesian vector autoregression, iterative proportional fitting, predictive densities, relative entropy, survey expectations 2026-09 Stealing profits: Spread-based temporal hierarchy forecasting for day-ahead electricity markets https://d.repec.org/n?u=RePEc:arx:papers:2609.23223&r=&r=for Day-ahead electricity price forecasts support trading and storage decisions, but for battery arbitrage predicting intraday price spreads is more relevant than predicting individual hourly prices. Here we show that a temporal hierarchy forecasting (THieF) framework that jointly reconciles forecasts of hourly electricity prices and all intraday price spreads consistently improves performance across two major European electricity markets and three different forecasting architectures. Using five years of out-of-sample data from Germany and Spain, we obtain accuracy improvements of up to 19.7% and profit gains of up to 10.4% relative to unreconciled hourly price forecasts. The gains persist even for a highly accurate pretrained TabPFN foundation model. Our results demonstrate that exploiting coherent relationships between economically relevant forecasting targets can improve both predictive accuracy and decision value, and that better statistical forecasts do not necessarily imply better economic decisions. Arkadiusz Lipiecki Nikolaos Kourentzes Rafal Weron 2026-09 Beyond Point Forecasts: A Survey on Probabilistic Forecasting for Time Series and Spatiotemporal Data https://d.repec.org/n?u=RePEc:arx:papers:2609.13345&r=&r=for Probabilistic forecasting is central to decision-making under uncertainty, yet its methodological landscape has become increasingly fragmented across temporal and spatiotemporal forecasting, statistical modeling, machine learning, and deep generative modeling. This survey develops a unified perspective by organizing probabilistic forecasting methods according to where and how uncertainty is introduced into the forecasting pipeline. Our taxonomy connects model-agnostic approaches including ensembles and distribution-free calibration, with model-intrinsic approaches spanning Bayesian modeling, parametric predictive distributions, distributional regression, and modern generative models, and further examines the emerging role of time series foundation models. Beyond methodological synthesis, we identify the assumptions, computational demands, and forms of uncertainty represented by different paradigms, and translate these distinctions into data-driven and domain-specific guidance for method selection. We complement the survey with a cross-paradigm empirical study on univariate, multivariate, and spatiotemporal forecasting tasks. The results reveal that no single uncertainty-quantification paradigm dominates across settings. Calibration, sharpness, predictive accuracy, and computational efficiency can lead to substantially different model preferences, while expressive generative models and zero-shot foundation models exhibit markedly different accuracy-efficiency trade-offs. Lastly, we identify unresolved challenges surrounding uncertainty in evolving dependency structures, physics-informed predictive distributions, forecasting extreme events, handling count-valued, directional, and continuous-time series, and the development of unified software resources. Our survey provides both a conceptual framework and a practical roadmap for probabilistic forecasting research. Donia Besher Rajdeep Pathak Madhurima Panja Tanujit Chakraborty 2026-09 Revisiting the Rules-versus-Discretion Debate: Forecasting Evidence from the Bank of England, 1870-1913 https://d.repec.org/n?u=RePEc:arx:papers:2609.10544&r=&r=for Under the classical gold standard, historians have long debated what guided the Bank of England's adjustments to Bank Rate: whether policy followed a mechanical gold-standard rule or discretion when City or exchange conditions required it, and whether domestic money-market stability or external convertibility carried greater weight. This paper revisits those questions with a London-specific monthly panel, 1870-1913, jointly testing ten domestic and external indicators the Court watched when setting the published minimum rate. The findings fit neither a single frozen channel nor unstructured ad hoc policy. Instead, the Bank appears to have drawn repeatedly on a multivariate information set-trade settlement, gold movements, City asset prices, bill-market conditions, and episodic convertibility pressure-with state-dependent weights across subperiods. In the confirmatory specification, exports, gold flow, and industrial share prices carry the clearest joint forecasting content for changes in Bank Rate. Gold flow forecasts rate changes even when reserve stock does not, separating bullion settlement from balance-sheet position. Bill-market and convertibility pressures also carry incremental forecasting content in the multivariate specification, though their prominence depends on how domestic and external indicators are modeled together. The overall pattern is most consistent with systematic discretion under the classical gold standard. Xi Chen 2026-06 Real GDP Forecasts by International Organisations https://d.repec.org/n?u=RePEc:rba:rbardp:rdp2026-05&r=&r=for We study forecasts for real gross domestic product growth by international organisations. These forecasts influence policy decisions by international organisations and national governments, and receive significant attention from the private sector. First, we compare the accuracy of forecasters and test the rationality of forecasts using a large dataset of forecasts by four international organisations (the International Monetary Fund, the World Bank, the European Commission and the Organisation for Economic Co-operation and Development) and private-sector forecasts. Second, we derive a new decomposition of differences in forecast accuracy into contributions from disagreement and the accuracy of the average forecast. Finally, we present theoretical results and empirical evidence on two explanations for the rejection of forecast rationality: the use of conditioning assumptions and the practice of making modal forecasts. Martin McCarthy Umberto Collodel Prakash Loungani forecasting; expectations; real GDP growth; international organisations; international financial institutions 2026-09 Does it add up? Reconciling forecasts and impulse responses for hierarchical macroeconomic data https://d.repec.org/n?u=RePEc:zbw:rwirep:343573&r=&r=for This paper introduces a mixed-frequency Gaussian state-space framework that embeds forecast reconciliation into Bayesian VAR modeling for hierarchical macroeconomic data. Using precision-based sampling to generate high-frequency latent estimates, we construct a consistent proxy for the forecast-error covariance matrix, enabling optimal reconciliation with short datasets. We prove the symptotic convergence of this estimator and show that forecast reconciliation can be formally derived as a special case of conditional forecasting, allowing straightforward implementation with standard state-space algorithms. We derive reconciled impulse response functions that ensure bottom-level structural responses aggregate exactly to the top-level impulse response. Applying the framework to UK and German regional economic data, we demonstrate improvements in the forecast accuracy alongside structurally consistent impulse responses. Blagov, Boris Krause, Clara forecast reconciliation, regional forecasts, mixed-frequency, hierarchical impulse responses 2026 Match forecasts in UEFA club competitions: Elo ratings versus Transfermarkt valuations https://d.repec.org/n?u=RePEc:arx:papers:2609.21674&r=&r=for The pre-season strengths of European football clubs are usually measured by two proxies in the literature. Football Club Elo Ratings provide strictly performance-based Elo ratings from the early days of the European Cups, while Transfermarkt valuations are crowd-based estimates of squad market values. This paper compares them by evaluating their ability to forecast the results of matches played in the UEFA Champions League and the UEFA Europa League between the seasons 2020/21 and 2024/25. The two indicators yield almost identical out-of-sample accuracy when used separately. Combining the two measures leads to a modest improvement, but the best aggregation procedure is sensitive to the forecast target. Our results suggest that seeding based on Elo ratings would be (closely) optimal. Gergely Csurilla L\'aszl\'o Csat\'o 2026-09 Prediction Markets Beat the Weather Forecast on Tomorrow's High Temperature https://d.repec.org/n?u=RePEc:arx:papers:2609.23969&r=&r=for The sooner we receive information, and the more accurate it is, the better planning decisions we can make. Every day, prediction markets let anyone bet on tomorrow's high temperature in cities around the world, creating a market-implied forecast built on dispersed information. We use the past five years of market data from the Kalshi exchange for seven American cities to extract, hour by hour, the market-implied forecast. We use this forecast as a measuring instrument to see how much information about the temperature the market makes public before the public forecasting system does. We race it against the leading American and European weather forecasts. In six of the seven cities we study, the market beats the most accurate single public forecast, the National Blend of Models (NBM). Aggregating every city-day, at the end of the market's first hour of trading it beats the best single public product by about 10 percent in root-mean-square error, and holds its lead through the day, overnight, and into the target day. Looking at how the forecasts move over time, we find the National Blend travels four times further toward the market between its postings than the market travels toward the NBM. The market does not react to new weather forecast updates; instead, the forecast slowly publishes information that the market had already shared publicly. Alexander W. Crosier 2026-09 OrderFusion+: Probabilistic Buy--Sell Price Trajectory Forecasting in Intraday Electricity Markets https://d.repec.org/n?u=RePEc:arx:papers:2609.23598&r=&r=for Intraday electricity markets enable participants to adjust energy positions close to delivery, with price forecasts necessary to support trading and the scheduling of flexible electricity resources as well as increasingly responsive consumers. Forecasting model specifications have progressed from using macro-features, such as renewable generation and load, to the micro-features of continuous orderbooks. A recent advanced deep learning model, OrderFusion, explicitly models micro-level buy-sell orderbook interactions. However, despite its superior comparative forecasting performance, it considers only one delivery product at a time, ignoring neighboring-product information. Moreover, when forecasting aggregated price indices such as the liquid German ID3, ID2, and ID1 products, it omits the information contained in price trajectories. In contrast, pretrained time-series foundation models have shown success in financial, renewable-energy, and day-ahead electricity price forecasting. However, their performance on intraday orderbook data remains an open research question of considerable practical importance. In this paper, we propose OrderFusion+, an open-source deep learning model that combines historical orders from the target and neighboring delivery products to forecast probabilistic buy-sell price trajectories. We benchmark OrderFusion+ against forecasting baselines and pretrained foundation models, and investigate dynamic market conditions through the designed dynamic masking mechanism, revealing insights into market efficiency. The implementation and forecasts can be found at: https://runyao-yu.com/OrderFusion/ Runyao Yu Derek W. Bunn 2026-09 Forecasting Indian Core Inflation: Simple Made Simpler https://d.repec.org/n?u=RePEc:een:camaaa:2026-83&r=&r=for Managing rapid economic growth in India naturally brings into focus the role of inflation forecasts for monetary and fiscal policy making. We investigate whether any of a large set of forecasting models improves upon a univariate auto-regression in forecasting core consumer price inflation. Using a monthly panel of forty macroeconomic and financial indicators we estimate nine classes of models that range from an auto-regression to various factor models, quantile regressions and machine learning specifications. In doing so, we also account for inflation expectations and climate change variables. Our root mean square forecast error model comparison metric operates at horizons of one, three, six and twelve months. With respect to the conditional mean, no model produces a forecast error significantly below that of an auto-regression at any horizon over the full comparison sample. With respect to the conditional distribution, quantile regressions that include estimated factors reduce forecast loss relative to a specification without such factors at every quantile and horizon. Our approach is general enough to be applicable to forecasting core inflation in other emerging market economies. Rishabh Choudhary Chetan Dave Chetan Ghate inflation forecasting in EMEs, core inflation, diffusion index models, quantile regression, machine learning, inflation targeting 2026-09 Testing Whether Volatility Model Gains Persist: A Prespecified Holdout in Tail Risk Forecasting https://d.repec.org/n?u=RePEc:cte:wsrepe:50798&r=&r=for Rankings of volatility models often change with the market, the evaluation period, and the forecast criterion, so a gain found in one setting may not carry over to another. We test this directly. Eight volatility models, four observation-driven and four stochastic volatility, are estimated for five equity indices by data cloning and compared on one-step-ahead forecasts. We assess joint value-at-risk and expected shortfall accuracy, calibration, predictive density accuracy, and forecast availability. In 2018–2023, nominally significant gains cluster in DAX and NIKKEI, with weaker evidence in FTSE. Neither holdout comparison is corroborated: the DAX estimate changes sign, and the NIKKEI estimate keeps its direction but is imprecise. Different criteria also favour different models. The results argue for validating a model in its intended market and for the criterion it is meant to serve, and they show how a prespecified holdout in a later period can test whether an advantage persists. Guo, Honfei Marín Díazaraque, Juan Miguel Veiga, Helena Forecast evaluation ; Holdout validation ; Model comparison ; Stochastic volatility ; Tail risk forecasting ; Volatility asymmetry 2026-09-18 WaVeFuse: Regime-Adaptive Equity Index Forecasting via Channel-Wise Wavelet Denoising and Vertical Attention Fusion https://d.repec.org/n?u=RePEc:arx:papers:2609.14733&r=&r=for Hybrid Deep Learning for equity index forecasting is limited by three problems: propagation of OHLCV noise into derived technical indicators (TIs), channel-indiscriminate multi-scale decomposition that conflates heterogeneous frequency signatures, and static multi-branch fusion that cannot adapt to market regime shifts. WaVeFuse addresses these limitations through a unified dual-branch architecture. Symlet-4 wavelet denoising (level 2, MAD soft threshold) suppresses microstructure noise in OHLCV. Seven low-lag TIs computed from denoised prices are encoded by a causal channel-wise continuous wavelet transform (Morlet, 32 scales) into a per-timestep scale-space matrix. A CNN-BiLSTM branch captures temporal dynamics, while a dual-layer Transformer (heads=4, dk in {16, 32}) models inter-scale spectral dependencies, and their representations are integrated by a 2-token softmax gate Vertical Attention Fusion (VAF) that dynamically reweights branches as market regimes shift. Evaluated under walk-forward validation (WFV) on KOSPI, DAX, NYSE Composite, and Russell 2000 (2010-2023), WaVeFuse achieves R2 = 0.81-0.96 and directional accuracy 70.5-78.3%. It outperforms seven state-of-the-art models by 8.9-20.2% MAE across twelve dataset-period configurations. Diebold-Mariano statistics (4.62-10.38, p Aashish Bohra Vivek Vijay 2026-09 Market-Informed Networks for Modeling and Forecast Evaluation of Financial Extremes https://d.repec.org/n?u=RePEc:arx:papers:2609.11575&r=&r=for Modeling the joint distribution of extreme values in high-dimensional financial time series is challenging because extremes are sparse and locally extreme observations are not necessarily extreme relative to their full marginal distribution. To address this, we introduce a time-dependent network H\"usler-Reiss model in which market-informed adjacency matrices determine how strongly observations contribute to the estimation. We propose binary and weighted specifications, including the Joint Extremes Adjacency Matrix (JEAM) which combines information about individual extremeness with historical patterns of joint extreme movements. In the forecasting evaluation part, covering one-minute stock returns from three sectors of the S&P 100, JEAM achieves the best out-of-sample log scores for both tail directions; improving scores by 12.5-13.6% in the lower tail and 11.4-14.9% in the upper tail. The results show that incorporating market-informed network structures in the estimation, improves forecast evaluation of extremes across time series. Ayla Jungbluth Johannes Lederer Simon Trimborn 2026-09 The factors behind output gap revisions https://d.repec.org/n?u=RePEc:ecb:ecbops:2026399&r=&r=for Estimates of potential output and the output gap are widely used in monetary, fiscal and structural policy analysis, but they are unobservable and subject to substantial real-time uncertainty. This paper examines revisions to output gap and potential growth estimates produced by the European Commission, the Eurosystem, the International Monetary Fund (IMF) and the Organisation for Economic Co-operation and Development (OECD) for the euro area and its member countries. Using annual forecast vintages covering up to 20 euro area countries from 2002 to 2025 and a balanced panel of 11 countries from 2007 to 2025, the paper compares the reliability of estimates across institutions, decomposes output gap revisions into their main sources and estimates the impact of real GDP data revisions and forecast errors on potential growth revisions. The results show sizeable differences across institutions: European Commission estimates revise least in the balanced country sample, OECD estimates revise most, and Eurosystem estimates have become markedly more stable over the past decade. Output gap revisions are driven mainly by revisions to real GDP data and potential growth, while nowcast errors play a smaller role. Panel regressions show that both real GDP data revisions and medium-term forecast errors are significantly associated with revisions to potential growth, implying that revised or unexpected GDP developments are to some extent absorbed into estimates of potential growth. The findings highlight the uncertainty surrounding real-time output gap estimates and support the use of complementary indicators of economic slack. JEL Classification: E23, E27, E32, C53, C82 Szörfi, Béla data revisions, euro area, forecast errors, output gap, potential growth, potential output, real-time estimation 2026-09 CAST: A Cross-Asset State-Space Trading System for Drawdown Control in Stock Markets https://d.repec.org/n?u=RePEc:arx:papers:2609.14205&r=&r=for Managing drawdown, the peak-to-trough decline in an investment portfolio's value, is a precondition for long-term survival in practical investment management. However, mainstream stock forecasting methods predominantly optimize returns or Sharpe ratios under the independent and identically distributed (i.i.d.) assumption. Real markets do not follow this assumption, triggering catastrophic drawdowns. We propose a cross-asset state-space trading system (CAST), consisting of two components: The predictor, Cross-Asset Collaborative Kalman Filter (CoKF), estimates each asset's latent state online, coupling all assets through their correlations and adaptively fusing multiple integrated-random-walk orders. The controller, Model Predictive Control (MPC), converts the predictor's forecast into trades, using forecast uncertainty as an explicit risk penalty that controls drawdown. We evaluate CAST on four real-world stock markets over a 15-year test window and show that it consistently occupies the return-drawdown Pareto frontier, achieving strong risk-adjusted performance while maintaining substantially lower maximum drawdown than competitive baselines. A stress test across crisis periods further demonstrates robust behavior under market shocks and distribution shift. Because the predictor and controller interact only through the predicted price path, both are plug-and-play, making CAST a modular, interpretable trading system. The code is available at https://github.com/FanBroWell/CAST Yu Peng Matloob Khushi Josiah Poon 2026-09 VertiFuseX: Generalizable Financial Forecasting via Multi-Stream Temporal Fusion https://d.repec.org/n?u=RePEc:arx:papers:2609.12793&r=&r=for Stock price prediction remains challenging due to the non-stationary and noisy nature of financial time series. Existing deep learning models often rely on rigid decision-level fusion, ad hoc hyperparameter tuning, and compressed final-layer outputs, causing information loss, overfitting, and limited cross-market generalization. We propose VertiFuseX, a hybrid LSTM architecture using penultimate-layer vertical fusion of multi-scale temporal representations. VertiFuseX stacks and reweights penultimate features from LSTM, Bi-LSTM, and St-LSTM branches, integrates a parallel DNN stream, and jointly optimizes all components via backpropagation under a fixed hyperparameter configuration. This preserves richer intermediate temporal information across scales. Evaluated on 15 years (2010-2024) of closing prices from 10 global equity indices using strict chronological out-of-sample testing with the final 365 trading days held out, VertiFuseX achieves 30-54% MAPE reductions and over 40% improvements in MAE and RMSE versus LSTM-based baselines, and outperforms seven state-of-the-art models across 33 metric-dataset comparisons. Ablation studies confirm penultimate-layer fusion drives these gains over final-layer fusion and decision-level ensembling. Gradient-based saliency analysis shows consistent emphasis on mid-range dependencies at lags 9-15 days. Economic validation via algorithmic trading simulation under extreme market regimes shows reduced maximum drawdowns and superior risk-adjusted returns. With 675k parameters, a 2.6 MB memory footprint, and 1.5 ms/sample inference latency, VertiFuseX offers a lightweight, interpretable, deployment-ready framework for robust financial forecasting. Aashish Bohra Vivek Vijay 2026-09 Learn the measure, estimate the moment: machine-learned drivers in dynamic conditional correlation models https://d.repec.org/n?u=RePEc:cdf:wpaper:2026/12&r=&r=for Realized measures are biased for the moments of returns. We propose a two-step approach to forecasting large correlation matrices: machine-learned forecasts of realized measures enter a dynamic conditional correlation model as drivers, and their weights are estimated by quasi-maximum likelihood on returns. The correlation recursion is run in a matrix-logarithm parametrization, so every forecast is a valid correlation matrix. For Dow Jones stocks, a learned volatility driver and this recursion improve on a dynamic conditional correlation model with realized drivers at horizons of one, five and 22 days. For S&P 500 stocks, the model fits monthly returns better than machine-learned projections of realized correlations, has no invalid forecast in any month, and trades less. The criterion that selects the weight on a realized driver matters as much as the model, and practitioners can obtain valid forecasts calibrated to returns with standard software. Xu, Yongdeng DCC-GARCH-X; Realized measures; Covariance forecasting; Forecast evaluation; Positive definiteness; Log-correlation coordinates; Nonlinear shrinkage 2026-09 Leaky-integrator reconstruction: taming error accumulation in recursive differenced time-series forecasting https://d.repec.org/n?u=RePEc:arx:papers:2609.23378&r=&r=for We introduce leaky-integrator reconstruction, a training-free method that cures the error accumulation of recursive differenced forecasting. Our first contribution is diagnostic: predicting one-step changes and integrating them by cumulative summation, the standard remedy for non-stationarity, is a discrete integrator with a pole on the unit circle, and we show this makes recursive rollout of a nonlinear model diverge, its 336-step error reaching several times that of a well-behaved forecaster (normalised MAE 1.6-3.8 versus about 0.8) across every neural architecture tested. Our second, central contribution is the fix: move the pole inside the unit circle with a leaky integrator H(z) = 1/(1 - gamma z^-1), gamma Zijiang Yang 2026-09