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on Econometric Time Series |
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Issue of 2026–05–18
thirteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Victor Chernozhukov; Christian Hansen; Lingwei Kong; Weining Wang |
| Abstract: | Structural estimation in economics often makes use of models formulated in terms of moment conditions. While these moment conditions are generally well-motivated, it is often unknown whether the moment restrictions hold exactly. We consider a framework where researchers model their belief about the potential degree of misspecification via a prior distribution and adopt a quasi-Bayesian approach for performing inference on structural parameters. We provide quasi-posterior concentration results, verify that quasi-posteriors can be used to obtain approximately optimal Bayesian decision rules under the maintained prior structure over misspecification, and provide a form of frequentist coverage results. We illustrate the approach through empirical examples where we obtain informative inference for structural objects, allowing for substantial relaxations of the requirement that moment conditions hold exactly. |
| Date: | 2026–05–08 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:07/26 |
| By: | Qitong Chen; Shuwen Lai |
| Abstract: | This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process, specifically an adjusted-range normalizer for scalars and a matrix normalizer for vectors, our approach avoids direct estimation of the long-run covariance matrix. Consequently, it eliminates the need for the ad hoc bandwidth, kernel, and lag-truncation choices required by traditional methods. We establish the asymptotic theory for these statistics, deriving pivotal null limiting distributions and proving test consistency. Monte Carlo simulations show that the proposed tests effectively mitigate the finite-sample size distortions associated with traditional heteroskedasticity and autocorrelation consistent (HAC) methods, while retaining strong empirical power against conditional predictability alternatives. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.07404 |
| By: | Samuel Mod\'ee; Yushu Li; Sjur Westgaard; Stein Andreas Bethuelsen |
| Abstract: | This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under various specifications of the transition probability matrix. Especially, we extend the two-regime common-variance setting of the Generalized Autoregressive Score (GAS) model from (Bazzi et al., 2017) to the general $K$-regime case with regime-specific means and variances. Our study contains comprehensive Monte Carlo simulations and we developed an open-source R package, \texttt{multiregimeTVTP}, for data simulation and parameter estimation. We find that the regime means, variances, and transition probabilities are reliably recovered, whereas the TVTP driving coefficients are harder to identify. Another finding from our paper is that the GAS score coefficient appears to be statistically non-identifiable, due to a ridge in the joint likelihood surface $(\sigma^2, A)$. In addition, we find that one-step point forecasts are remarkably robust to TVTP misspecification, but filtered regime probabilities are not, so correct specification matters most for characterizing regime dynamics rather than short-horizon forecasting. An empirical application to U.S. Treasury zero-coupon yield changes at four maturities (1961-2024) shows that an exogenous specification driven by the lagged yield level dominates the constant and lagged-change models in fit, while the GAS specification fails to converge, with $\hat{A}$ collapsing to zero, reflecting the same identifiability issue observed in simulation. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.14976 |
| By: | Juan Diego Cafferata Salazar; Guglielmo Maria Caporale; Luis Alberiko Gil-Alana |
| Abstract: | This paper uses fractional integration and cointegration methods to examine the persistence and long-run relationship between the S&P 500 index and the nominal yield to maturity of 10-year US Treasury bonds (GS10) over the period from January 1954 to December 2024. The results indicate that both series are highly persistent and can be characterised as non-stationary processes with an order of integration close to 1. Granger causality tests imply unidirectional causality running from stock prices (S&P 500) to bond yields (GS10). Further, both standard and fractional cointegration tests indicate the existence of a long-run relationship between the two series. |
| Keywords: | persistence, fractional integration, cointegration, stock prices, bond yields |
| JEL: | C22 E43 G12 C32 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12649 |
| By: | Han Chen (College of Finance and Statistics, Hunan University); Yijie Fei (College of Finance and Statistics, Hunan University); Yiren Wang (College of Finance and Statistics, Hunan University); Jun Yu (Faculty of Business Administration, University of Macau) |
| Abstract: | Block correlation models have emerged as powerful tools for analyzing dependence in high-dimensional financial time series. Predetermined group assignments have recently been used to define block structures, but these approaches can suffer from statistical inefficiency. This paper introduces a novel block correlation matrix specification and employs an efficient likelihood-based k-means algorithm to estimate the underlying block structure. We demonstrate that both the optimal number of groups and the group memberships are consistently estimated. Furthermore, we establish the asymptotic distribution of the estimated correlations. Simulation studies reveal the strong performance of the proposed method in finite samples. Applying this method to U.S. stock return data, we find that it outperforms existing block-forming techniques. |
| Keywords: | Block correlation matrix; Group structure; Generalized Fisher transformation; k-means; Score-driven model |
| JEL: | C32 C38 C55 C58 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202639 |
| By: | Zhu, Xianghe; Yao, Qiwei |
| Abstract: | Traditional graph representations are insufficient for modelling real-world phenom ena involving multi-entity interactions, such as collaborative projects or protein complexes, necessitating the use of hypergraphs. While hypergraphs preserve the intrinsic nature of such complex relationships, existing models often overlook tem poral evolution in relational data. To address this, we introduce a first-order autore gressive (i.e. AR(1)) model for dynamic non-uniform hypergraphs. This is the first dynamic hypergraph model with provable theoretical guarantees, explicitly defining the temporal evolution of hyperedge presence through transition probabilities that govern persistence and change dynamics. This framework provides closed-form ex pressions for key probabilistic properties and facilitates straightforward maximum likelihood inference with uniform error bounds and asymptotic normality, along with a permutation-based diagnostic test. We also consider an AR(1) hypergraph stochastic block model (HSBM), where a novel Laplacian enables exact and effi cient latent community recovery via a spectral clustering algorithm. Furthermore, we develop a likelihood-based change-point estimator for the HSBM to detect struc tural breaks. The efficacy and practical value of our methods are comprehensively demonstrated through extensive simulation studies and compelling applications to a primary school interaction data set and the Enron email corpus, revealing insightful community structures and significant temporal changes. |
| Keywords: | dynamic hypergraphs; autoregressive process; higher-order interactions; dynamic stochastic block model; spectral clustering; change-point detection |
| JEL: | C1 |
| Date: | 2026–04–06 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:137673 |
| By: | Peter Reinhard Hansen; Chen Tong |
| Abstract: | The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations. The conditional expectation of the latent Gaussian component is governed by a redescending location score, so extreme observations are automatically discounted rather than propagated. This structure motivates the Gauss-Cauchy Convolution (GCC) filter for state-space models with Gaussian latent dynamics and heavy-tailed measurement errors. In an application to log realized volatility for the Technology Select Sector SPDR Fund, the GCC filter separates persistent latent variation from transient measurement noise and improves on Gaussian, Student-$t$, Huber, and related robust alternatives. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.01665 |
| By: | Marc-Oliver Pohle; Tanja Zahn; Sebastian Lerch |
| Abstract: | Skill scores, which measure the relative improvement of a forecasting method over a benchmark via consistent scoring functions and proper scoring rules, are a standard tool in forecast evaluation, yet their sampling uncertainty is rarely rigorously quantified. With modern forecasting applications being increasingly multivariate and involving evaluations across multiple horizons, variables, spatial locations, and forecasting methods, standard tools like the pairwise Diebold-Mariano forecast accuracy test or pointwise confidence intervals fail to account for the multiple comparison problem, leading to inflated Type I error rates and invalid joint inference. To address the lack of a coherent, statistically rigorous framework for quantifying uncertainty across these multi-dimensional evaluation problems, we introduce simultaneous confidence bands for expected scores and skill scores. Our framework provides a versatile tool for joint inference that is applicable to any forecast type from mean and quantile to full distributional forecasts. We develop a bootstrap implementation and show that our bands are valid under multivariate extensions of the classical Diebold-Mariano assumptions. We demonstrate the practical utility of the approach in two case studies by quantifying the benefits of time-varying parameter models for macroeconomic forecasting, and by comparing data-driven and physics-based models in probabilistic weather forecasting. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.03997 |
| By: | Martin Bruns; Helmut Luetkepohl; James McNeil (University of East Anglia, School of Economics; DIW Berlin and Freie Universitat Berlin; Department of Economics, Dalhousie University) |
| Abstract: | Several recent studies consider a set of proxies to identify different monetary policy shocks for different regions in the world. We show that the way the proxies are used to identify the monetary policy shocks may lead to correlated shocks and dubious structural analysis and we demonstrate how to overcome the problem of correlated shocks. We illustrate that, if correlated shocks are used in applied studies, key statistics of interest such as impulse responses and forecast error variance decompositions can be severely distorted and we consider bench- mark studies on monetary policy in the euro area (EA), the US and the UK to demonstrate the problems. |
| Keywords: | Structural vector autoregression; proxy VAR; GMM; correlated structural shocks |
| Date: | 2026–05–05 |
| URL: | https://d.repec.org/n?u=RePEc:dal:wpaper:daleconwp2026-01 |
| By: | Daniel Andrew Coulson; David S. Matteson; Martin T. Wells |
| Abstract: | Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional difficulty is summarizing the estimated evolving dependence structure for downstream decision-making tasks. We propose a Bayesian approach based on a low-rank factor representation, with latent states evolving under a dynamic shrinkage prior and observation errors following a multivariate factor stochastic volatility model. This specification allows locally adaptive regularization of the estimated correlation structure over time and informative uncertainty quantification. We establish, to our knowledge, a first-of-its-kind posterior contraction result for dynamically regularized Bayesian models, showing contraction around the true model parameters at an explicit rate under averaged Hellinger distance. To summarize the estimated correlation matrices, we build on the information-theoretic concept of total correlation to obtain a scalar measure of cross-sectional dependence. Simulation studies show improved accuracy and responsiveness relative to competing methods in a range of challenging scenarios. We then apply our method to monitoring the correlation evolution of equity portfolios during periods of financial market stress, providing an ex post framework for assessing the changing benefits of diversification in backtesting analyses. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.06818 |
| By: | Laurent Ferrara (SKEMA Business School, UniCA - Université Côte d'Azur); Aikaterini Karadimitropoulou (Department of Economics, University of Piraeus); Athanasios Triantafyllou (Audencia Business School) |
| Abstract: | We investigate the macroeconomic effects of commodity price uncertainty by explicitly accounting for comovement across commodity markets. Using quarterly realized volatilities of major agricultural, metals, and energy commodity prices, we estimate a hierarchical dynamic factor model that decomposes uncertainty into a global component, common to all commodities, and group-specific components capturing sectoral uncertainty. The estimated uncertainty factors are then embedded into country-specific Structural VAR models to assess the dynamic macroeconomic responses to uncertainty shocks through impulse response functions. We focus in particular on business investment and exports across a panel of advanced and emerging economies. Our results show that a global commodity price uncertainty shock generates sizable and persistent recessionary effects on investment and trade worldwide. Benchmark comparisons indicate that this global commodity uncertainty shock produces larger and more persistent macroeconomic contractions than standard uncertainty measures. Importantly, we show that, once global uncertainty is accounted for, commodity-specific uncertainty shocks exhibit differentiated effects. Increases in agricultural and metals price uncertainty lead to contractionary outcomes, whereas energy-specific uncertainty shocks generate positive short-run responses in investment and exports. These findings provide new empirical evidence that oil price uncertainty can be expansionary when it reflects sector-specific dynamics rather than global demand uncertainty. Overall, our framework offers a novel way to disentangle "bad" and "good" commodity price uncertainty. |
| Keywords: | Commodity prices, uncertainty shocks, comovement, recessionary effects, positive macroeconomic impact |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05607366 |
| By: | Diego Vásquez-Escobar |
| Abstract: | Este estudio caracteriza la dinámica del ciclo económico colombiano desde el enfoque de ciclo de crecimiento mediante herramientas que fortalecen la anticipación y el diagnóstico para la política económica. Se construye un índice de difusión agregado cíclico (IDA*) a partir de componentes cíclicos wavelet de 41 series usando el filtro biortogonal 17/11, y se fechan las fases de mayores brechas respecto a la tendencia mediante el algoritmo no paramétrico CFEAT, adecuado para series sin tendencia y centradas en cero. La descomposición multiescala separa oscilaciones de alta frecuencia, cíclicas y tendenciales, y describe cada episodio en términos de duración, amplitud, energía y persistencia, aportando insumos para la vigilancia temprana y la calibración temporal de la política macroeconómica. Los resultados muestran que las cronologías de crecimiento del PIB y del IDA* registran contracciones más largas y expansiones más cortas que las cronologías clásicas en niveles, y que el IDA* anticipa el componente cíclico del PIB. Además, las fases 1987–1989 (IDA*) y 1990–1993 (PIB), ausentes en la cronología clásica, exhiben persistencia bajo la descomposición multiescala. Finalmente, la ausencia de evidencia de dependencia de duración indica que episodios pico-valle prolongados —como el del PIB de 14 trimestres— no son improbables. En conjunto, los hallazgos introducen hechos nuevos y fortalecen la anticipación macroeconómica. ***ABSTRACT: This study characterizes the dynamics of the Colombian business cycle from a growth cycle perspective using techniques not previously applied in the national literature and directly relevant for macroeconomic monitoring and policy design. A cyclic aggregate diffusion index (IDA*) is constructed from the wavelet based cyclical components of 41 series using the biorthogonal 17/11 multiresolution filter, and the phases of largest deviations from trend are dated using the nonparametric CFEAT algorithm, which requires detrended and mean centered series. The multiscale decomposition separates high frequency noise, cyclical oscillations, and trend movements, providing an anatomy of each episode in terms of duration, amplitude, energy, and persistence, and offering inputs for early warning surveillance and timely policy calibration. The results show that the growth cycle chronologies of GDP and IDA* display longer contractions and shorter expansions than their classical level based counterparts, and that IDA* systematically anticipates the cyclical component of GDP. Moreover, the 1987–1989 (IDA*) and 1990–1993 (GDP) phases—absent from the classical chronology—exhibit clear persistence under the multiscale decomposition. Finally, the absence of duration dependence indicates that prolonged episodes—such as the 14 quarter GDP peak to trough—cannot be ruled out. Overall, the findings introduce new stylized facts and strengthen macroeconomic diagnostic and anticipatory capacity. |
| Keywords: | Ciclo de crecimiento, Wavelet multirresolución (MRA), Cronología económica (CFEAT), Índice de Difusión Agregado (IDA*), Datación del ciclo económico, Growth cycle, Multiresolution wavelet analysis (MRA), Business cycle dating (CFEAT), Aggregate diffusion index (IDA*), Business cycle chronology |
| JEL: | C22 C32 C43 E27 E32 E44 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:bdr:borrec:1352 |
| By: | Simon Scheidegger |
| Abstract: | This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.14493 |