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on Forecasting |
| By: | Tobias Adrian; Domenico Giannone; Matteo Luciani; Mike West |
| Abstract: | Central banks monitor macroeconomic risk through two traditions: scenario analysis, regularly used since the mid-1990s, and distributional forecasting, practiced since the late 1960s. The two are complementary but separate: scenarios provide narratives without probabilities, while predictive distributions provide probabilities with limited economic interpretation. Treating baseline forecasts and scenarios as conditional predictive densities, and distributional forecasts as reference predictive distributions, places both within a common framework and clarifies their roles. The Scenario Synthesis assigns weights to scenarios consistent with the reference distribution, offering a practical and reproducible tool for risk assessment and policy deliberation under deep uncertainty. |
| Keywords: | scenarios; fan charts; growth-at-risk; model uncertainty; Bayesian predictive synthesis |
| JEL: | C1 C11 C53 E32 E37 E58 |
| Date: | 2026–09–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:103751 |
| By: | Marcus Buckmann (Bank of England); Galina Potjagailo (Bank of England); Philip Schnattinger (Bank of England) |
| Abstract: | We propose the Blockwise Boosted Inflation Model (BBIM), a boosted tree framework that decomposes inflation dynamics into predictive components aligned with an open-economy hybrid Phillips curve. Demand and supply contributions are identified by imposing monotonicity constraints, ensuring theory-consistent links between inflation and key indicators. Applied to monthly UK CPI inflation, the model shows that the recent surge has been driven mainly by global supply shocks transmitted through supply chains. We also uncover an L-shaped Phillips curve relationship between inflation and labour market tightness, with tight labour markets amplifying recent inflationary pressures. By contrast, earlier episodes saw non-linearities more strongly tied to broader slack, particularly during recessions. The model further accounts for trend shifts informed by inflation expectations. Short-term household expectations have recently displayed persistent non-linear effects, temporarily raising trend inflation and prolonging inflationary pressures, while longer-term expectations remain anchored. Out-of-sample, the BBIM delivers competitive forecasting performance relative to linear benchmarks and unstructured machine learning methods. Our approach provides a flexible yet interpretable framework that combines economic structure with machine learning for policy-relevant analysis of inflation dynamics. |
| Keywords: | Inflation;Phillips curve;boosted decision trees;machine learning |
| JEL: | E31 E37 C14 C53 |
| Date: | 2025–09–26 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:023265 |
| By: | Prengle, Scott H. |
| Abstract: | Diebold and Li (2006) showed that a simple autoregressive model of the Nelson-Siegel yield curve factors produces genuinely useful 12-month-ahead forecasts. Replicated on an extended U.S. Treasury sample running through 2026 — roughly 26 years beyond their original 1985-2000 window — that result does not hold: the model loses to a naive random-walk forecast on every tenor tested, under both expanding and rolling estimation windows, with degradation frequently exceeding 10%. The mechanism is identifiable and consistent with independent structural work: the zero-lower-bound period introduced a materially different factor dynamic that the forecasting specification could not accommodate. Rather than treat this as a dead end, this paper develops and formally tests an alternative: a small number of recurring, economically interpretable curve-shape states — fewer in number than they first appear, once rate level and curve shape are properly separated. Seven falsifiable hypotheses are tested: bootstrap cluster stability, permutation-tested temporal persistence, chi-square correspondence with Fed policy phase and NBER recession dating (with effect sizes reported), a formally BIC-gated comparison showing a unified hidden Markov model outperforms static clustering (robust to leave-one-episode-out testing), and surrogate-tested spectral hypotheses returning informative negative results. Three analytical errors identified and corrected during testing are reported explicitly. The resulting framework is deliberately descriptive rather than predictive, and is extended into an operational monthly monitoring tool built on causal (filtering-based) inference rather than retrospective smoothing. The paper's central claim is narrower than a forecasting model would be: the curve's useful information may lie in its current state rather than its future trajectory. |
| Keywords: | term structure; treasury yields; Nelson-Siegel; Diebold-Li; hidden Markov model; regime switching; causal filtering; random-walk benchmark |
| JEL: | C22 E43 G12 |
| Date: | 2026–08–07 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:130391 |
| By: | Marcus Buckmann (Bank of England); Galina Potjagailo (Bank of England) |
| Abstract: | This paper discusses how economic theory can be integrated into machine learning (ML) models to enhance their interpretability and applicability for policy analysis. While ML methods offer considerable flexibility and strong predictive performance, they are often criticised for their 'black box' nature and lack of economic transparency. A growing body of research addresses this limitation by introducing structure into ML models − most notably through Block-Additive Models (BAMs) and theory-consistent monotonicity constraints. BAMs group predictors into economically meaningful blocks and impose additivity across blocks, while permitting non-linearities and interactions within them. This architecture enables clear attribution of each block’s contribution to the model’s predictions. Monotonicity constraints further improve interpretability by aligning the model’s directional responses with economic theory, allowing for the separation of opposing effects − such as distinguishing between supply- and demand-driven components of inflation. Empirical evidence shows that these structured ML approaches retain strong predictive performance while yielding economically meaningful narratives. |
| Keywords: | Interpretable machine learning;theory-aligned constraints;macroeconomic analysis |
| JEL: | C10 C14 C53 |
| Date: | 2025–09–26 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:023266 |
| By: | Florian Huber; Aubrey Poon; Dan Zhu |
| Abstract: | We develop a hierarchical Bayesian panel quantile regression model in which unit-specific coefficient paths are smoothed across quantiles by Gaussian processes, while a common time effect absorbs aggregate shocks. Componentwise-monotone Bernstein polynomials, perturbed by unit-specific deviations, deliver soft noncrossing, and we provide identification conditions together with a bound on the crossing probability. Applying the model to 33 countries over 1979--2023, we find that global temperature shocks generate a systemic, non-diversifiable downside risk to output growth. This risk is concentrated in the lower tail and disproportionately affects emerging markets. Finally, we apply our framework to risk analysis and show that the model reduces out-of-sample tail-risk forecast loss by roughly one-third relative to country-specific quantile regressions. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.04664 |
| By: | Reis, Ricardo |
| Abstract: | This article uses inflation expectations to investigate the mechanisms that linked supply and demand shocks to inflation outcomes during 2021–2024. It describes several theoretical mechanisms through which shocks led to inflation, highlighting the role of expectations in this process. It uses multiple sources of expectations data for the United States, Euro area, and United Kingdom to evaluate each of these channels. Finally, it surveys the literature that has used expectations data to make sense of the 2021–2024 inflation surge. The article applies the results from this investigation to assess how well-anchored inflation expectations were during the surge and at the end of it. |
| Keywords: | inflation disaster;market expectations;surveys;Phillips curve;fiscal theory;doves |
| JEL: | E31 E52 D84 |
| Date: | 2026–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:138478 |
| By: | Rawend Brahem (Central Bank of Tunisia) |
| Abstract: | Forecasting inflation in the presence of changing economic conditions, external shocks, and evolving transmission mechanisms remains an active area of research. This paper applies machine learning (ML) models to forecast headline and core inflation in Tunisia at 1-, 3-, and 6-month horizons, comparing their performance with standard econometric benchmarks within a rolling forecasting framework. Conformal prediction intervals are used to assess forecast uncertainty, while SHAP values serve as an exploratory tool to examine the contribution of explanatory variables to model predictions. The results reveal a clear horizon-dependent pattern, with the predictive gains of ML models increasing at medium and longer horizons. These gains are particularly pronounced at the 6- month horizon, where Support Vector Regression reduces the RMSE by more than 40 percents relative to the best-performing benchmark. Furthermore, SHAP analysis suggests that the relative contribution of predictors varies across forecasting horizons, with inflation persistence playing a more prominent role at short horizons and monetary, external, and commodity price variables becoming more relevant at longer horizons. Overall, these findings suggest that machine learning methods are most valuable as a complement to, rather than a substitute for, traditional forecasting approaches, particularly at longer horizons where nonlinearities become more pronounced. |
| Keywords: | Inflation Forecasting; Machine Learning; Conformal Inference; SHAP Values; Tunisia |
| JEL: | C53 E31 E37 |
| Date: | 2026–09–08 |
| URL: | https://d.repec.org/n?u=RePEc:gii:giihei:heidwp25-2026 |
| By: | Dominik Manuel Buchegger; Lukas Gonon |
| Abstract: | Implied volatility surfaces summarise the option market and are central to many financial applications. Forecasting their future evolution requires modelling two-dimensional geometry, temporal dependence, and predictive uncertainty while preserving economic admissibility. We propose a conditional latent diffusion framework for generating joint 30-step trajectories of implied volatility surfaces and underlying returns. An arbitrage-aware autoencoder learns a low-dimensional surface representation, while the diffusion model captures the conditional joint evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios while also outperforming the persistence benchmark in point forecasting. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22478 |
| By: | Isaiah Andrews; Suproteem Sarkar |
| Abstract: | People increasingly use language models to support life decisions. Many such decisions involve a probabilistic forecast: How likely is a major life event, a natural disaster, or an economic outcome? Users of language models may implicitly trust that these forecasts fall out of a coherent world model. In this paper, we evaluate the coherence of language model probabilistic forecasts through a procedure that builds on a theorem due to de Finetti. We elicit forecasts from language models across events generated from stock returns data. We then use linear programs to compute the largest Dutch-book profit - the profit an arbitrageur could guarantee by betting against model-generated probabilities - which we use as a measure of incoherence. Our procedure does not require outcome labels, so we can evaluate coherence even in settings where outcomes are not observed or have not yet resolved. We find substantial evidence of incoherence in language model forecasts. Such incoherence increases when there are richer logical relationships between events, and irrelevant contextual details can increase incoherence by an order of magnitude. We conclude by discussing how alternative training strategies may improve probabilistic coherence. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.02797 |
| By: | Demetrio Lacava; Paolo Santucci de Magistris |
| Abstract: | Market efficiency relies fundamentally on stable liquidity. Consequently, forecasting liquidity dynamics is a priority for both investors and regulators. We introduce a new tail-risk metric, Illiquidity-at-Risk (IlliQaR), designed to quantify the magnitude of extreme liquidity dry-ups. Relying upon the realized Amihud (a precise illiquidity measurement derived from high-frequency data as the ratio of realized volatility to trading volume) we assess the predictive power of various linear and non-linear econometric models, with a specific focus on the impact of discontinuous jump components. Accounting for these jumps is essential for achieving accurate probability coverage and better IlliQaR predictions during periods of systemic stress, where standard continuous models systematically underestimate the severity of liquidity evaporation. Our empirical analysis, encompassing the S&P 500 index and a cross-section of 25 large U.S. equities, demonstrates that incorporating jumps significantly improves forecasts of illiquidity. Our results suggest that individual stock IlliQaR violations often cluster during periods of S&P 500 liquidity stress. This indicates that Illiquidity at Risk is not just a localized concern but a systemic one, where the main index acts as a leading indicator for extreme dry-ups in individual stock liquidity. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.00943 |
| By: | Stefania D'Amico; Thomas B. King; Francisco Torralba |
| Abstract: | The public pays close attention to Federal Reserve communications about future monetary policy, but it remains an open question how those communications shape the public’s expectations for the path of policy rates. We explore how market expectations adjust to the information provided in the “dot plot” of the Summary of Economic Projections, which contains the Federal Open Market Committee’s assessment of the appropriate future path of the federal funds rate. The results shed light on the market interpretation of forward guidance and its efficacy as a communication tool. We find that financial markets respond to the Federal Reserve’s “dot plot” projections by adjusting their expectations for future interest rates, but only partially and gradually, reflecting the understanding that these projections are conditional forecasts rather than firm commitments. Over time, both market expectations and FOMC projections for interest rates tend to converge, showing that the dot plot is informative to market participants. This gradual adjustment highlights the dot plot’s role as a communication tool that shapes, but does not dictate, market expectations. |
| Keywords: | Summary of Economic Projections (SEP); SEP federal funds rate projections; interest rate expectations; market reaction; forward guidance |
| JEL: | E43 E58 G13 |
| Date: | 2026–09–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:103737 |
| By: | Benedikt Ballensiefen; Fabricius Somogyi; Hannah L Winterberg |
| Abstract: | We study the determinants of US dollar demand across market participants and traded instruments using survey-based exchange rate and macroeconomic expectations. To empirically establish the relevance of survey-based expectations for currency flows, we leverage granular foreign exchange trading data and present three main findings. First, end-user investors increase their dollar purchases when they expect the US dollar to appreciate. Investment funds and non-dealer banks adjust their synthetic dollar borrowing in the FX swap market in response to forecasted changes in synthetic dollar funding costs. Second, cross-sectionally, investors rebalance along the factor structure of currency risk into dollars following an expected dollar appreciation. Third, the predictive power of survey forecasts weakens when forecaster disagreement or uncertainty rises. Overall, our findings show that long-horizon expectations predict dollar demand across spot, forward, and swap currency markets. |
| Keywords: | Exchange rate expectations; dollar demand; currency flows; FX swaps; survey forecasts |
| Date: | 2026–09–04 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2026/186 |
| By: | Hervé Andrès (Milliman France, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris); Alexandre Boumezoued (Milliman France); Benjamin Jourdain (MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, MATHRISK - Mathematical Risk Handling - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique - Université Gustave Eiffel - CERMICS UMR 9032 - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - CNRS - Centre National de la Recherche Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris) |
| Abstract: | We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the paths of the associated equity indices (e.g. the S&P 500), we first study how vanilla options implied volatility can be predicted using the past trajectory of the underlying asset price. Our empirical study reveals that a large part of the movements of the at-the-money-forward implied volatility for up to two years time-to-maturities can be explained using the past returns and their squares. Moreover, we show that this feedback effect gets weaker when the time-to-maturity increases. Building on this new stylized fact, we fit to historical data a parsimonious version of the SSVI parameterization (Gatheral and Jacquier, 2014) of the implied volatility surface relying on only four parameters and show that the two parameters ruling the at-the-money-forward implied volatility as a function of the time-to-maturity exhibit a path-dependent behavior with respect to the underlying asset price. Finally, we propose a model for the joint dynamics of the implied volatility surface and the underlying asset price. The latter is modelled using a variant of the path-dependent volatility model of Guyon and Lekeufack and the former is obtained by adding a feedback effect of the underlying asset price onto the two parameters ruling the at-the-money-forward implied volatility in the parsimonious SSVI parameterization and by specifying Ornstein-Uhlenbeck processes for the residuals of these two parameters and Jacobi processes for the two other parameters. Thanks to this model, we are able to simulate highly realistic paths of implied volatility surfaces that are free from static arbitrage. |
| Keywords: | Implied volatility modelling SSVI Path-dependent volatility Simulation Arbitrage, Arbitrage, Simulation, Path-dependent volatility, SSVI, Implied volatility modelling |
| Date: | 2026–04–01 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04362544 |