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on Forecasting |
| By: | Runze Li; Rui Zhou; David Pitt |
| Abstract: | High-frequency death counts are now widely available and contain timely information about intra-year mortality dynamics, but most stochastic mortality models are still estimated on annual data and therefore update only when annual totals are released. We propose a mixed-frequency state-space (MF--SS) extension of the Lee--Carter framework that jointly uses annual mortality rates and monthly death counts. The two series are linked through a shared latent monthly mortality factor, with the annual period factor defined as the intra-year average of the monthly factors. The latent monthly factor follows a seasonal ARIMA process, and parameters are estimated by maximum likelihood using an EM algorithm with Kalman filtering and smoothing. This setup enables real-time intra-year updates of the latent state and forecasts as new monthly observations arrive without re-estimating model parameters. Using U.S. data for ages 20--90 over 1999--2019, we evaluate intra-year annual nowcasts and one- to five-year-ahead forecasts. The MF--SS model produces both a direct annual forecast and an annual forecast implied by aggregating monthly projections. In our application, the aggregated monthly forecast is typically more accurate. Incorporating monthly information substantially improves intra-year annual nowcasts, especially after the first few months of the year. As a benchmark, we also fit separate annual and monthly Lee--Carter models and combine their forecasts using temporal reconciliation. Reconciliation improves these independent forecasts but adds little to MF--SS forecasts, consistent with MF--SS pooling information across frequencies during estimation. The MF--SS aggregated monthly forecasts generally outperform both unreconciled and temporally reconciled Lee--Carter forecasts and produce more cautious predictive intervals than the reconciled Lee--Carter approach. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.05702 |
| By: | Sahaj Raj Malla; Shreeyash Kayastha; Rumi Suwal; Harish Chandra Bhandari; Rajendra Adhikari |
| Abstract: | This study develops a robust machine learning framework for one-step-ahead forecasting of daily log-returns in the Nepal Stock Exchange (NEPSE) Index using the XGBoost regressor. A comprehensive feature set is engineered, including lagged log-returns (up to 30 days) and established technical indicators such as short- and medium-term rolling volatility measures and the 14-period Relative Strength Index. Hyperparameter optimization is performed using Optuna with time-series cross-validation on the initial training segment. Out-of-sample performance is rigorously assessed via walk-forward validation under both expanding and fixed-length rolling window schemes across multiple lag configurations, simulating real-world deployment and avoiding lookahead bias. Predictive accuracy is evaluated using root mean squared error, mean absolute error, coefficient of determination (R-squared), and directional accuracy on both log-returns and reconstructed closing prices. Empirical results show that the optimal configuration, an expanding window with 20 lags, outperforms tuned ARIMA and Ridge regression benchmarks, achieving the lowest log-return RMSE (0.013450) and MAE (0.009814) alongside a directional accuracy of 65.15%. While the R-squared remains modest, consistent with the noisy nature of financial returns, primary emphasis is placed on relative error reduction and directional prediction. Feature importance analysis and visual inspection further enhance interpretability. These findings demonstrate the effectiveness of gradient boosting ensembles in modeling nonlinear dynamics in volatile emerging market time series and establish a reproducible benchmark for NEPSE Index forecasting. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.08896 |
| By: | Arundeep Chinta; Lucas Vinh Tran; Jay Katukuri |
| Abstract: | Time Series Foundation Models (TSFMs) have emerged as a promising approach for zero-shot financial forecasting, demonstrating strong transferability and data efficiency gains. However, their adoption in financial applications is hindered by fundamental limitations in uncertainty quantification: current approaches either rely on restrictive distributional assumptions, conflate different sources of uncertainty, or lack principled calibration mechanisms. While recent TSFMs employ sophisticated techniques such as mixture models, Student's t-distributions, or conformal prediction, they fail to address the core challenge of providing theoretically-grounded uncertainty decomposition. For the very first time, we present a novel transformer-based probabilistic framework, ProbFM (probabilistic foundation model), that leverages Deep Evidential Regression (DER) to provide principled uncertainty quantification with explicit epistemic-aleatoric decomposition. Unlike existing approaches that pre-specify distributional forms or require sampling-based inference, ProbFM learns optimal uncertainty representations through higher-order evidence learning while maintaining single-pass computational efficiency. To rigorously evaluate the core DER uncertainty quantification approach independent of architectural complexity, we conduct an extensive controlled comparison study using a consistent LSTM architecture across five probabilistic methods: DER, Gaussian NLL, Student's-t NLL, Quantile Loss, and Conformal Prediction. Evaluation on cryptocurrency return forecasting demonstrates that DER maintains competitive forecasting accuracy while providing explicit epistemic-aleatoric uncertainty decomposition. This work establishes both an extensible framework for principled uncertainty quantification in foundation models and empirical evidence for DER's effectiveness in financial applications. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.10591 |
| By: | Anna Perekhodko; Robert \'Slepaczuk |
| Abstract: | Accurate volatility forecasting is essential in banking, investment, and risk management, because expectations about future market movements directly influence current decisions. This study proposes a hybrid modelling framework that integrates a Stochastic Volatility model with a Long Short Term Memory neural network. The SV model improves statistical precision and captures latent volatility dynamics, especially in response to unforeseen events, while the LSTM network enhances the model's ability to detect complex nonlinear patterns in financial time series. The forecasting is conducted using daily data from the S and P 500 index, covering the period from January 1 1998 to December 31 2024. A rolling window approach is employed to train the model and generate one step ahead volatility forecasts. The performance of the hybrid SV-LSTM model is evaluated through both statistical testing and investment simulations. The results show that the hybrid approach outperforms both the standalone SV and LSTM models and contributes to the development of volatility modelling techniques, providing a foundation for improving risk assessment and strategic investment planning in the context of the S and P 500. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.12250 |
| By: | Verona, Fabio |
| Abstract: | Inflation dynamics reflect forces operating at different cycles, from short-lived shocks to longterm structural trends. We introduce the sum-of-the-cycles (SOC) method, which exploits this multifrequency structure of inflation for forecasting. SOC decomposes inflation into cyclical components, applies forecasting models suited to their persistence, and recombines them into an aggregate forecast. Across U.S. inflation measures and horizons, SOC consistently outperforms leading time-series benchmarks, reducing forecast errors by about 25 percent at short horizons and nearly 50 percent at long horizons. During the 2020-21 inflation surge, when many models - including advanced machine-learning methods - struggled, SOC retained strong performance by incorporating shortage indicators. Beyond accuracy, SOC enhances interpretability: financial variables dominate high- and business-cycle frequencies, Phillips Curve models are most informative at medium frequencies, and factor-based methods, forecast combinations, and shortage indices prevail at low frequencies. This combination of accuracy and transparency makes SOC a practical complement to existing tools for inflation forecasting and policy analysis. |
| Keywords: | inflation forecasting, frequency decomposition, cycles, forecast combination, shortage indicators, Phillips curve, macro-finance |
| JEL: | C22 C53 E31 E32 E37 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:bofrdp:335013 |
| By: | Chellai, Fatih |
| Abstract: | Forecast accuracy evaluation is a cornerstone in fields as diverse as finance, public health, energy, and meteorology. However, traditional reliance on single-error metrics—such as MAE, RMSE, or MAPE—offers only a fragmented view of a model’s performance, often obscuring critical dimensions like systematic bias, volatility, directional behavior, or shape fidelity. To overcome these limitations, this study proposes the Unified Forecast Accuracy Index (UFAI), a multidimensional and composite metric that consolidates several facets of forecasting quality into a single, interpretable score. UFAI integrates four normalized sub-indices—bias, variance, directional accuracy, and shape preservation—each capturing a distinct performance characteristic. The framework accommodates multiple weighting schemes: equal weighting for simplicity, expert-informed weighting to reflect domain-specific priorities, and data-driven weighting based on statistical principles such as Principal Component Analysis and entropy measures. This flexibility enables users to adapt the index to diverse forecasting objectives and application contexts. The article details the mathematical formulation of each sub-index, discusses the theoretical soundness and practical implications of different weighting strategies, and demonstrates the utility of UFAI through comparative model evaluations. Emphasis is placed on the index’s normalization, interpretability, robustness to outliers, and extensibility to future use cases such as multi-horizon and probabilistic forecasts. By offering a more integrated and context-aware assessment tool, the UFAI marks a significant advancement in forecast evaluation methodology, supporting more reliable model selection and ultimately enhancing decision-making in data-driven environments. |
| Keywords: | Forecast evaluation, Unified forecast accuracy index, Composite metrics, Model comparison |
| JEL: | C1 C2 C4 |
| Date: | 2025–12–23 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:127449 |
| By: | Giovanni Ballarin; Lyudmila Grigoryeva; Yui Ching Li |
| Abstract: | Model combination is a powerful approach for achieving superior performance compared to selecting a single model. We study both theoretically and empirically the effectiveness of ensembles of Multi-Frequency Echo State Networks (MFESNs), which have been shown to achieve state-of-the-art macroeconomic time series forecasting results (Ballarin et al., 2024a). The Hedge and Follow-the-Leader schemes are discussed, and their online learning guarantees are extended to settings with dependent data. In empirical applications, the proposed Ensemble Echo State Networks demonstrate significantly improved predictive performance relative to individual MFESN models. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.13642 |
| By: | Kyriakopoulou, Dimitra |
| Abstract: | We propose a ridge-regularized Factor-Augmented Vector Autoregression (FAVAR) for forecasting macro–fiscal systems in data-rich environments where the cross-sectional dimension is large relative to the available sample. The framework combines principal-component factor extraction with a shrinkage-based VAR for the joint dynamics of observed macro–fiscal variables and latent components. Applying the model to Greece, we show that the extracted factors capture meaningful real and nominal structures, while the ridge-regularized VAR delivers stable impulse responses and coherent short- and medium-term dynamics for variables central to the sovereign debt identity. A recursive out-of-sample evaluation indicates that the ridge-FAVAR systematically improves medium-term forecasting accuracy relative to standard AR benchmarks, particularly for real GDP growth and the interest–growth differential. The results highlight the usefulness of shrinkage-augmented factor models for macro–fiscal forecasting and motivate further econometric work on regularized state-space and structural factor VARs. |
| Keywords: | FAVAR, Ridge Regression, Forecasting, High-Dimensional Data, Fiscal Policy, Debt Dynamics, Macro–Fiscal Modelling |
| JEL: | C32 C38 C53 C55 E62 H63 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:127158 |
| By: | Sayed Akif Hussain; Chen Qiu-shi; Syed Amer Hussain; Syed Atif Hussain; Asma Komal; Muhammad Imran Khalid |
| Abstract: | This study proposes a novel hybrid deep learning framework that integrates a Large Language Model (LLM) with a Transformer architecture for stock price forecasting. The research addresses a critical theoretical gap in existing approaches that empirically combine textual and numerical data without a formal understanding of their interaction mechanisms. We conceptualise a prompt-based LLM as a mathematically defined signal generator, capable of extracting directional market sentiment and an associated confidence score from financial news. These signals are then dynamically fused with structured historical price features through a noise-robust gating mechanism, enabling the Transformer to adaptively weigh semantic and quantitative information. Empirical evaluations demonstrate that the proposed Hybrid LLM-Transformer model significantly outperforms a Vanilla Transformer baseline, reducing the Root Mean Squared Error (RMSE) by 5.28% (p = 0.003). Moreover, ablation and robustness analyses confirm the model's stability under noisy conditions and its capacity to maintain interpretability through confidence-weighted attention. The findings provide both theoretical and empirical support for a paradigm shift from empirical observation to formalised modelling of LLM-Transformer interactions, paving the way toward explainable, noise-resilient, and semantically enriched financial forecasting systems. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.02878 |
| By: | Chu-An Liu; Andrey L. Vasnev |
| Abstract: | This paper proposes corrected forecast combinations when the original combined forecast errors are serially dependent. Motivated by the classic Bates and Granger (1969) example, we show that combined forecast errors can be strongly autocorrelated and that a simple correction--adding a fraction of the previous combined error to the next-period combined forecast--can deliver sizable improvements in forecast accuracy, often exceeding the original gains from combining. We formalize the approach within the conditional risk framework of Gibbs and Vasnev (2024), in which the combined error decomposes into a predictable component (measurable at the forecast origin) and an innovation. We then link this correction to efficient estimation of combination weights under time-series dependence via GLS, allowing joint estimation of weights and an error-covariance structure. Using the U.S. Survey of Professional Forecasters for major macroeconomic indices across various subsamples (including pre and post-2000, GFC, and COVID), we find that a parsimonious correction of the mean forecast with a coefficient around 0.5 is a robust starting point and often yields material improvements in forecast accuracy. For optimal-weight forecasts, the correction substantially mitigates the forecast combination puzzle by turning poorly performing out-of-sample optimal-weight combinations into competitive forecasts. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.09999 |
| By: | Nuno Silva |
| Abstract: | This paper asks how best to estimate and forecast firms’ residualized sales growth volatility, a standard measure of idiosyncratic uncertainty. Using a comprehensive dataset of Portuguese firms from 2006 to 2022, I compare the most common approaches used in the literature with a novel quantile-based method that exploits past cross-sectional information and contemporaneous macroeconomic variables and adjusts for the predictability in sales growth rates. I then estimate forecasting models and conduct a simulation exercise to assess the in-sample and out-of-sample performance of all approaches. The paper contributes to the literature by showing that quantile-based estimates and forecasts outperform traditional methods and that sales growth volatility can be measured with reasonable precision, making it suitable for wider application in empirical work. These findings support the application of quantile-based volatility measures to other low-frequency economic variables, especially those characterized by fat-tailed distributions. |
| JEL: | C53 D22 G30 L25 G32 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ptu:wpaper:w202525 |
| By: | Gongao Zhang; Haijiang Zeng; Lu Jiang |
| Abstract: | Financial institutions and regulators require systems that integrate heterogeneous data to assess risks from stock fluctuations to systemic vulnerabilities. Existing approaches often treat these tasks in isolation, failing to capture cross-scale dependencies. We propose Uni-FinLLM, a unified multimodal large language model that uses a shared Transformer backbone and modular task heads to jointly process financial text, numerical time series, fundamentals, and visual data. Through cross-modal attention and multi-task optimization, it learns a coherent representation for micro-, meso-, and macro-level predictions. Evaluated on stock forecasting, credit-risk assessment, and systemic-risk detection, Uni-FinLLM significantly outperforms baselines. It raises stock directional accuracy to 67.4% (from 61.7%), credit-risk accuracy to 84.1% (from 79.6%), and macro early-warning accuracy to 82.3%. Results validate that a unified multimodal LLM can jointly model asset behavior and systemic vulnerabilities, offering a scalable decision-support engine for finance. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.02677 |
| By: | Gómez García Facundo Gonzalo; Manzano Quiroga Jeremías Ángel; Bernasconi María Sol |
| Abstract: | We assess the forecasting performance of Gemini 2.0 Flash Thinking Experimental with Apps for Argentina’s seasonally adjusted quarter-over-quarter real GDP growth over 2021–2024. Using a transparent prompt-engineering protocol, we elicit point forecasts at three horizons and evaluate them in real time against the Central Bank’s Relevamiento de Expectativas de Mercado (REM). Across data vintages, Gemini delivers accuracy comparable to expert consensus—especially at nowcast and one-quarter-ahead horizons—while operating at effectively zero marginal cost. We also document where performance deteriorates (regime shifts and data revisions) and show that simple prompt safeguards improve stability. Overall, general-purpose LLMs can complement conventional workflows by providing competitive short-horizon forecasts with minimal implementation overhead. |
| JEL: | E0 E3 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:aep:anales:4806 |
| By: | Bloom, Nicholas; Kawakubo, Taka; Meng, Charlotte; Mizen, Paul; Riley, Rebecca; Senga, Tatsuro; Van Reenen, John |
| Abstract: | We link new forecast and management data on over 20, 000 firms to data on productivity in manufacturing and services. The panel survey was administered in the UK in July 2017 and November 2020, coinciding with two periods of considerable uncertainty from Brexit and Covid. We find that better-managed firms make more accurate forecasts for firm-level turnover and macro-level GDP. Uniquely, we show better-managed firms are also aware that they make more accurate forecasts and have greater confidence in their predictions. This highlights how superior forecasting ability enables well-managed firms to make improved operational and strategic choices. |
| Keywords: | management; productivity; expectations; uncertainty; forecasting |
| JEL: | L20 M20 O32 O33 |
| Date: | 2025–12–18 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:130291 |
| By: | Pablo Hidalgo; Julio E. Sandubete; Agust\'in Garc\'ia-Garc\'ia |
| Abstract: | This study investigates the contribution of Intrinsic Mode Functions (IMFs) derived from economic time series to the predictive performance of neural network models, specifically Multilayer Perceptrons (MLP) and Long Short-Term Memory (LSTM) networks. To enhance interpretability, DeepSHAP is applied, which estimates the marginal contribution of each IMF while keeping the rest of the series intact. Results show that the last IMFs, representing long-term trends, are generally the most influential according to DeepSHAP, whereas high-frequency IMFs contribute less and may even introduce noise, as evidenced by improved metrics upon their removal. Differences between MLP and LSTM highlight the effect of model architecture on feature relevance distribution, with LSTM allocating importance more evenly across IMFs. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.12499 |