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on Econometric Time Series |
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Issue of 2026–08–10
nineteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Gonzalez-Casasus, Oriol; Schorfheide, Frank |
| Abstract: | VARs are often estimated with Bayesian techniques to cope with model dimensionality. The posterior means define a class of shrinkage estimators, indexed by hyperparameters that determine the relative weight on maximum likelihood estimates and prior means. In a Bayesian setting, it is natural to choose these hyperparameters by maximizing the marginal data density. However, this is undesirable if the VAR is misspecified. In this paper, we derive asymptotically unbiased estimates of the multi-step forecasting risk and the impulse response estimation risk to determine hyperparameters in settings where the VAR is (potentially) misspecified. The proposed criteria can be used to jointly select the optimal shrinkage hyperparameter, VAR lag length, and to choose among different types of multi-step-ahead predictors; or among IRF estimates based on VARs and local projections. The selection approach is illustrated in a Monte Carlo study and an empirical application. |
| Keywords: | Forecasting; Local projections; Model misspecification; Shrinkage estimation |
| JEL: | C11 C32 C52 C53 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19915 |
| By: | Mark W. Watson |
| Abstract: | The persistent surge in U.S. inflation that began in 2021 caught forecasters and policymakers by surprise. The 2021 inflation shocks were viewed as transitory, not persistent, leading to large forecast errors in late 2021 and 2022. This paper asks whether time series models – using only data on current and past inflation, but incorporating stochastic volatility and exhibiting time-varying persistence – performed better. Univariate models, using real-time data, did not. Multivariate models, incorporating sectoral inflation measures, did. |
| JEL: | C32 E37 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35435 |
| By: | Nathan Schor; Minchul Shin |
| Abstract: | We introduce ForeComp, an R package for comparing predictive accuracy using Diebold–Mariano type tests of equal predictive ability with standard and fixed-smoothing inference. The package provides a common interface for loss-differential based testing and includes Plot Tradeoff, a visual diagnostic for bandwidth sensitivity and the size–power tradeoff. We illustrate the toolkit with Survey of Professional Forecasters applications and Monte Carlo evidence on finite-sample performance. |
| Keywords: | forecast comparison; Diebold–Mariano test; fixed-b asymptotics; fixed-m asymptotics; long-run variance estimation; R package |
| JEL: | C12 C22 C52 C53 |
| Date: | 2026–08–04 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedpwp:103596 |
| By: | A. Monta\~n\'es; E. Ruiz |
| Abstract: | Dynamic Factor Models (DFMs) are popular to reduce dimensionality being customary in the empirical analysis of large systems of macroeconomic and/or financial variables. In this context, the common underlying factors and their loadings are often extracted using Principal Components (PC), which are consistent and asymptotically normal under very general conditions. Consequently, inference on the factor loadings, which is crucial for the correct interpretation of the underlying factors, is often based on their asymptotic distribution with the limit covariance matrix of the loadings consistently estimated using HAC estimators. In this paper, we analyse the performance of the finite sample asymptotic approximation when constructing confidence intervals and testing about estimated PC loadings. We show that this approximation is seriously affected when the cross-sectional dimension is not large enough. We propose using HAR inference and a subsampling procedure to correct the MSE of the loadings to take into account the uncertainty associated with the estimation of the covariance matrix and of the factors, respectively. The relevance of the results is illustrated in an empirical analysis of economic convergence among the US states. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.12568 |
| 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: \emph{high dimensionality}, \emph{nonstationarity}, and \emph{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: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.14279 |
| By: | Sara Casella; Jesús Fernández-Villaverde; Stephen Hansen; Ryohei Oishi; Minchul Shin |
| Abstract: | Standard macroeconomic data do not cleanly separate the systematic and nonsystematic components of monetary policy. We show that incorporating unstructured text data into the structural estimation of a DSGE model can sharpen this distinction. We augment a standard state-space model with a non-core measurement block that links structural shocks to time series derived from FOMC transcripts, using a spike-and-slab prior to let the data select which series are informative. In a medium-scale New Keynesian model for the U.S., incorporating text improves predictive performance and materially alters structural inference: the new model estimates a lower response of the policy rate to inflation, higher price stickiness and lower price indexation, implying a flatter and less backward-looking price Phillips curve. |
| Keywords: | unstructured data; text as data; DSGE models; spike-and-slab priors; monetary policy; Phillips curve; FOMC transcripts |
| Date: | 2026–07–31 |
| URL: | https://d.repec.org/n?u=RePEc:fip:feddwp:103591 |
| By: | Inoue, Atsushi; Kilian, Lutz |
| Abstract: | Some studies have expressed concern that the Gaussian-inverse Wishart-Haar prior typically employed in estimating sign-identified VAR models may be unintentionally informative about the implied prior for the structural impulse responses. We discuss how this prior may be reported and make explicit what impulse response priors a number of recently published studies specified, allowing the readers to decide whether they are comfortable with this prior. We discuss what features to look for in this prior in the absence of specific prior information about the responses, building on the notion of weakly informative priors in Gelman et al. (2013), and in the presence of such information. Our empirical examples illustrate that the Gaussian-inverse Wishart-Haar prior need not be unintentionally informative about the impulse responses. Moreover, even when it is, there are empirically verifiable conditions under which this fact becomes immaterial for the substantive conclusions. |
| JEL: | C32 C52 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20159 |
| By: | Hauzenberger, Niko; Marcellino, Massimiliano; Pfarrhofer, Michael; Stelzer, Anna |
| Abstract: | We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use Gaussian processes (GPs) and compress the input space with structured and unstructured MI-DAS variants. This yields several versions of GP-MIDAS with distinct properties and implications, which we evaluate in short-horizon now- and forecasting exercises with both simulated data and data on quarterly US output growth and inflation in the GDP deflator. Our proposed framework leverages macroeconomic Big Data in a computationally efficient way and offers gains in predictive accuracy along several dimensions. |
| JEL: | C11 C22 C53 E31 E37 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19965 |
| By: | Jonas E. Arias; Juan F. Rubio-Ramirez; Daniel F. Waggoner |
| Abstract: | The results of nearly 100 prominent studies in empirical macroeconomics have been called into question by Baumeister and Hamilton (2018). We show that their concern about distributional asymmetry for a typical question of interest under a uniform prior with respect to the Haar measure is actually driven by an unacknowledged sign restriction. We also demonstrate that such a prior induces symmetric prior distributions over individual impulse responses conditional on the reduced-form parameters, or more generally when the prior over the reduced-form covariance matrix rules out correlation among the residuals, as in the typical implementation of the Minnesota prior. Furthermore, we provide a theory for avoiding the pitfalls of Baumeister and Hamilton’s critique. Key to our theory is a proposition establishing that any restriction can be decomposed into three types: scale, label, and economic. We use this theory to develop an algorithm for inference based on the unit modulus normalization that tackles a practical problem commonly faced by users of Bayesian SVAR methods. |
| Keywords: | structural vector autoregressions; unit modulus normalization |
| JEL: | C11 C32 |
| Date: | 2026–07–22 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedpwp:103578 |
| By: | Chang, Jinyuan; Du, Yue; Huang, Guanglin; Yao, Qiwei |
| Abstract: | We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method (J. R. Stat. Soc. Ser. B. Stat. Methodol. 85 (2023) 127–148) for which the convergence rates of the associated estimators may suffer from small eigengaps as the asymptotic theory is based on some matrix perturbation analysis, the proposed new method enjoys faster convergence rates which are free from any eigengaps. It achieves this by turning the problem into a joint diagonalization of several matrices whose elements are determined by a basis of a linear system, and by choosing the basis carefully to avoid near colinearity (see Proposition 5 and Section 4.3). Furthermore, unlike the generalized eigenanalysis-based method which requires the two factor loading matrices to be full-ranked, the proposed new method can handle rank-deficient factor loading matrices. Illustration with both simulated and real matrix time-series data shows the advantages of the proposed new method. |
| Keywords: | CP-decomposition;dimension-reduction;matrix time series;non-orthogonal joint diagonalization;and phrases. CP-decomposition;nonorthogonal joint diagonalization;dimension reduction |
| JEL: | C1 |
| Date: | 2026–06–30 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:130774 |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Dingli Wang (University of California, Riverside) |
| Abstract: | Risk managers often work with a fitted forecasting model they cannot replace even when its tail forecasts need adjustment. We propose a median-anchored rule that multiplies the distances from the fitted median to Value-at-Risk (VaR) and Expected Shortfall (ES) by a common positive multiplier. The rule preserves VaR--ES ordering, and minimizing VaR check loss gives a closed-form weighted-quantile estimator. We establish consistency, give an asymptotic distribution under high-level conditions accounting for baseline estimation, and derive a VaR coverage-error bound at the forecast origin. When the same multiplier correctly adjusts both VaR and ES, the adjusted pair has lower conditional zero-homogeneous Fissler--Ziegel (FZ0) risk at that origin. Monte Carlo experiments examine this condition and several forms of misspecification. In rolling S&P~500 forecasts the adjustment lowers FZ0 loss in all four GARCH cells, each pairwise significant, with the largest and most robust gain, 10.4%, for Gaussian GARCH at the 1% tail; the 5% gains do not survive the most conservative family-wise adjustments. A quantile-regression baseline marks the boundary: when the fitted tail is already flexible, one multiplier adds little. Filtered historical simulation quantifies what standardized residuals and conditional scales add when available. |
| Keywords: | Backtesting; Elicitability; Fissler--Ziegel Score; Forecast Evaluation; Model Risk; Quantile Regression |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:ucr:wpaper:202604 |
| By: | Sankalp Gilda |
| Abstract: | Finance, sensing, and demand streams violate the exchangeability that IID conformal prediction and the IID bootstrap assume, and existing libraries implement either a general resampling engine or conformal calibration without the other. tsbootstrap provides block, residual, sieve, and wild resampling, classical bootstrap confidence intervals, and adaptive conformal calibrators (EnbPI, ACI, NexCP, AgACI) through a single typed API in which a specification object selects each method. In a controlled coverage study the IID bootstrap undercovers sharply under dependence; dependence-aware methods reduce the coverage deficit, the sieve nearest to nominal under short-memory linear dependence. On the shared fixed-statistic path a compiled backend runs several times faster than arch, and a streaming reduce avoids materializing the $O(Bn)$ replicate tensor, limiting peak extra memory to $O(B)$ for the statistic array. The software is MIT licensed (v0.6.1). |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.06690 |
| By: | Xinxian Chen; Peter Reinhard Hansen; Chen Tong |
| Abstract: | We propose the Split-Session Cluster GARCH model for heavy-tailed multivariate dependence among asset returns decomposed into overnight and intraday components. The model uses convolution-$t$ distributions to allow tail behavior to differ across clusters defined by trading sessions and, within each session, by economic sectors. It also accommodates block-structured conditional correlation matrices, preserving parsimony and scalability in high-dimensional settings. The resulting likelihood remains tractable and yields a score-driven specification for dynamic correlations. We apply the model to U.S. equity returns in six-asset and 100-asset applications. The results reveal pronounced tail heterogeneity between overnight and intraday returns. Model comparisons show that session-specific tail parameters substantially improve fit relative to a common multivariate-$t$ specification, while sector-level tail partitioning delivers additional gains concentrated mainly in the overnight component. In the 100-asset application, asset-level tail heterogeneity delivers the strongest out-of-sample likelihood and global minimum-variance (GMV) portfolio performance. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.03669 |
| By: | Jushan Bai; Peng Wang |
| Abstract: | We develop a factor-model framework for causal inference in panels with policy interventions. Treatment effects are represented as structural changes in treated units' exposure to latent common shocks and, in extensions, changes in the factor process itself. The approach does not impose the standard parallel-trends restriction, accommodates one or many treated units, and targets systematic effects when unit-time idiosyncratic effects are not point identified. We provide estimation and inference under both fixed and treatment-dependent factor processes. Simulations show coverage close to nominal levels. In applications to California tobacco control and German reunification, the method produces estimates broadly consistent with synthetic control while delivering formal confidence intervals. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.29691 |
| By: | Daniele Angelini |
| Abstract: | Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence, because the associated Kolmogorov--Smirnov (KS) statistic undergoes a phase transition when $H>1/2$. In this regime, the classical limit collapses to a non-functional absolute Gaussian law and finite-sample convergence becomes severely distorted. This paper introduces a regime-adaptive KS/GL--KS framework based on the discrete Gr\"{u}nwald--Letnikov (GL) fractional derivative. The GL filter removes the low-frequency long-memory singularity while preserving the finite-dimensional $H$-self-similarity needed for distributional identification. We derive the filtered empirical-process limit, prove consistency and local asymptotic behavior of the resulting Hurst estimator, and validate the method through Monte Carlo simulations. Financial applications to realized volatility and equity index prices show how the procedure detects rough volatility and persistent, anti-persistent, or efficient market states. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.27932 |
| By: | O’Neill, Eoghan; Velasco, Sofia |
| Abstract: | The question of how oil supply news shocks transmit to real activity, financial conditions, and regional labor markets is back at the center of the macroeconomic research agenda. To answer this question, we introduce the Factor Bayesian Additive Regression Tree (FABART) model, a nonlinear factor-augmented vector autoregression model, and apply it to a large U.S. macro-financial dataset with externally identified oil supply news shocks. The framework combines a large macro-financial information set with a flexible nonparametric measurement equation, allowing nonlinear transmission to emerge from the data rather than being imposed through a pre-specified functional form. We find that adverse oil supply news shocks generate stronger and more persistent contractions in real activity than the expansions associated with favorable shocks of comparable magnitude, with especially pronounced differences in industrial production, financial variables, and equity prices. Employment responses are highly heterogeneous across U.S. states, with substantially stronger contractions in manufacturing-intensive regions, while energy-producing states display partially offsetting dynamics following adverse oil supply news shocks. Across shock magnitudes, nonlinearities arise mainly between very small and moderate oil-price movements: small shocks generate weak and imprecisely estimated responses, while moderate shocks already produce economically meaningful effects on industrial production and regional employment. Larger shocks do not systematically generateproportionally stronger responses across variables and shock signs. JEL Classification: C11, C32, E32, Q43 |
| Keywords: | dynamic factor model, non-parametric techniques, nonlinear models, oil price shocks |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263265 |
| By: | Giuseppe Cavaliere; Luca Fanelli; Marco Mazzali |
| Abstract: | We propose a novel econometric methodology for Structural Vector Autoregressions with external instruments (`proxy-SVARs' or `SVAR-IVs') in panel data characterized by strong cross-sectional dependence, dynamic heterogeneity, and limited availability of direct external instruments for the shocks of interest. For each unit, we specify a Factor-Augmented proxy-SVAR (`proxy-FA-SVAR') that incorporates factors summarizing cross-sectional information from the non-policy variables of the system. The effects of the policy shocks are then recovered indirectly by estimating unit-specific policy reaction functions through a Minimum Distance approach. Identification relies on global instruments for the non-policy shocks; that is, proxies common to all units in the panel, internally constructed from a separate SVAR estimated on factors for the policy and non-policy variables. These global instruments can be complemented with local (idiosyncratic) instruments constructed from auxiliary unit-level SVARs. Their joint use renders the proxy-FA-SVARs overidentified and therefore statistically testable. We illustrate the methodology by estimating government spending multipliers for Italian NUTS-2 regions using annual data. The global and local instruments for the regional output shocks are obtained from Blanchard-Perotti-type SVARs. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.13879 |
| By: | Anamol Khadka; Milan Arjel; Ayush Lataula; Aayam Dhakal; Prajun Trital; Mingmar Sherpa; Biman Rimal |
| Abstract: | This study examines the dynamic relationship between the global oil prices and Nepal Stock Exchange (NEPSE) using an integrated approach which combines traditional econometric techniques with machine learning and explainable AI techniques. For this, Daily data of International Oil prices and NEPSE index is analyzed from approximately thirteen years (June 2013 to June 2026) using Granger causality, EGARCH(1, 1), and DCC-GARCH models to examine different properties like predictive relationships, asymmetric volatility behaviour, and time-varying correlations. To further supplement the econometric analysis, Machine Learning Models like Random Forest, LightGBM, and XGBoost algorithms were used to capture nonlinear relationships, along with explainable artificial intelligence techniques like SHAP values, Partial Dependence Plots, and Individual Conditional Expectation plots to further interpret the results of the model. The results from the econometric analysis showed a statistically significant unidirectional Granger causality from Brent crude oil to NEPSE with a four-day lag, high volatility persistence in both markets, and weak yet highly time-varying conditional correlations. Among the machine learning models, XGBoost achieves the best performance, and explainability analysis reveals that NEPSE own momentum and short-term volatility mainly influence its own behaviour and oil-related information serves as a minor, method-dependent contributor. The findings demonstrate that econometric and explainable machine learning approaches provide insights into the oil and equity market relationship in a way that each approach complements the result of one another. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.11922 |
| By: | Yurii Sholomytskyi |
| Abstract: | This paper examines the statistical properties of the IMF’s World Economic Outlook (WEO) projections over 1999–2023 for 29 economies. The optimism of WEO growth forecasts is well established; we confirm it and look behind it at two features of how the forecasts are built. First, the growth of the systemic economies (the United States and China) appears to be underutilized in the projections: forecasts embed less of the cross-country growth comovement present in the data, a gap we term forecast fragmentation that did not narrow over the sample. Second, the conditional growth–inflation link present in the historical data is weakly represented in the projections. These patterns suggest that structural models, in which such cross-country and real–nominal linkages can be verified through estimation, could be a useful complement to expert judgment, serving as a baseline check for medium-term anchors. |
| Keywords: | IMF; World Economic Outlook; Forecast error; Optimism bias; Forecast fragmentation |
| Date: | 2026–07–31 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2026/164 |