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on Econometric Time Series |
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Issue of 2026–02–02
twelve papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Boyao Wu; Jiti Gao; Deshui Yu |
| Abstract: | We consider a general class of dynamic network autoregressions for high-dimensional time series with network dependence, extending existing dynamic models by allowing for timevarying model coefficients, cross-sectionally dependent errors and a general network structure smoothly evolving along the time. A nonparametric local linear kernel method is proposed to estimate these time-varying coefficients involved, and a recursive-design bootstrap procedure is developed to construct valid confidence intervals for time-varying coefficients in the presence of cross-sectional dependent errors. We establish asymptotic properties for the proposed local–linear based estimator and the bootstrap procedure under mild conditions. Both the proposed estimation and bootstrap procedures are illustrated using simulated and two real datasets. Our work contributes to high-dimensional time series associated with network effects and sheds light on bootstrap inference for locally stationary processes. |
| Keywords: | cross-sectional dependence, dynamic network autoregression, high-dimensional time-series, MA(∞) representation |
| JEL: | C14 C31 C33 D85 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:msh:ebswps:2025-8 |
| By: | Nicolas Hardy; Dimitris Korobilis |
| Abstract: | We revisit macroeconomic time-varying parameter vector autoregressions (TVP-VARs), whose persistent coefficients may adapt too slowly to large, abrupt shifts such as those during major crises. We explore the performance of an adaptively-varying parameter (AVP) VAR that incorporates deterministic adjustments driven by observable exogenous variables, replacing latent state innovations with linear combinations of macroeconomic and financial indicators. This reformulation collapses the state equation into the measurement equation, enabling simple linear estimation of the model. Simulations show that adaptive parameters are substantially more parsimonious than conventional TVPs, effectively disciplining parameter dynamics without sacrificing flexibility. Using macroeconomic datasets for both the U.S. and the euro area, we demonstrate that AVP-VAR consistently improves out-of-sample forecasts, especially during periods of heightened volatility. |
| Keywords: | Bayesian VAR; time-varying parameters; stochastic volatility; macroeconomic forecasting; uncertainty. |
| JEL: | C11 C32 C53 E32 E37 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:gla:glaewp:2025_12 |
| By: | Hasan Fallahgoul; Jiti Gao |
| Abstract: | This paper introduces a theoretically robust framework for conditional mean estimation associated with maximum likelihood estimation (MLE) in state space models with nonstationary time series, integrating the classical Kalman filter with Bayesian inference. We propose a dierence-based approach using optimally designed summary statistics from observable data, overcoming the intractability of traditional Kalman filter statistics reliant on latent states. Our formulation creates a direct mapping between feasible statistics and structural parameters, enabling clean separation between state dynamics and measurement noise. Under mild regularity conditions, we prove the consistency and asymptotic normality of the estimators, achieving the Cram´er–Rao lower bound for eciency. The methodology extends to non-Gaussian innovations with finite moments, ensuring robustness. Monte Carlo approximations preserve asymptotic eciency under controlled sampling rates, while finite sample bounds and robustness to model misspecification and data contamination confirm reliability. These theoretical advances are complemented by a comprehensive simulation study demonstrating superior performance compared to conventional approaches. These results advance the theoretical foundations of state space modelling, providing a statistically ecient and computationally feasible alternative to conventional approaches. |
| Keywords: | estimation theory, Kalman filter, nonstationarity, resampling technique |
| JEL: | C11 C15 C21 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:msh:ebswps:2025-7 |
| By: | Dimitris Korobilis |
| Abstract: | I introduce a high-dimensional Bayesian vector autoregressive (BVAR) framework designed to estimate the effects of conventional monetary policy shocks. The model captures structural shocks as latent factors, enabling computationally efficient estimation in high-dimensional settings through a straightforward Gibbs sampler. By incorporating time variation in the effects of monetary policy while maintaining tractability, the methodology offers a flexible and scalable approach to empirical macroeconomic analysis using BVARs, well-suited to handle data irregularities observed in recent times. Applied to the U.S. economy, I identify monetary shocks using a combination of high-frequency surprises and sign restrictions, yielding results that are robust across a wide range of specification choices. The findings indicate that the Federal Reserve’s influence on disaggregated consumer prices fluctuated significantly during the 2022–24 high-inflation period, shedding new light on the evolving dynamics of monetary policy transmission. |
| Keywords: | Disaggregated consumer prices; Latent factors; High-dimensional Bayesian VAR; Time-varying parameters; Sign restrictions; High frequency data |
| JEL: | C11 C32 C55 E31 E52 E58 E66 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:gla:glaewp:2025_09 |
| By: | Daniel J. Lewis; Karel Mertens |
| 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: | 2026–01–12 |
| URL: | https://d.repec.org/n?u=RePEc:fip:feddwp:102343 |
| By: | Harrison Katz |
| Abstract: | Compositional time series, vectors of proportions summing to unity observed over time, frequently exhibit structural breaks due to external shocks, policy changes, or market disruptions. Standard methods either ignore such breaks or handle them through ad-hoc dummy variables that cannot extrapolate beyond the estimation sample. We develop a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism that captures structural breaks through three interpretable parameters: a unit direction vector specifying which components gain or lose share, an amplitude controlling the magnitude of redistribution, and a logistic gate governing the timing and speed of transition. The model preserves compositional constraints by construction, maintains innovation-form DARMA dynamics for short-run dependence, and produces coherent probabilistic forecasts during and after structural breaks. We establish that the directional shift corresponds to geodesic motion on the simplex and is invariant to the choice of ILR basis. A comprehensive simulation study with 400 fits across 8 scenarios demonstrates that when the shift direction is correctly identified (77.5% of cases), amplitude and timing parameters are recovered with near-zero bias, and credible intervals for the mean composition achieve nominal 80% coverage; we address the sign identification challenge through a hemisphere constraint. An empirical application to fee recognition lead-time distributions during COVID-19 compares baseline, fixed-effects, and intervention specifications in rolling forecast evaluation, demonstrating the intervention model's superior point accuracy (Aitchison distance 0.83 vs. 0.90) and calibration (87% vs. 71% coverage) during structural transitions. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.16821 |
| By: | Jonas E. Arias; Juan F. Rubio-Ramirez; Minchul Shin |
| Abstract: | We develop a new algorithm for inference in structural vector autoregressions (SVARs) identified with sign restrictions that can accommodate big data and modern identification schemes. The key innovation of our approach is to move beyond the traditional accept-reject framework commonly used in sign-identified SVARs. We show that embedding the elliptical slice sampling within a Gibbs sampler can deliver dramatic gains in computational speed and render previously infeasible applications tractable. To illustrate the approach in the context of sign-identified SVARs, we use a tractable example. We further assess the performance of our algorithm through two applications: a well-known small-SVAR model of the oil market featuring a tight identified set, and a large SVAR model with more than ten shocks and 100 sign restrictions. |
| Keywords: | large structural vector autoregressions; sign restrictions; elliptical slice sampling |
| JEL: | C32 |
| Date: | 2025–01–22 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedpwp:102347 |
| By: | Anthony Britto |
| Abstract: | Time series often exhibit non-ergodic behaviour that complicates forecasting and inference. This article proposes a likelihood-based approach for estimating ergodicity transformations that addresses such challenges. The method is broadly compatible with standard models, including Gaussian processes, ARMA, and GARCH. A detailed simulation study using geometric and arithmetic Brownian motion demonstrates the ability of the approach to recover known ergodicity transformations. A further case study on the large macroeconomic database FRED-QD shows that incorporating ergodicity transformations can provide meaningful improvements over conventional transformations or naive specifications in applied work. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.11237 |
| By: | Aknouche, Abdelhakim; Dimitrakopoulos, Stefanos; Rabehi, Nadia |
| Abstract: | A general class of seasonal autoregressive integrated moving average models (SARIMA), whose period is an independent and identically distributed random process valued in a finite set, is proposed. This class of models is named random period seasonal ARIMA (SARIMAR). Attention is focused on three subsets of them: the random period seasonal autoregressive (SARR) models, the random period seasonal moving average (SMAR) models and the random period seasonal autoregressive moving average (SARMAR) models. First, the causality, invertibility, and autocovariance shape of these models are revealed. Then, the estimation of the model components (coefficients, innovation variance, probability distribution of the period, (unobserved) sample-path of the random period) is carried out using the Expectation-Maximization algorithm. In addition, a procedure for random elimination of seasonality is developed. A simulation study is conducted to assess the estimation accuracy of the proposed algorithmic scheme. Finally, the usefulness of the proposed methodology is illustrated with two applications about the annual Wolf sunspot numbers and the Canadian lynx data. |
| Keywords: | EM algorithm, irregular seasonality, non-integer period, random period, random period seasonal ARMA models. |
| JEL: | C10 C18 C22 |
| Date: | 2025–12–06 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:127200 |
| By: | Alessio Brini; Ekaterina Seregina |
| Abstract: | We propose Mixed-Panels-Transformer Encoder (MPTE), a novel framework for estimating factor models in panel datasets with mixed frequencies and nonlinear signals. Traditional factor models rely on linear signal extraction and require homogeneous sampling frequencies, limiting their applicability to modern high-dimensional datasets where variables are observed at different temporal resolutions. Our approach leverages Transformer-style attention mechanisms to enable context-aware signal construction through flexible, data-dependent weighting schemes that replace fixed linear combinations with adaptive reweighting based on similarity and relevance. We extend classical principal component analysis (PCA) to accommodate general temporal and cross-sectional attention matrices, allowing the model to learn how to aggregate information across frequencies without manual alignment or pre-specified weights. For linear activation functions, we establish consistency and asymptotic normality of factor and loading estimators, showing that our framework nests Target PCA as a special case while providing efficiency gains through transfer learning across auxiliary datasets. The nonlinear extension uses a Transformer architecture to capture complex hierarchical interactions while preserving the theoretical foundations. In simulations, MPTE demonstrates superior performance in nonlinear environments, and in an empirical application to 13 macroeconomic forecasting targets using a selected set of 48 monthly and quarterly series from the FRED-MD and FRED-QD databases, our method achieves competitive performance against established benchmarks. We further analyze attention patterns and systematically ablate model components to assess variable importance and temporal dependence. The resulting patterns highlight which indicators and horizons are most influential for forecasting. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.16274 |
| By: | Kim Christensen; Ulrich Hounyo; Mark Podolskij |
| Abstract: | In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely sampled jump-diffusion process are available. The test is then based on asset returns, which are deflated by the seasonal component and therefore homoskedastic under the null. To construct our test statistic, we extend the concept of pre-averaged bipower variation to a general It\^o semimartingale setting via a truncation device. We prove a central limit theorem for this statistic and construct a positive semi-definite estimator of the asymptotic covariance matrix. The $t$-statistic (after pre-averaging and jump-truncation) diverges in the presence of stochastic volatility and has a standard normal distribution otherwise. We show that replacing the true diurnal factor with a model-free jump- and noise-robust estimator does not affect the asymptotic theory. A Monte Carlo simulation also shows this substitution has no discernable impact in finite samples. The test is, however, distorted by small infinite-activity price jumps. To improve inference, we propose a new bootstrap approach, which leads to almost correctly sized tests of the null hypothesis. We apply the developed framework to a large cross-section of equity high-frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility, but important sources of heteroskedasticity remain present in the data. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.16613 |
| By: | Marc Wildi |
| Abstract: | Forecasting entails a complex estimation challenge, as it requires balancing multiple, often conflicting, priorities and objectives. Traditional forecast optimization criteria typically focus on a single metric -- such as minimizing the mean squared error (MSE) -- which may overlook other important aspects of predictive performance. In response, we introduce a novel approach called the Smooth Sign Accuracy (SSA) framework, which simultaneously considers sign accuracy, MSE, and the frequency of sign changes in the predictor. This addresses a fundamental trade-off (the so-called accuracy-smoothness (AS) dilemma) in prediction. The SSA criterion thus enables the integration of various design objectives related to AS forecasting performance, effectively generalizing conventional MSE-based metrics. We further extend this methodology to accommodate non-stationary, integrated processes, with particular emphasis on controlling the predictor's monotonicity. Moreover, we demonstrate the broad applicability of our approach through an application to, and customization of, established business cycle analysis tools, highlighting its versatility across diverse forecasting contexts. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.06547 |