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on Econometric Time Series |
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Issue of 2026–06–15
ten papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Todd E. Clark; Florian Huber; Gary Koop |
| Abstract: | This paper proposes a vector autoregression augmented with nonlinear factors that are modeled nonparametrically using regression trees. There are four main advantages of our model. First, modeling potential nonlinearities nonparametrically lessens the risk of misspecification. Second, the use of factor methods ensures that departures from linearity are modeled parsimoniously. In particular, they exhibit functional pooling where a small number of nonlinear factors are used to model common nonlinearities across variables. Third, Bayesian computation using MCMC is straightforward even in very high-dimensional models, allowing for efficient, equation-by-equation estimation, thus avoiding computational bottlenecks that arise in popular alternatives such as the time-varying parameter VAR. Fourth, existing methods for identifying structural economic shocks in linear factor models can be adapted for the nonlinear case in a straightforward fashion using our model. Exercises involving artificial and macroeconomic data illustrate the properties of our model and its usefulness for forecasting and structural economic analysis. |
| Keywords: | Nonparametric VAR; nonlinear factor model; regression trees; macroeconomic forecasting; scenario analysis |
| JEL: | C11 C32 C53 |
| Date: | 2026–06–02 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedcwq:103355 |
| By: | Kpante Emmanuel Gnandi (INSA Toulouse); Fredy Pokou (MRE, CRIStAL); Jules Sadefo Kamdem (MRE) |
| Abstract: | Transition-related financial markets are increasingly exposed to abrupt repricing episodes, elevated volatility, and heterogeneous macro-financial shocks. Under such conditions, conventional Gaussian-linear forecasting frameworks may provide an incomplete representation of the dependence structure linking fossil-energy, renewable-energy, technology, and utility-sector assets. This paper investigates whether transition-related financial returns exhibit residual non-linear predictability after controlling for heavy-tailed multivariate linear dynamics. To address this question, we develop a hybrid forecasting framework combining Student-t Vector Autoregressions with nonlinear recurrent residual learning architectures. The empirical analysis considers six major exchange-traded funds representing broad equity markets and key transition-sensitive sectors. The results reveal substantial departures from Gaussian-linear behavior, including excess kurtosis, volatility clustering, and remaining nonlinear dependence after econometric filtering. Out-of-sample forecasting experiments show that the proposed framework consistently improves predictive accuracy relative to conventional VAR models, standalone machine-learning methods, and alternative hybrid specifications. The forecasting gains become more pronounced during periods of macro-financial stress, particularly during the COVID-19 crisis and the Ukraine-related energy shock. Overall, the findings suggest that transition-related financial systems exhibit regime-sensitive and heavy-tailed predictive dynamics that are insufficiently captured by standard Gaussian-linear models alone. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.26890 |
| By: | Silvia Goncalves; Ana Maria Herrera; Lutz Kilian; Elena Peavento; Iones Kelanemer Holban |
| 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 $\sqrt{T}$-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. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.13519 |
| By: | Yuxin Tao; Feiyu Jiang; Xiaofeng Shao |
| Abstract: | Residual-based goodness-of-fit tests for parametric time-series models are often complicated by parameter-estimation effects, which can alter the limiting behavior of diagnostic statistics. We propose a sample-splitting generalized spectral test (in the spirit of Escanciano(2006)) for assessing conditional mean specification in linear and nonlinear time-series models. The procedure estimates the model parameter on a fitting subsample and constructs a generalized spectral Cramer-von Mises statistic from residuals computed on a checking/testing subsample. The statistic aggregates pairwise conditional mean restrictions over all lags and is therefore bandwidth-free and free of truncation-lag selection. Under mild regularity conditions and a score-alignment condition, the residual-based process has the same limiting null distribution as the infeasible oracle process based on the true errors. Although the resulting limiting law is still non-pivotal, it can be consistently approximated by a simple multiplier bootstrap that does not require generating bootstrap time series or re-estimating parameters. Such an oracle-equivalence property is in sharp contrast to the original full-sample test, for which parameter estimation contributes an additional first-order term to the limiting process, and requires re-estimating parameters in each bootstrapped sample. We further establish consistency of the proposed test against fixed alternatives and nontrivial power against local alternatives. Extensive simulations and real data analyses show that the proposed test controls size well, has comparable power, and delivers substantial computational savings in models where repeated estimation is costly. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.29315 |
| By: | Vicente Esteve (Universidad de Valencia, Spain); Nicola Rubino (Universidad de Valencia, Spain) |
| Abstract: | This paper investigates the long-run dynamics and sustainability of the Italian public debt-to-GDP ratio from 1861 to 2024. To address the presence of non-stationary volatility, we employ the recently de- veloped Time-Transformed Test methodology proposed by Kurozumi, Skorobotov, and Tsarev (2023). By utilizing the cumulative variance profile this approach homogenizes volatility across the time domain, en- suring the asymptotic validity of the STADF and GSTADF statistics and overcoming the size distortions inherent in standard recursive unit root tests. Our empirical findings confirm multiple explosive íbubbleí episodes in Italyís fiscal history, specifically identifying three critical periods of exuberance: the 1913 anticipatory wartime shock, the 1978-1998 structural imbalance, and the 2020 exogenous pandemic-induced spike. While the 1978-1998 episode represents a unique two-decade era of structural divergence sustained by high private savings and debt monetization, the 2020 episode is identified as a temporary yet sig- nificant systemic shock. The study demonstrates that accounting for the evolution of the variance profile is imperative for a reliable fiscal analysis, offering an early-warning benchmark for monitoring modern debt-stabilization rules and evaluating Italyís current fiscal resilience amidst rising debt projections for 2025-2026. |
| Keywords: | Public Debt Sustainability, Explosive Bubbles, Time-Varying Volatility, GSADF, Italian Economy, Variance Profile |
| JEL: | C12 C22 E62 H62 H63 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:eec:wpaper:2610 |
| By: | Joel M. David; Raffaella Giacomini; Xiyu Jiao; Weining Wang |
| Abstract: | State-dependent local projections (LPs) are widely used to estimate how responses to exogenous aggregate shocks vary as a function of observable state variables, yet their causal interpretation remains unclear. We show that this interpretation obtains under the sufficient condition that the conditional mean is linear in the aggregate shock at each horizon, and that this condition holds in a broad class of canonical micro–macro environments, including first-order perturbation solutions of heterogeneous-agent models and macro-finance models. Under this condition, LPs recover causal impulse responses without requiring specification of the full data-generating process. We further show that the causal interpretation of state-dependent LPs is robust to the choice of state variable. By contrast, commonly used linear interaction LPs generally fail to recover causal objects. We therefore develop a sieve-based nonparametric LP estimator that restores causal interpretation and delivers valid pointwise and uniform inference in micro–macropanels. Empirically, allowing for nonparametric state dependence materially changes both the pattern of heterogeneous firm investment responses and their aggregate implications for the transmission of monetary policy shocks |
| Date: | 2026–01–30 |
| URL: | https://d.repec.org/n?u=RePEc:bri:uobdis:26/829 |
| By: | Zhiruo Zhang; Firmin Doko Tchatoka; Qazi Haque |
| Abstract: | We develop a Bayesian framework that combines adaptive shrinkage with variable selection to address over-parameterisation and sparsity in high-dimensional panel vector autoregressions (PVARs). The proposed approach employs Laplace-based spike-and-slab priors to enable flexible modelling of dynamic cross-sectional interdependencies and unit-specific heterogeneity. Monte Carlo evidence shows that the method delivers improvements in estimation accuracy and forecasting performance relative to existing regularisation approaches. We illustrate its empirical relevance in two applications. The first investigates financial contagion in euro area sovereign bond markets, while the second examines international forecasting performance in a multi-country macroeconomic panel. The results highlight the benefits of adaptive, component-specific shrinkage for capturing heterogeneous spillover structures in complex panel systems. |
| Keywords: | dynamic interdependency, cross-sectional heterogeneity, Bayesian Lasso, variable selection, spike and slab prior, financial contagion |
| JEL: | C32 C54 C55 E17 F41 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-40 |
| By: | Jiaze Sun; Kelvin J. L. Koa; Ruiyang Ni; Yize Liu; Haonan Chen; Ke-Wei Huang |
| Abstract: | Financial forecasting is difficult due to low signal-to-noise ratios, latent factors, heavy tails, regime shifts, and jumps. Real-world benchmarks offer limited failure attribution: researchers can observe underperformance, but often cannot isolate why because mechanisms are unobservable and entangled. Real financial data reveal only one realized path, making it difficult to assess tail-risk calibration or data efficiency. We introduce FinStressTS, a mechanism-aware synthetic benchmark that links model behavior to controlled structural causes. FinStressTS comprises 30 diagnostic environments around six mechanism families: volatility clustering, multi-scale persistence, heavy-tailed shocks, regime switching, self-exciting jumps, and zero-inflated processes. We evaluate two tasks: point forecasting, using NMAE across five settings, and probabilistic forecasting, using CRPS under known data-generating mechanisms. We benchmark 15 models, from classical methods (HAR, VAR) to Transformer forecasters (PatchTST, iTransformer) and deep probabilistic architectures (DeepAR, TSFlow), and use learning curves to measure sample efficiency. Our evaluation reveals three insights. First, performance is mechanism-dependent: autoregressive and linear models are highly competitive, and often outperform Transformer-based models, in several volatility-, tail-, and jump-driven environments. Second, distributional alignment matters: parametric probabilistic models such as DeepAR calibrate well in stationary settings, while flexible models can help when distributions become multimodal or sparse. Third, neural models often require more data to match simple baselines, with larger gains mainly when learning latent regimes or complex distributions. FinStressTS provides an open framework for diagnosing failure modes and advancing risk-aware forecasting. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.03184 |
| By: | Pinjaman, Saizal |
| Abstract: | This document, A Simple Note on Augmented Autoregressive Distributed Lag Model (A-ARDL), provides a concise explanation of the Augmented ARDL (AARDL) approach introduced by Ronald McNown and colleagues. The note discusses the motivation behind AARDL, particularly its role in addressing weaknesses in the conventional ARDL bounds testing procedure when the dependent variable is stationary, I(0). It explains how the augmented framework helps distinguish genuine cointegration relationships from degenerate cases by introducing additional testing procedures on lagged independent variables. |
| Keywords: | Augmented ARDL, Long Run Relationship, Short Run Relationship, Cointegration |
| JEL: | C22 C32 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:341087 |
| By: | Ajay Kumar Verma; Jul Jon Ramirez General; Yvan Landry Ndzonde Fonkou |
| Abstract: | This study looks at the statistical properties and predictability using deep learning methods of the U.S. aggregate bond index in daily observations spanning 2018 to February 2026. We first establish that index levels are extremely persistent and consistent with unitroot behavior (Dickey and Fuller), while log returns are covariance-stationary with weak linear dependence and pronounced volatility clustering characteristic of ARCH-type processes (Engle; Bollerslev). Motivated by the trade-off between stationarity and information retention, we construct a "stationary but maximally persistent" representation via fractional differencing (Granger and Joyeux; Hosking) following the procedure of L\'opez de Prado, and evaluate shorthorizon forecast using two neural paradigms: (i) Multilayer Perceptrons (MLPs) trained on lagged vectors with joint lag-length and hyperparameter tuning (Hornik et al.; Rumelhart et al.); and (ii) Convolutional Neural Networks (CNNs) trained on Gramian Angular Field (GAF) image encodings (Wang and Oates). Empirically, MLPs match the strong naive persistence benchmark on levels, collapse toward near-zero forecasts on returns, and achieve the strongest incremental performance on the fractionally differenced series, where moderate dependence remains but unit-root drift is attenuated. In contrast, CNN-GAF models deliver consistently negative out-of-sample R 2 across all three representations. Overall, the results imply that, for short-horizon forecasting of broad bond indices, the primary determinant of predictive performance is the transformation of the series-its degree of stationarity and memory-rather than architectural complexity. Lag-based models remain competitive under persistence, while GAFbased CNNs are better suited to pattern-based tasks than to persistence-dominated next-step prediction. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.27977 |