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on Forecasting |
| By: | Philippe Goulet Coulombe |
| Abstract: | Average forecast accuracy is not the same as forecast reliability. I treat forecast loss differentials relative to a benchmark as a return series. I then evaluate these returns using risk-adjusted performance measures from finance, including the Sharpe ratio, Sortino ratio, Omega ratio, and drawdown-based metrics. I also introduce the Edge Ratio capturing a model's propensity to deliver uniquely informative predictions relative to the forecasting frontier. I apply this framework to U.S. macroeconomic forecasting, comparing econometric benchmarks, machine learning models, a foundation model (TabPFN), and the Survey of Professional Forecasters. While it is often feasible to beat professional forecasters in terms of average accuracy, it is much harder to beat them on a risk-adjusted basis. They rarely exhibit catastrophic failures and often achieve high Edge Ratios, plausibly reflecting the value of contextual judgment. Nonetheless, selected machine learning methods deliver attractive risk profiles for specific targets. The framework naturally extends to meta-analyses across targets, horizons, and samples, illustrated with a density forecast evaluation and the M4 competition. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.09712 |
| By: | Philippe Goulet Coulombe |
| Abstract: | Needless to say, linear dynamics are pervasive in economic time series, particularly autoregressive ones. While gradient boosting with trees excels at capturing nonlinearities, it is inefficient in small samples when much of the predictive content is linear, expending splits to approximate relationships better captured by simple linear terms. This paper proposes LGB+, a boosting procedure operating on a more inclusive set of basis functions. The idea comes in two flavors. LGB+ evaluates a tree and a linear candidate at each step against out-of-bag data; only the winner advances. The simpler variant, LGB^A+, alternates on a fixed schedule: a block of tree updates, then a greedy linear correction, repeat. Both designs avoid ex ante commitments to any particular functional form or predictor selection. Because the prediction is the sum of a linear and a tree component, forecasts decompose natively into linear and nonlinear contributions, and so does permutation-based variable importance and historical proximity weights. In a quarterly U.S. macroeconomic forecasting exercise, LGB+ delivers strong gains for targets with pronounced autoregressive dynamics or mixed linear-nonlinear signals. Variables dominating the linear channel are those operating through autoregressive persistence or near-accounting relationships to the target (e.g., initial claims for unemployment and building permits for housing starts). |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.09740 |
| 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: | O32 O33 |
| Date: | 2025–12–18 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:138480 |
| By: | Andrea Carriero; Florian Huber; Davide Pettenuzzo |
| Abstract: | We study double descent and benign overfitting in macroeconomic forecasting. We document that double-descent risk curves arise in standard macroeconomic datasets that are driven by a small number of latent factors, and we characterize when the underlying benign-overfitting mechanism holds. The conditions of Bartlett et al. (2020) are satisfied under the exact factor model and can also hold under the more realistic approximate factor model, provided idiosyncratic variances are not too dispersed across series. Because macroeconomic panels have only moderate dimensions, the overparameterization ratio N/T required by the theory is not naturally available. Our solution is to augment the data with synthetic copies from an estimated factor model and we prove that this strategy converges to a kernel ridge regression with a factor-structured kernel. Using monthly (FRED-MD) and quarterly (FRED-QD) US data, the resulting estimator consistently outperforms the Stock-Watson factor model for point forecasting across all series and horizons, with gains that are pervasive, statistically significant, and increasing with the forecast horizon. Our results suggest that benign overfitting, when it works, succeeds because overparameterization implicitly constructs a well-behaved kernel, not because overparameterization is intrinsically desirable. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15358 |
| By: | Jonas F. Frederiksen; Muneya Matsui; Rasmus S. Pedersen |
| Abstract: | We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test statistic converges to a nonstandard limit involving non-Gaussian stable random variables. As a consequence, conventional critical values can yield severely distorted inference: a nominal 5$\%$ test may reject a true null as often as 70$\%$ of the time. To establish these results, we develop a new stable limit theorem for strongly mixing, infinite-variance time series processes. Building on this theory, we consider sub-sampling-based inference that remains valid irrespective of tail-heaviness and requires no estimation of long-run variances or tail indices. An application to risk forecasts for emerging-market exchange rates shows that accounting for heavy tails can substantially alter conclusions about predictive performance relative to standard procedures. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.16866 |
| By: | Patrick Woitschig; Mike West |
| Abstract: | We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian dynamic linear models (DLMs) for asset price series. This represents reduced-form volatility leverage and feedback effects through use of realized volatility proxies in conditional DLMs for prices or returns, coupled with the synthesis of higher frequency data to track and anticipate volatility fluctuations. Analysis is computationally straightforward, extending conjugate-form Bayesian analyses for sequential filtering and model monitoring with simple and direct simulation for forecasting. A main applied setting is equity return forecasting with daily prices and realized volatility from high-frequency, intraday data. Detailed empirical studies of multiple S&P sector ETFs highlight the improvements achievable in asset price forecasting relative to standard models and deliver contextual insights on the nature and practical relevance of volatility leverage and feedback effects. The analytic structure and negligible extra computational cost will enable scaling to higher dimensions for multivariate price series forecasting for decouple/recouple portfolio construction and risk management applications. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.12099 |
| By: | Sanjiv R Das; Taranag Goyal; Mohini Yadav |
| Abstract: | Using Chronos-2, an open-source time-series foundation model, we evaluate pretrained time-series models for economic and financial forecasting with an emphasis on whether multivariate (MV) inputs improve accuracy relative to univariate (UV) baselines. The study covers two panels -- the Magnificent-7 equities and U.S. Treasury interest rates -- as well as a combined panel, using rolling monthly evaluations from 2000--2025. We vary input window lengths and forecast horizons and report RMSE and MAPE. Across datasets, MV forecasts consistently outperform UV forecasts, with especially strong gains for interest rates and meaningful improvements for equities. Series-level comparisons show MV improvements in every case, and error dispersion is generally lower under MV inputs. We also provide parameter-heatmap and time-series visualizations. However, mixing time series across equity and interest rate markets reduces forecast accuracy, indicating that adding noisy context degrades model performance. Overall, the results indicate that foundation models can leverage cross-series information to improve forecast accuracy in finance, and that the benefits are strongest when related series are modeled jointly under disciplined rolling protocols. Other than using an open-source foundation model, this paper also showcases how AI may be used for financial research. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.21504 |
| By: | Runyao Yu; Julia Lin; Derek W. Bunn; Jochen Stiasny; Wentao Wang; Yujie Chen; Tara Esterl; Peter Palensky; Jochen L. Cremer |
| Abstract: | Accurate and efficient imbalance electricity price forecasting is critical for industrial energy trading systems, especially as battery assets and automated bidding pipelines increasingly participate in balancing markets. However, real-time forecasting is complicated by nonlinear market-rule-based price formation, heterogeneous input signals, and incomplete data availability caused by communication delays, publication lags, and measurement outages. This paper proposes a market-rule-informed neural forecasting framework that embeds imbalance price formation rules into the latent space of an expressive neural network. The proposed framework preserves raw signal information while exploiting transparent market-rule priors. We further analyze operational robustness by removing price-component information and characterize how forecasting performance scales with input length and forecasting horizon. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines, demonstrating that market-rule priors and expressive neural networks should be jointly used for accurate and computationally sustainable forecasting in industrial energy trading applications. The implementation is publicly available at https://runyao-yu.github.io/MRINN/. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.09061 |
| By: | Marco Gregnanin; Johannes De Smedt; Giorgio Gnecco; Maurizio Parton |
| Abstract: | Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing temporal patterns within the time series data. In this research, we study the statistical significance of the inclusion of geometric patterns in enhancing forecasting accuracy within the context of time series analysis. We introduce the Time-Geometric model, a combination of models designed to exploit both geometric and temporal patterns. The contribution of this research lies in advancing the domain of univariate time series prediction, as demonstrated through extensive empirical evaluations. Our findings underscore that leveraging geometric patterns, captured through Graph Neural Networks, yields statistically significant improvements in forecasting accuracy. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.21192 |
| By: | Mathias Mesfin |
| Abstract: | This paper compares gradient boosting and long short-term memory (LSTM) architectures for intraday directional prediction in Micro E-Mini Nasdaq 100 futures (MNQ). Motivated by recent foundation-model research on financial candlestick data, including the Kronos architecture, we test whether five-minute OHLCV bar sequences contain exploitable sequential predictive structure at the scale of a single instrument dataset. Using 944 trading days from 2021-2025, four model configurations are evaluated under strict expanding-window walk-forward validation across three out-of-sample periods. The target variable is whether the session close exceeds the 10:30 AM open by more than ten points. No configuration produces statistically significant out-of-sample accuracy above the 51.8% base rate. Combined OOS accuracies range from 50.00% to 50.89% across gradient boosting variants, while the LSTM achieves 50.59%. Permutation tests yield p-values of 0.135 for the best gradient boosting model and 0.515 for the LSTM, indicating no statistically significant predictive edge. Feature importance instability across walk-forward folds suggests noise fitting rather than stable structural signal capture. The results indicate that four years of single-instrument five-minute OHLCV data are insufficient for reliable sequential ML-based intraday forecasting. The primary contribution is a documented evaluation of a Kronos-inspired architecture on a constrained real-world dataset, providing an empirical lower bound on data scale requirements for sequential financial ML. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.17724 |
| By: | Emmanouil Sofianos (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Thierry Betti (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Theophilos Papadimitriou (DUTH - Democritus University of Thrace); Amélie Barbier-Gauchard (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Periklis Gogas (DUTH - Democritus University of Thrace) |
| Abstract: | Forecasting public debt is essential for effective policymaking and economic stability, yet traditional approaches face challenges due to data scarcity. While machine learning (ML) has demonstrated success in financial forecasting, its application to macroeconomic forecasting remains underexplored, hindered by short historical time series and low-frequency (e.g., quarterly/annual) data availability. This study proposes a novel hybrid framework integrating dynamic stochastic general equilibrium (DSGE) modeling with ML techniques to address these limitations, focusing on the evolution of France's public debt. We first generate a large artificial macroeconomic dataset using an estimated DSGE model for France, which allows for efficient training of ML algorithms. These trained models are then applied to actual historical data for directional debt forecasting. The results show that the best machine learning model is an XGBoost achieving 90% accuracy, outperforming an elastic net model, used as benchmark. Our results highlight the viability of combining structural economic models with data-driven techniques to improve macroeconomic forecasting. |
| Keywords: | public debt, machine learning, France, forecasting, DSGE, DSGE forecasting France machine learning public debt |
| Date: | 2026–03–05 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05620169 |
| By: | OBIDAJU, INNOCENT |
| Abstract: | This study examined the trend, behaviour, and forecasting of TETFund allocation to universities, polytechnics, and colleges of education in Nigeria using a quantitative time series approach based on ARIMA modeling. The findings revealed that allocations across all categories exhibit a consistent upward trend and are stationary in levels around a deterministic trend which indicates that they are trend-stationary processes. Model estimation showed that the autoregressive and moving average components are statistically insignificant, leading to the adoption of a parsimonious ARIMA (0, 0, 0) model with a deterministic trend for all categories. Diagnostic tests, including checks for serial correlation and heteroskedasticity, confirmed that the models are statistically adequate, with residuals behaving as white noise and exhibiting constant variance. Forecast results projected a steady increase in TETFund allocations up to 2036, following a smooth linear trajectory; however, these projections are purely trend-driven and do not capture potential structural breaks or external shocks. Overall, the study concludes that TETFund disbursement is largely policy-driven and influenced by fiscal and macroeconomic conditions rather than historical allocation patterns, underscoring the importance of stable fiscal policy, effective planning, and adaptive funding strategies in sustaining tertiary education development in Nigeria. |
| Keywords: | Budgetary Allocation, Funding gap, Tertiary Education Funding (TETFund), ARIMA Modeling, Forecasting, Time Series |
| JEL: | H30 |
| Date: | 2026–05–08 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129024 |
| By: | Namhyoung Kim; Jae Wook Song |
| Abstract: | Predicting cross-sectional stock returns is challenging due to low signal-to-noise ratios and evolving market regimes. Classical factor models offer interpretability but limited flexibility, while deep learning models achieve strong performance yet often underutilize financial priors. We address this gap with PRISM-VQ (PRior-Informed Stock Model with Vector Quantization), a dynamic factor framework that integrates expert prior factors, vector-quantized discrete latent factors learned from cross-sectional structure, and a structure-conditioned Mixture-of-Experts to generate time-varying factor loadings. Vector quantization acts as an information bottleneck that suppresses noise while capturing robust market structure, with discrete codes serving both as latent factors and as routing signals for temporal expert specialization. Experiments on CSI 300 and S&P 500 show consistent improvements in cross-sectional return prediction and portfolio performance over strong baselines while preserving interpretability. Our code is available at https://github.com/finxlab/PRISM-VQ. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.13407 |
| By: | Safira, Dinda Ayu; Kuswanto, Heri; Ahsan, Muhammad; Sibbertsen, Philipp |
| Abstract: | This study proposes an optimized estimation approach for Self-Exciting Threshold Autoregressive (SETAR) models by integrating the Majorization-Minimization Group Least Absolute Shrinkage and Selection Operator (MM-gLASSO) algorithm, with a primary focus on improving forecasting performance in complex regime-switching environments. While SETAR models are powerful in capturing non-linear regimes and asymmetric dynamics in time series data, they often suffer from high-dimensional parameter spaces. This typically leads to high-dimensional parameter spaces that cause overfitting and reduced forecasting stability. We address this by employing the MM algorithm to simplify the complex, non-differentiable gLASSO penalty into a more manageable surrogate function. This ensures stable convergence and allows for simultaneous variable selection and parameter estimation across multiple regimes. The gLASSO penalty is specifically utilized to ensure that irrelevant lags are excluded consistently across the threshold structure. We provide a detailed derivation of the estimation procedure and evaluate its performance through extensive simulation studies. The results indicate that the MM-gLASSO framework significantly outperforms traditional methods, particularly in terms of sparsity recognition and parameter consistency. Finally, an empirical application on PM2.5 concentration demonstrates the model's superior forecasting capability and its effectiveness in identifying structural transitions in real-world time series data. |
| Keywords: | gLASSO, MM algorithm, nonlinear time series, regime detection, SETAR model |
| JEL: | C13 C32 C53 Q53 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-746 |
| By: | Gustav Olaf Yunus Laitinen-Fredriksson Lundstr\"om-Imanov; Hafize Gonca C\"omert |
| Abstract: | Microsimulation models used by ministries of finance and central banks rely on parametric processes for lifetime earnings that capture only first and second moments of the conditional distribution and miss long-range nonlinear structure. We propose SAGA, a decoder-only transformer for irregular tabular panel sequences, paired with a split conformal calibration wrapper that delivers individual-level prediction intervals with finite-sample marginal coverage guarantees. Trained on the longitudinal Swedish LISA register over 1990 to 2022, comprising 2, 143, 817 individuals and 61, 284, 903 person-years, the model forecasts annual labor earnings at horizons of one to thirty years and aggregates them by Monte Carlo into present-discounted lifetime earnings distributions. Against the canonical Guvenen, Karahan, Ozkan, and Song parametric process and tabular and recurrent baselines, SAGA reduces continuous ranked probability score by 31.9 percent at the ten-year horizon and mean absolute error by 37.7 percent at the twenty-year horizon. Conformal intervals achieve nominal coverage to within 0.4 percentage points marginally and within 2.4 percentage points on the worst-case demographic subgroup. The reconstructed lifetime earnings Gini coefficient is 0.327 against the partially observed truth of 0.341 and the GKOS estimate of 0.378. Model weights, calibration tables, and a synthetic equivalent dataset are released for replication outside the protected SCB MONA environment. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.19014 |
| By: | Stanis{\l}aw M. S. Halkiewicz |
| Abstract: | We propose and analyse rolling-origin conformal prediction for time-series forecasting. The method calibrates the conformal quantile against the $m$ most recent pseudo-out-of-sample forecast errors, adapting to serial dependence, volatility clustering, and distributional drift that invalidate classical conformal guarantees. Under H\"{o}lder-$\beta$ local stationarity and $\alpha$-mixing, we establish a four-term coverage-error decomposition and derive the optimal calibration window $m^{\star} \asymp T^{2\beta/(2\beta+1)}$ with coverage-error rate $O(T^{-\beta/(2\beta+1)})$. A Le Cam two-point construction shows this rate is minimax-optimal over the H\"{o}lder-$\beta$ model class. The Bahadur representation is proved under both $\alpha$-mixing and the physical-dependence framework of Wu (2005). An oracle inequality formalises Winkler cross-validation as an adaptive window selector; the required uniform concentration condition is established in an appendix. Validation on six real series and 93 M4 competition series confirms the theory: rolling-origin calibration outperforms full-history calibration in 86\% of comparisons (median Winkler improvement 12.3\%), maintains coverage within $\pm2\%$ of the 90\% target at short and medium horizons, and the cross-frequency log-log regression slope $0.614$ ($95\%$ CI $[0.424, 0.805]$) is consistent with the theoretical $2/3$ after controlling for frequency fixed effects. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.08422 |
| By: | Eshwar Sai Kandimalla; Sravan Chowdary Kankanala; Sumana Bhimineni; Hem Sundhar Korukunda; Vivek Yelleti |
| Abstract: | Financial market forecasting is inherently uncertain, yet most deep learning approaches rely on point predictions that provide only single-value estimates without quantifying uncertainty. Such predictions are insufficient for risk-aware decision-making, as they fail to capture the range of possible outcomes and the associated confidence of forecasts.The problem can be solved using prediction intervals, which allow obtaining an upper and lower bound for the prediction, thus enabling uncertainty representation in the model. Yet, the current methods tend to disregard relationships between assets or cannot simultaneously ensure good calibration and sharpness of the resulting intervals in dynamically changing market regimes. In our work, we propose a spatio-temporal graph-based approach with a bi-level chaotic fusion technique to solve this problem. Our model uses separate nonlinear transformation functions to estimate the interval center and width. Additionally, a volatility-aware gating mechanism is used to make predictions dependent on the regime in which the market operates. Temporal dependencies are considered by embedding graph structures and sequentially modeling them. Training is conducted according to a Lower-Upper Bound Estimation (LUBE) objective. Our experimental results show significant improvements compared to existing baselines (LSTM, GRU, GCN, HGNN) when applied to data from 2016 to 2026 with 43 leading companies in eight sectors of the NSE. It provides the lowest Winkler score (0.0778), tightest prediction intervals (PIAW = 0.1407), and highest coverage (PICP = 96.6%), with all differences statistically significant (p |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.16324 |
| By: | Ujjwala Vadrevu |
| Abstract: | Accurate forecasting of the Volatility-Covariance Matrix (VCV) is central to regulatory capital adequacy processes such as the Internal Capital Adequacy Assessment Process (ICAAP) and the Comprehensive Capital Analysis and Review (CCAR). Traditional econometric models, including GARCH-family and Exponentially Weighted Moving Average (EWMA) approaches, suffer from parametric rigidity, distributional assumptions, and numerical instability under stress, leading to systematic underestimation of tail risk. This paper proposes and validates a novel Hybrid Gaussian Process Regression-Historical Simulation (GPR-HS) framework for estimating Value-at-Risk (VaR) and Expected Shortfall (ES) across a diversified portfolio of seven major global equity indices. The framework decouples the VCV estimation problem: individual asset volatilities are modelled dynamically using Univariate GPR with a Matern 5/2 kernel, while inter-asset correlations are estimated via stable historical covariance. A key methodological contribution is the Aggressive Noise Initialization (ANI) strategy, which sets the initial White Noise kernel variance equal to the empirical variance of the training returns, ensuring Gram matrix positive-definiteness, regularization, and conservative, regulatory-compliant forecasts. Evaluated using an expanding window forward-chaining cross-validation scheme over June 2020 -June 2025, the GPR-HS framework achieves regulatory compliance in the majority of test splits; including a 100% ES pass rate at the portfolio level, while outperforming the static Historical VaR benchmark in 71.4% of univariate cases by Quadratic Loss and 100% of cases by violation count. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.17275 |
| By: | Massimo Giannini |
| Abstract: | This paper assesses whether NASA Black Marble nightlight intensity can serve as an early indicator of annual taxable income at the Italian municipal level, where official data are released with a 12--18 month lag. Using a panel of 7{, }631 municipalities over 2012--2021, we compare four recurrent neural network architectures (LSTM, BiLSTM, GRU, Transformer) against six benchmarks: simple persistence, panel fixed effects, autoregressive distributed lag, and two spatial econometric specifications (SAR, Spatial Durbin) on a queen-contiguity matrix. Models are trained on 2012--2019 and evaluated out-of-sample on 2020--2021 with a cross-sectional Diebold--Mariano test. A single-layer GRU achieves a median forecast error of 1.07 million euros across the cross-section of municipalities -- approximately $4\%$ of the median municipal IRPEF income of 29 million euros -- statistically dominating every benchmark (DM $>4$ against persistence, $>40$ against spatial linear models, all $p |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.08782 |
| By: | Gabriel Rodriguez (Departamento de Economía de la Pontificia Universidad Católica del Perú); Fiorela Liza (Pontificia Universidad Católica del Perú); Miguel Ataurima Arellano (CAF-Development Bank of Latin America and the Caribbean y Pontificia Universidad Católica del Perú) |
| Abstract: | Using daily equity market data for Latin American (Latam) and high-income (HI) countries over 2008-2023, this paper estimates GARCH and GJR models to forecast Value at Risk (VaR) and Expected Shortfall (ES). The performance of a broad set of heavy-tailed and asymmetric distributions is evaluated, including the Normal (N), Skewed Normal (skN), Student’s t (S), skewed S (skS), generalized hyperbolic skS (GHskS), normal inverse Gaussian (NIG), skewed NIG (skNIG), normal reciprocal inverse Gaussian (NRIG), and skewed NRIG (skNRIG). The key findings can be summarized as follows: (i) for VaR forecasting, asymmetric distributionsare preferred at both confidence levels, and at the 99% level heavy tails are also required; (ii) for ES forecasting, at both confidence levels the selected models rely on asymmetric heavy-tailed distributions, with GHskS emerging as the dominant specification; (iii) for VaR forecasting, modeling leverage effects is necessary for most HI countries, whereas this is required for only about half of the Latam countries; and (iv) for ES forecasting, volatility specification plays a more limited role than in VaR forecasting. Palabras claves: Valor al Riesgo, Pérdida Esperada, Modelos GARCH, Distribuciones de Colas Pesadas, Países LATAM, Países de Altos Ingresos, Mercados Bursátiles, Mercados Forex. JEL Classification-JE: C52, C53, G17 |
| Keywords: | Value at Risk, Expected Shortfall, GARCH Models, Heavy-Tailed Distributions, Latin American Countries, High-Income Countries, Equity Markets, Forex Markets. |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:pcp:pucwps:wp00554 |