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on Econometric Time Series |
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Issue of 2026–07–20
24 papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Xu, Yongdeng (Cardiff University, Cardiff, UK); Lyu, Juyi (Loughborough University, UK); Lu, Wenna (Cardiff Metropolitan University, Cardiff, UK) |
| Abstract: | This paper evaluates an Adaptive LASSO-MGARCH model for multivariate volatility forecasting, with an application to green and conventional bonds, equities, energy commodities, and EU carbon allowances. By introducing coefficient-specific adaptive penalisation directly into the multivariate GARCH variance equations, the model delivers a sparse and data-driven volatility spillover structure while preserving positive definiteness of the conditional covariance matrix. Using daily data on green and conventional bonds, equities, energy commodities, and carbon allowances, we show that adaptive regularisation substantially reduces model complexity and improves economic interpretability relative to an unpenalised MGARCH benchmark. Out-of-sample forecasting experiments at multiple horizons demonstrate that the Adaptive LASSO-MGARCH model consistently achieves lower covariance forecast losses, and statistical tests based on the White reality check confirm that these improvements are significant across alternative loss functions. |
| Keywords: | Adaptive LASSO; Multivariate GARCH; Volatility Forecasting; High-Dimensional; Green Finance |
| JEL: | C32 C58 G17 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2026/4 |
| By: | Denise R. Osborn; Jing Tian; Jan P.A.M. Jacobs |
| Abstract: | Four sources of seasonality are distinguished for quarterly time series: (i) seasonal unit roots, (ii) deterministic seasonal shifts, (iii) trending deterministic seasonals, and (iv) stationary stochastic seasonality. The identification of relevant UC models is discussed, including the role of a stationary seasonal lag term when the innovations are correlated. Methodologically, the importance of unit root testing for seasonal UC model specification is emphasized, with the proposed approach applied to quarterly U.S. government expenditure series. |
| Keywords: | trend-cycle-seasonal decomposition, univariate unobserved com-ponents models, correlated component models |
| JEL: | C22 E32 E37 H50 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-57 |
| By: | Degui Li; Yuying Sun; Boyao Wu |
| Abstract: | In this paper, we introduce a flexible time-varying multi-layer network vector autoregression (VAR) model framework for large-scale time series, allowing agents in dynamic systems to interact through multiple channels and incorporating multiple adjacency matrices to capture network spillover effects. We propose a penalized model averaging method to determine a time-varying optimal combination of multi-layer network VAR candidate models whose number may be divergent. Under some regularity conditions, the asymptotic properties such as asymptotic optimality and convergence rates of the proposed time-varying weight estimation are derived in the contexts of both the in-sample fitting and out-of-sample prediction. In addition, we extend the conformal prediction method to construct prediction bands for locally stationary time series. Monte-Carlo simulation studies and an empirical application to forecast CPI inflation by combining multiple network information are given to illustrate reliable finite-sample estimation and predictive performance of the developed methodology. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.25292 |
| By: | Lewis, Daniel; Mertens, Karel |
| Abstract: | We approximate the finite-sample distribution of impulse response function (IRF) estimators that are just-identified with a weak instrument using the conventional local-to-zero asymptotic framework. Since the distribution lacks a mean, we assess bias using the mode and conclude that researchers prioritizing robustness against weak instrument bias should favor vector autoregressions (VARs) over local projections (LPs). Existing testing procedures are ill-suited for assessing weak instrument bias in IRF estimates, and we propose a novel simple test based on the usual first-stage F-statistic. We investigate instrument strength in several applications from the literature, and discuss to what extent structural parameters must be restricted ex-ante to reject meaningful bias due to weak identification. |
| Keywords: | Local projections; Vector autoregressions; Instrumental variables; Weak instruments; Impulse responses; dynamic causal effects |
| JEL: | C32 C36 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20990 |
| By: | Sílvia Gonçalves; Ana María Herrera; Iones Kelanemer Holban; Lutz Kilian; Elena Pesavento |
| Abstract: | We propose a semiparametric local projection estimator of nonlinear impulse response functions for a broad class of structural dynamic models relevant for applied macroeconomics, including models with nonlinearly transformed regressors, state dependent coefficients and nonlinear interactions between shocks and state variables. The estimator is based on a doubly robust moment condition that identifies the average response function as a linear functional of a nonparametric conditional mean, augmented by a density ratio that captures the effect of shifting the shock of interest. We combine this moment condition with cross-fitting that handles serial dependence. The resulting estimator is √ T -consistent and asymptotically normal. We examine the finite-sample performance of the estimator across a range of nonlinear data generating processes and illustrate its use in two empirical examples. |
| Keywords: | impulse response; local projection; semiparametric estimation; double machine learning; nonlinear structural model; potential outcomes |
| JEL: | C14 C32 E52 Q43 |
| Date: | 2026–06–30 |
| URL: | https://d.repec.org/n?u=RePEc:fip:feddwp:103495 |
| By: | Ayush Jha |
| Abstract: | Predictive dependence in time series need not be confined to the conditional mean. Outside the Gaussian setting, causal content may arise through conditional scale, tail behavior, asymmetry, or other distributional features, implying that no single Granger-type test provides a complete characterization of predictive dependence. This paper develops a framework for distributional Granger causality based on a finite collection of channel-specific restrictions. Under suitable determinacy conditions, the channel menu is shown to be complete, yielding an identification result that links distributional Granger non-causality to a finite set of testable hypotheses. Building on this representation, we develop an adaptive sequential testing procedure that allocates inferential resources across channels while maintaining familywise error control through an alpha-investing mechanism. A policy-invariant validity theorem establishes finite-sample size control under arbitrary admissible selection rules, while an asymptotic efficiency theorem shows that a confidence-bound allocation rule achieves power equivalent to that of an infeasible oracle benchmark. The theoretical guarantees are derived from primitive mixing and moment conditions together with a circular-block permutation scheme. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.22230 |
| By: | Likai Chen; Weining Wang |
| Abstract: | Forecasting is a central goal of time-series analysis. This review centers on three major developments in recent AI-based time-series forecasting: transformers, large pretrained models for zero-shot forecasting, and diffusion-based generative forecasters. We connect these methods to the econometric tradition built around the vector autoregression (VAR) through a common object: the conditional distribution of the future given the past. The review is organized around three long-standing challenges: high dimensionality, nonstationarity, and nonlinearity. We argue that modern methods make progress by expanding the classical forecasting template: they allow more flexible dynamics, use larger information sets and training corpora, and represent richer predictive distributions. Yet they often lack the inferential and structural tools that make classical models useful for testing, explanation, and policy analysis. We close by outlining open problems where econometric tools remain important. |
| Date: | 2026–01–30 |
| URL: | https://d.repec.org/n?u=RePEc:bri:uobdis:26/838 |
| By: | Chudik, Alexander; Kilian, Lutz |
| Abstract: | This paper proposes mean group and pooled estimators of impulse responses based on mixed-frequency auxiliary distributed lag (DL), autoregressive distributive lag (ARDL), or vector autoregressive distributed lag (VARDL) estimating equations. Our setup assumes that the data are generated by a high-frequency VAR process. While the shock of interest is directly observed at high frequency, the outcome variable is only observed as a temporally aggregated variable at a lower frequency. We derive the asymptotic distributions of the six proposed estimators. Monte Carlo experiments show that pooled estimators generally perform better than the corresponding mean group estimators for relevant sample sizes. An empirical illustration to the pass-through from daily wholesale gasoline price shocks to monthly consumer price inflation illustrates the usefulness of the proposed methods. |
| Keywords: | Mixed frequencies |
| JEL: | C22 Q43 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21162 |
| By: | Sangmyung Ha |
| Abstract: | We propose two procedures for determining the number of dynamic factors, extending Bai and Ng (2002) and Ahn and Horenstein (2013) to dynamic factor models where lagged factors may directly influence the observed variables. As an intermediate step, we develop a simple and computationally efficient alternating least squares algorithm that directly estimates the dynamic factors, rather than their static representations. By working with these direct estimates, our approach enables joint determination of the number of factors and the filter length. Our test is shown to be consistent under weaker conditions than those in Bai and Ng (2007) and Amengual and Watson (2007). We apply our procedures to estimate the number of primitive shocks in a large panel of US macroeconomic time series. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.26142 |
| By: | Shujie Li (Paderborn University); Yuanhua Feng (Paderborn University) |
| Abstract: | Many economic and financial series exhibit non-stationarity as well as long-memory behavior in both the first and second moments. To capture both non-stationarity and long-memory characteristics simultaneously, a general dual-trend and dual longmemory framework is proposed. In this framework, the error term of the semiparametric FARIMA model is assumed to exhibit a slowly changing scale and longmemory heteroskedasticity. A four-step estimation procedure is proposed, including a trend and a FARIMA model estimation for the first moment, followed by a scaling function and a long-memory volatility model estimation for the second moment. Three long-memory EGARCH-type models and the FIGARCH model are employed in the final stage. Our results indicate that the proposed approach can effectively model the selected economic series exhibiting dual-trend and dual long-memory features. |
| Keywords: | dual-trend, dual long-memory, semi-strong FARIMA, modulus FILog- GARCH, modified FIEGARCH, FIEGARCH and FIGARCH |
| JEL: | C22 C14 C58 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:174 |
| By: | Kyriakopoulou, Dimitra |
| Abstract: | We develop a ridge-regularized Factor-Augmented Vector Autoregression (FAVAR) framework for modeling macro-fiscal dynamics in settings where the number of predictors is large relative to the available sample. Rather than relying on an unrestricted factor decomposition, the high-dimensional information set is summarized through two economically interpretable latent factors, namely a real activity factor and a nominal-financial factor, extracted from separate data blocks. These factors are embedded in a regularized VAR together with key observable macro-fiscal variables, including real GDP growth, inflation, the primary balance, and the interest-rate-growth differential, allowing macroeconomic conditions to be linked to sovereign debt dynamics through a nonlinear accounting identity. In an application to Greece, the extracted factors capture major business-cycle, inflationary, and financing episodes, while impulse responses are economically plausible and dynamically stable. Recursive out-of-sample forecasting exercises show that the model performs comparatively well for inflation and financing conditions at selected horizons, while simple autoregressive benchmarks remain difficult to outperform for persistent real activity variables. Overall, the results highlight the usefulness of combining structured factor extraction with ridge regularization to obtain a parsimonious and interpretable framework for macro-fiscal modelling, scenario analysis, and debt sustainability assessment. |
| 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:129519 |
| By: | Li Chen (Paderborn University); Yuanhua Feng (Paderborn University) |
| Abstract: | Motivated by more and more semi- or nonparametric models applied in time series forecasting and their demonstrated superior performance in many empirical researches, this paper explores the adoption and integration of a semiparametric ARMA model in an enterprise system landscape. We begin by reviewing basic construction of the semiparametric ARMA model, the iterative plug-in algorithm for estimating the trend component of trend stationary times series, forecast techniques and quality measurements, which were well researched and published with the R package smoots. Subsequently, we showcase a novel approach to adopt the semiparametric ARMA model in a forecast application based on SAP Analytics Cloud (SAC), which leverages the platform’s strengths in system integrity, state-of-the-art user interface (UI) design as well as seamless connection to a R engine with smoots package embedded. The forecast application addresses key challenges in terms of cost efficiency, user experience, and the requirement for in-house statistical or machine learning expertise while adopting such statistical algorithms in enterprise context. Finally, we empirically evaluate the forecast quality of the integrated semiparametric ARMA model using real-world data, demonstrating promising results overall. |
| Keywords: | Time series forecasting, semiparametric algorithm, forecasting accuracy, smoots package, SAP Analytics Cloud, enterprise adoption |
| JEL: | C01 C02 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:176 |
| By: | Li Chen (Paderborn University) |
| Abstract: | To address enterprise adoption challenges beyond model accuracy, including usability for non-expert users, trust and explainability, and cost efficiency, this paper proposes a hybrid architecture, in which a business AI agent acts as an orchestrator and a time series Model Context Protocol(MCP) server provides reusable forecasting capabilities along a seven-stage forecasting lifecycle. In the proposed architecture, the agent interprets the user request, reasons over the available context, invokes appropriate MCP tools, and translates structured tool outputs into business-oriented explanations. The implemented time series MCP server is evaluated on three real-world datasets under two experimental settings: a zero-shot forecasting setup, in which the agent compares the available forecasting tools, and a diagnostic-aware setup, in which the agent first analyzes data quality, seasonality, stationarity, structural breaks, and influencing factors before selecting a forecasting strategy. The results show that forecasts produced through the MCP server can reach plausible quality levels across all datasets. The diagnostic-aware workflow improved forecast accuracy and explanation quality. The experiments further show that no single model family dominates across all settings: automatic ARIMA achieved the highest aggregate accuracy score but required the highest runtime, while Chronos-2 and Toto 2.0 provided competitive accuracy-runtime trade-offs. Exponential smoothing remained a fast and interpretable baseline. The findings suggest that an MCP-based architecture can make heterogeneous forecasting methods accessible, auditable, and cost-aware for enterprise AI agents, while still requiring clear task specification, governance, and human oversight. |
| Keywords: | time series forecasting, Model Context Protocol, AI agents, AutoML, time series foundation models, enterprise analytics, explainable forecasting, design-based research |
| JEL: | C01 C02 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:178 |
| By: | Oliver Kojo Ayensu (Paderborn University); Yuanhua Feng (Paderborn University); Dominik Schulz (Paderborn University) |
| Abstract: | This paper considers two tractable special cases of the fractionally integrated asymmetric power ARCH (FIAPARCH) model, called FIGJR-GARCH and FITGARCH, which exhibit improved numerical stability relative to the general FIAPARCH specification. Under a restriction on the leverage parameter, almost sure positivity of the conditional variance process is ensured by the Conrad and Haag (2006) conditions. Building on these parametric specifications, we develop semiparametric extensions. In this framework, we first estimate the time-varying long-run component for unconditional variance by a local linear estimator, and then estimate the time-invariant parameters in GARCH-type short-run component by a quasi maximum likelihood estimator based on descaled returns. Next, we construct pointwise confidence bands for inference on the long-run component. An application to equity returns suggests that part of the persistence attributed to fractional integration in parametric long-memory GARCH models may instead reflect long-run variation in the unconditional variance. The empirical evidence also suggests that individual stocks exhibit more pronounced long-run variation in volatility than aggregate indices. |
| Keywords: | EGARCH family, FIGJR-GARCH, FITGARCH, QMLE based on descaled returns, scale function estimation, semiparametric GARCH model |
| JEL: | C14 C22 C51 C58 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:175 |
| By: | Amengual, Dante; Fiorentini, Gabriele; Sentana, Enrique |
| Abstract: | We propose specification tests for Gaussian SVAR models identified with short- and long-run restrictions that assess the theoretical justification of the chosen identification scheme by checking the independence of the structural shocks. We consider both moment tests that focus on their coskewness and cokurtosis and contingency table tests with discrete and continuous grids. Our simulations confirm the finite sample reliability of resampling versions of our proposals, and their power against interesting alternatives. We also apply them to two influential studies: Kilian (2009) with short-run restrictions in oil markets and Blanchard and Quah (1989) with long-run ones for the aggregate economy. |
| Keywords: | Coskewness; Cokurtosis; Moment tests; Oil market; Pseudo maximum likelihood estimators |
| JEL: | C32 C52 E32 Q41 Q43 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20975 |
| By: | Canova, Fabio; Fosso, Luca |
| Abstract: | We study the consequences of using a deterministic steady state in Vector Autoregressive (VAR) models, when the data may display structural breaks, transitional dynamics or low-frequency fluctuations. We document upward biases in the estimated coefficients. Distortions are amplified by the identification scheme. Allowing the steady state to be stochastic reduces the biases. We propose a spike-and-slab prior to differentiate between the two alternative long-run specifications. We revisit two well-known controversies: (i) the dynamics of hours in response to technology shocks; (ii) the habit formation hypothesis and the hump-shaped response of consumption and inflation to income shocks. |
| JEL: | E32 C32 E52 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21205 |
| By: | Brianti, Marco; Forni, Mario; Gambetti, Luca; Granese, Antonio |
| Abstract: | Building on a frequency-domain identification within a nonlinear Structural Dynamic Factor Model, we study the nonlinear transmission of demand and supply shocks, the two shocks accounting for the bulk of fluctuations in U.S. macroeconomic variables. Supply shocks propagate symmetrically and are well described by linear dynamics. Demand shocks, by contrast, display strong sign asymmetries: contractionary shocks generate larger and more persistent declines in real activity, with limited adjustment of prices and nominal wages, an asymmetry amplified in booms. A New Keynesian model with downward nominal wage rigidity rationalizes these findings, highlighting the role of nominal rigidities as a source of nonlinearities. |
| JEL: | C32 C51 E12 E32 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21333 |
| By: | Li Chen (Paderborn University); Yuanhua Feng (Paderborn University) |
| Abstract: | Building upon our previous work that integrated a semi-parametric ARMA model into the SAP ecosystem, this paper introduces an enhanced forecasting application for SAP Analytics Cloud (SAC), termed deseatsForecast. The application leverages a data-driven seasonal semiparametric ARMA (S-Semi-ARMA) algorithm and novelly addresses two critical gaps in the practical deployment of advanced semiparametric models within enterprise environments. Specifically, the proposed deseatsForecast application enables robust estimation of slowly-changing seasonal patterns jointly with trend components through a data-driven Iterative Plug-In (IPI) algorithm for bandwidth selection. Secondly, the application provides native support for panel data structures, thereby extending its applicability to multidimensional business datasets commonly encountered in enterprise settings. The paper begins with a review of the data-driven S-Semi-ARMA model and the estimation procedures for trend, seasonal, and residual components. Subsequently, forecasting techniques based on the S-Semi-ARMA framework are presented, followed by a brief description of the architecture and design of the deseatsForecast application, with particular emphasis on its extensions relative to the smootsForecast application. Finally, the forecasting application is empirically validated using OECD passenger car registration data for multiple countries and a comparative study against SAP’s autoML-based forecasting approach is conducted. The empirical results demonstrate consistently strong forecast performance of the deseatsForecast application and highlight its superior forecast accuracy and transparency compared with the current autoML approach in SAP. |
| Keywords: | Time series forecasting, semiparametric algorithm, forecasting accuracy, deseats, SAP Analytics Cloud, enterprise adoption |
| JEL: | C01 C02 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:177 |
| By: | Miguel D. Ramirez (Department of Economics, Trinity College) |
| Keywords: | Block Granger causality test, Gregory-Hansen cointegration single-break test, Impulse Response Function (IRF), public capital stock, Johansen Cointegration test, labor productivity, KPSS no unit root test, single-break (Zivot-Andrews test), Variance Decompositions (VDCs), and vector error correction model (VECM). |
| JEL: | C22 O40 O54 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:tri:wpaper:2601 |
| By: | Mounir Atlassi (University Mohamed V, Rabat); Mohamed Karim (University Mohamed V, Rabat); Ilham Dkhissi (BEAR Lab - RBS - UIR - BEAR Lab - Rabat Business School - International University of Rabat) |
| Abstract: | This paper examines the dynamics of tax revenues and fiscal structure in Morocco over the period 2000-2024, with a particular focus on the temporal behavior of major tax components and their adjustment to revenue fluctuations. Building on the literature on fiscal dynamics in emerging economies, the study emphasizes the role of tax composition in shaping revenue stability. The empirical analysis relies on autoregressive integrated moving average (ARIMA) models. Unit root tests are first conducted to determine the stochastic properties of the series, followed by model identification, estimation, and diagnostic validation. The results indicate that all tax series are integrated of order one, suggesting persistent shocks and long-lasting effects. The findings also reveal heterogeneous dynamic patterns across tax instruments: personal income tax is sensitive to short-term fluctuations, corporate income tax exhibits dynamics consistent with a highly cyclical tax base, while value added tax displays greater stability due to its broader base. These results highlight the central role of fiscal structure in shaping revenue resilience. The paper contributes to the literature by showing that fiscal performance depends not only on the level of taxation, but also on the stochastic behavior and dynamic properties of its components. |
| Keywords: | revenue volatility, fiscal shocks, tax composition, cyclical dynamics, fiscal resilience, fiscal resilience cyclical dynamics revenue volatility fiscal shocks tax composition C22 H21 H23 E62 |
| Date: | 2026–05–29 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05637487 |
| By: | Cimadomo, Jacopo; Giannone, Domenico; Lenza, Michele; Monti, Francesca; Sokol, Andrej |
| Abstract: | We design a Bayesian Mixed-Frequency vector autoregression (VAR) model for fiscal monitoring, i.e., to nowcast the government deficit-to-GDP ratio in real time and provide a narrative for its dynamics. The model incorporates both monthly cash and quarterly accrual fiscal indicators, together with other high-frequency macroeconomic and financial variables, as well as real GDP and the GDP deflator. Our model produces timely monthly density nowcasts of the annual deficit ratio, while governments and official institutions generally only publish their point predictions bi-annually. Based on a database of real-time vintages of macroeconomic, financial and fiscal variables for Italy, we show that the nowcasts of the annual deficit to GDP ratio of our model are similarly or more accurate than those of the European Commission, depending on the month in which the nowcast is produced. Our scenario analysis compares the dynamics of the deficit ratio associated with a monetary and a typical recession, finding a more muted response in the latter case. |
| Keywords: | Nowcasting; Mixed-frequency; Monetary policy shock |
| JEL: | C11 E52 E62 E63 H68 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21160 |
| By: | Guglielmo Maria Caporale; Luis Alberiko Gil-Alana; Guillermo Perez Tellechea |
| Abstract: | This paper examines persistence in the real GDP growth rates of the US, UK and Japan. For this purpose, both univariate and multivariate parametric and semiparametric fractional integration methods are used. The results indicate cross-country heterogeneity. Specifically, in the case of the US and the UK the order of integration is close to 0, and the null hypothesis of short memory cannot be rejected for either country. By contrast, the order of integration is significantly positive in the case of Japan, the corresponding series exhibiting long memory with the effects of shocks being long-lived. A plausible explanation for the higher degree of persistence in the case of Japan is its demographic decline, rigid labour markets and entrenched corporate savings behaviour. These findings are robust to using different estimation methods. Impulse response analysis is also carried out to compare VAR and VARFI specifications. The results show that conventional VAR models may underestimate both the duration of domestic shocks and the persistence of cross-country transmission mechanisms. |
| Keywords: | real GDP, growth rates, long memory, fractional integration, multivariate models, persistence |
| JEL: | C22 C32 O40 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12781 |
| By: | Jordi Llorens-Terrazas; Mika Meitz |
| Abstract: | We propose a flexible framework for modeling the predictive distributions of nonlinear, possibly multivariate time series. Our approach expresses a general predictive distribution in an appropriate generative representation that is based on a folklore result from measure theoretic probability. This representation provides a direct simulation-based approximation to the predictive distribution, enabling straightforward computation of forecasts for the conditional mean and variance, fan charts, value at risk, expected shortfall, joint tail risks, and other quantities of interest. We estimate this generative representation using a version of conditional generative adversarial networks and provide a formal statistical analysis of estimation under weak temporal dependence. Specifically, estimation is expressed as a particular minimax problem and we establish consistency of its approximate solutions in Hausdorff distance. The empirical relevance of the approach is illustrated using applications to equity returns, realized variance, and realized covariances. The proposed method is also computationally manageable, with estimation in our applications taking approximately one minute on a standard laptop. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.16773 |
| By: | Emre Yusuf; Ren Takahashi; Jayabrata Bhaduri |
| Abstract: | Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.15452 |