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on Econometric Time Series |
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Issue of 2026–11–09
seventeen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Sylvia Kaufmann (Study Center Gerzensee) |
| Abstract: | Factor models condense the common dynamics of high-dimensional data into a few factors. Inducing sparsity in the factor loading matrix identifies strong factorseries associations, so that factors load on distinct groups of series and can be interpreted. The paper reviews an order-invariant Bayesian approach to sparse factor estimation. The model is estimated without pre-imposing rotational identification restrictions, and factor position and sign are identified by post-processing the MCMC output. Since extracted factors are distinct, the restriction of independent factor innovations can be relaxed. The resulting reduced-form state equation, also in a factor augmented VAR with observed factors, allows for further structural analysis. To handle the recent pandemic period, we introduce a Covid factor that loads on the series only from 2020 onwards, while we assume the remaining factors and their dynamics to stay the same. An application to FRED-QD data, spanning the period 2000Q1 to 2024Q1, identifies interpretable group-specific factors in addition to the pervasive ones, and the Covid factor captures the transitory, extreme volatility at the onset of the pandemic across many series. Impulse responses to a policy shock identified by maximizing the forecast error variance of the term spread are consistent with a monetary policy shock, although uncertainty remains considerable. Allowing for weakly correlated idiosyncratic innovations is a promising extension that would bring parametric sparse factor models closer to approximate factor models. |
| Date: | 2026–11 |
| URL: | https://d.repec.org/n?u=RePEc:szg:worpap:2605 |
| By: | Hongyu Yao; Zhengyang Chi; Junbin Gao |
| Abstract: | We propose a structured continuous-time stochastic volatility model for one-day-ahead integrated-variance forecasting. The model introduces a jointly evolving realized-measure state that feeds directly into latent variance dynamics, while correlated Brownian innovations capture return-linked dependence. Parameters are estimated through simulation-based predictive learning, and Monte Carlo simulation forecasts integrated variance. Across 17 equity indices, the proposed model shows strong out-of-sample performance relative to GARCH, GARCH-It\^o, Realized GARCH, HAR, and HEAVY benchmarks under QLIKE, MSE, and MAE. Ablation results show that realized-measure feedback provides substantial incremental forecasting value within the proposed framework, while return-linked Brownian dependence contributes more modest complementary gains. The results support incorporating measurement-driven information directly into continuous-time latent volatility dynamics to improve integrated-variance forecasting. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.17732 |
| By: | Silva Lopes, Artur |
| Abstract: | Several reasons explain the absence of a precise, complete and widely accepted definition of trend for economic time series, and the existence of two major disparate models is one of the most important. A recent operational proposal tried to overcome this difficulty resorting to a statistical test with good asymptotic properties against both those alternatives. However, this proposal may be criticized because it rests on a tool for inductive, not deductive, inference. Besides criticizing this recent definition, drawing heavily on previous ones, the paper provides a new general proposal, more complete, containing several necessary but no sufficient condition(s). A version specialized to certain macroeconomic time series is also presented and discussed. |
| Keywords: | trend, trend-cycle decomposition, macroeconomy, statistical testing |
| JEL: | C12 C18 C22 B41 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:344307 |
| By: | Xiaochun Liu |
| Abstract: | Weakly dependent idiosyncratic errors are standard in mean factor models, but quantile factor models have been analyzed only under independence. The mean-case definition of weak dependence, a bound on the eigenvalues of the error covariance matrix, does not carry over: I show that it neither implies nor is implied by the property that controls quantile estimation, since uncorrelated errors can share a pervasive quantile component. I instead define approximate quantile factor models through a concentration condition on the idiosyncratic array. Under it, the quantile factor analysis (QFA) estimator is consistent at a rate that deteriorates by the square root of a dependence constant, which is minimax optimal, and the number of factors is consistently estimated. Dependence changes the asymptotic variance, for which I provide HAC and thresholded estimators. Monte Carlo experiments confirm these predictions. In FRED-QD and FRED-MD, standard errors ignoring dependence understate uncertainty, most strongly in the tails. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.33461 |
| By: | Junjie Guo; Endong Wang; Ke-Li Xu |
| Abstract: | Local projections (LPs) have become a standard tool for estimating dynamic effects in macroeconomics and are typically implemented using ordinary least squares (OLS) for a given lag order. We propose an alternative approach that exploits additional lags as excluded instrumental variables (IVs). Under a finite-order model with martingale-difference shocks, the resulting (optimally weighted) IV estimator is never asymptotically less efficient than OLS and, as we show, can deliver substantial efficiency gains when data are persistent. For the unit-root AR(1) data with i.i.d. errors, our baseline IV estimator (with one overidentifying restriction) has asymptotic variance $2-h^{-1}$, compared with $h$, the asymptotic variance of the OLS lag-augmented estimator in Montiel Olea and Plagborg-M{\o}ller (2021), for an integer propagation horizon $h$. We then develop IV-based LP inference that is robust to unknown persistence and moderate local model misspecification, whereas the recursive VAR-based inference is generally not robust to the latter. We also characterize the trade-off between the degree of misspecification and the number of additional lag controls. Through simulations and an empirical application, we demonstrate that the proposed method can yield meaningfully shorter confidence intervals for impulse responses than OLS in finite samples. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.13269 |
| By: | Larissa Nawo (HEC Montréal) |
| Abstract: | How do financial conditions shape U.S. macroeconomic tail risk, and what is their incremental forecasting value beyond standard macroeconomic predictors? Using quarterly U.S. data from 1971Q1 to 2026Q1, this paper compares macro-only and macro-financial Bayesian VARs. First-lag financial-conditions coefficients are negative for GDP growth and positive for unemployment, with 95% posterior credible intervals excluding zero; second-lag coefficients have opposite signs. Adding financial conditions to the Gaussian VAR raises predicted probabilities of negative GDP growth by 1.5 and 2.5 percentage points at four- and eight-quarter horizons and lowers GDP tail quantiles. However, out-of-sample tests do not establish a general forecast-accuracy improvement. Student- forecast innovations, simulated with the same Gaussian posterior parameter draws, produce heavier predictive tails. Their positive GDP log-score differences reverse when 2020Q1–2021Q4 forecast targets are excluded, while CRPS favors Gaussian innovations in several comparisons. Financial conditions change measured tail risk without consistently improving forecast accuracy. |
| Keywords: | Financial conditions; macroeconomic tail risk; recession risk; macroeconomic vulnerability |
| JEL: | C53 E32 E44 G01 |
| Date: | 2026–10–07 |
| URL: | https://d.repec.org/n?u=RePEc:ris:riskmr:023860 |
| By: | Schick, Manuel; Opschoor, Anne |
| Abstract: | This paper proposes forecasting joint tail risks for key macroeconomic indicators, GDP growth, inflation, and unemployment, using the US Survey of Professional Forecasters (SPF). By incorporating SPF consensus forecasts into the conditional mean of AR-GARCH-type models, the accuracy of univariate and multivariate predictive densities is significantly improved. Modeling a constant correlation matrix captures strong dependencies, particularly between GDP growth and unemployment. Using US data from 1990 to 2024, we show that the joint modeling framework enables scenario-based analysis in which predictive densities, conditioned on adverse developments in other variables, differ substantially from the baseline marginal distributions. The framework allows for a formal out-of-sample evaluation of joint predictive densities and a transparent assessment of conditional tail risks. |
| Keywords: | Growth-at-Risk; Multivariate Predictive Densities; GARCH; Tail Risk; Macroeconomic Forecasting |
| Date: | 2026–04–24 |
| URL: | https://d.repec.org/n?u=RePEc:awi:wpaper:0771 |
| By: | Nina Maria Brehl; Geraldine Dany-Knedlik; Laura Pagenhardt |
| Abstract: | This paper proposes a framework for nowcasting the income distribution in real time. Decile means of the annual U.S. household income distribution are combined with a panel of about 80 quarterly macroeconomic indicators in a mixed-frequency dynamic factor model (DFM) and evaluated pseudo-real-time from 1990 to 2024. Relative to an autoregressive benchmark, the DFM reduces decile-level nowcast errors by 16% on average and by up to 25% in the middle of the distribution; improvements are smallest at the two tails, with the volatile bottom decile the hardest to nowcast. The DFM also substantially improves directional accuracy, raising the share of detected turning points from 7% under the benchmark to 45%. The signal is available about eighteen months before the official release, and a news decomposition shows that labor-market releases carry more weight at the bottom of the distribution and price releases at the top. For inequality measures, the DFM does not improve on the benchmark. The framework complements microsimulation and functional approaches by supplying timely, evaluable decile-level signals from standard state-space tools for distributional surveillance and as real-time priors when micro data are delayed. |
| Keywords: | Nowcasting, mixed-frequency dynamic factor models, income distribution, inequality, turning point detection |
| JEL: | C32 C38 C53 D31 E27 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:diw:diwwpp:dp2187 |
| By: | Ruodu Wang; Jingcheng Yu |
| Abstract: | Expected Shortfall (ES) measures the average size of tail losses. Its sequential backtests typically also require a Value-at-Risk (VaR) forecast. We develop two e-backtesting methods using only observed losses and ES forecasts: one for iid losses only and the other for time series under an AR-GARCH conditional VaR structure. Under the stated assumptions, both control false rejections at any stopping time. For the time-series method, validity requires a fixed parameter--quantile pair representing the conditional VaR path and a positive report margin. The time-series statistic takes an infimum over possible parameter and VaR values. We choose the betting process $(\lambda_t)$ by maximizing an empirical growth rate averaged across candidate parameters. We compute the statistic by continuous VaR profiling on a dense parameter grid. For grid approximations, we prove convergence to the continuous infimum, together with convergence of the probability of false rejection, as the grid is refined over a fixed monitoring period. Lower and upper bounds for the VaR infimum on the parameter grid control the accuracy of the numerical profiling. Simulations, including ES reports that change from over-reporting to under-reporting, and an application to daily NASDAQ losses provide numerical comparisons with VaR--ES e-processes and fixed-sample ES backtests, assessing detection frequencies and the timing of rejections. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.17681 |
| By: | Nymoen, Ragnar (Dept. of Economics, University of Oslo); Castle , Jennifer (Magdalen College, Oxford) |
| Abstract: | Nominal exchange rate regressions, in which the h-period change in the nominal exchange rate (NER) is regressed on the h-th lag of the real exchange rate (RER), are used to assess whether the RER predicts future NER adjustment. We show that these regressions are generally mis-specified relative to a VAR-type data generating process, and that the reliability of inference about the RER’s predictive power depends critically on the horizon, on whether the RER is stationary, and on the sample size. Monte Carlo simulations show that, when the RER is stationary, the regressions estimate horizon-dependent projection coefficients rather than the adjustment coefficient, and cannot reveal shifts in the adjustment mechanism. When the RER is non-stationary, conventional tests reject the null of no predictive power far too often. At long horizons the regression also becomes spurious in the sense of Granger and Newbold, and non-standard critical values do not solve the problem. Empirically, we revisit the finding of Eichenbaum, Johannsen and Rebelo (2021) that, under inflation targeting, the RER predicts NER changes at horizons of three years and longer. NER-regressions for Norway and the UK reproduce this finding on the original sample period. However, the estimates shrink as the sample is extended. For the UK, for example, the lagged RER becomes insignificant once the regression is re-specified to have near white-noise residuals. The empirical regularity is therefore less robust than it appears, which matters for the assessment of monetary policy models that have been calibrated to match it. |
| Keywords: | Nominal exchange rate regression; Exchange rate predictability; Relative PPP; Cointegration; Equilibrium correction; Spurious regression; Direct projections; Inflation targeting |
| JEL: | C22 C32 E52 F31 |
| Date: | 2026–10–30 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:osloec:2026_005 |
| By: | Duy Nguyen |
| Abstract: | We study the asymptotic properties of the nonlinear stochastic GMM algorithm proposed by Chen, Lee, Liao, Seo, Shin and Song for recursively estimating parameters defined by possibly nonlinear and overidentified moment restrictions $\E[g(X, \beta^*)]=0$. Each observation updates estimates of the moment Jacobian, inverse covariance matrix and Gauss--Newton preconditioner at a cost independent of sample size. For linear and nonlinear instrumental-variable moments, we derive an exact rank-two Sherman--Morrison--Woodbury update. The algorithm combines preconditioned stochastic approximation with iterate averaging. Under a preconditioned monotonicity condition, satisfied globally in linear models and locally around a consistent pilot estimate in general, we establish almost sure convergence and rates, as well as a functional central limit theorem with the efficient GMM variance. These results require four moments of the moment function and its Jacobian when the step exponent exceeds $2/3$. The inverse Gauss--Newton matrix consistently estimates this variance, and a projected linearised statistic enables online testing of overidentifying restrictions. We extend the results to $L$-dependent data with long-run variance weights under stronger moment assumptions. Simulations show that the averaged estimator approaches offline two-step GMM in accuracy and coverage at $10^6$ observations, while requiring a fraction of its computing time and fixed memory at up to $10^7$ observations. The online test achieves correct size and comparable power. In an application estimating the effect of a third child on weeks worked using $254{, }654$ women from the 1980 US Census, single-pass estimates agree with offline GMM within a fraction of a standard error on average across data orderings, and both methods yield the same overidentification-test conclusion in most orderings. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12873 |
| By: | Daniel Lewis; Yatheesan Selvakumar |
| Abstract: | Empirical researchers frequently make statements about the impacts of macroeconomic shocks at multiple horizons that require confidence bands that are simultaneously valid across those horizons, not just pointwise (for a single horizon). Increasing evidence suggests that available macroeconomic instruments are typically weak. We show that commonly-used simultaneous bands under strong identification can readily be adapted to be robust to weak instruments based on the Anderson and Rubin (1949) statistic. Our proposed sup-AR band is efficient amongst bands that control worstcase coverage. All robust bands considered are equivalent to their Wald counterparts under strong identification, at least asymptotically and under local alternatives. A simulation study demonstrates the advantages of the bands over the current default of projection methods. Simultaneously-valid robust inference continues to deliver economically meaningful conclusions in most applications considered; validity guarantees come at surprisingly low cost. |
| Date: | 2026–11–03 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:22/26 |
| By: | Periklis Gogas |
| Abstract: | 4Cast Lab is a free, open-source application for machine learning, econometrics and statistical analysis that runs on the user's own computer, with no installation, no programming and no data leaving the machine. It was developed at the E|M|E|F Lab, Department of Economics, Democritus University of Thrace, for researchers, analysts, instructors and students in any field. Its Forecasting mode trains eight learning algorithms (with three kernels for SVM/SVR), implemented from scratch, under leakage-safe validation for time-ordered data; it selects models by cross-validation, compares the selected model with every alternative and with naive benchmarks through formal tests of predictive accuracy, and documents each run in a methods report and a Python script that the user can export. Its Estimation mode covers the core of applied econometrics, from OLS with robust inference to ARIMA, ARDL, VAR/VECM and GARCH. This paper describes the design, the interface and the workflow of version 4.6.2, reports a validation of 1, 234 numerical results against statsmodels, linearmodels, arch, scikit-learn and NIST certified values, illustrates the workflow with three examples, and discusses current limitations. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.16800 |
| By: | Antonio F. Galvao; Ulrich Hounyo; Jiahao Lin |
| Abstract: | This paper develops a smoothed generalized method of moments (GMM) framework for panel quantile models with individual-specific fixed-effects and endogenous regressors. By smoothing the indicator in the quantile moment conditions and profiling out the individual effects through smoothed individual quantile restrictions, the proposed estimator can be implemented using standard GMM algorithms. We establish consistency, asymptotic normality, and feasible inference under weak time dependence as both panel dimensions diverge. This dependence structure accommodates dynamic panel specifications, serially dependent disturbances, lagged instruments, and within-individual heteroskedasticity and autocorrelation consistent inference. Monte Carlo simulations show that the estimator is nearly unbiased under endogeneity and yields generally accurate inference while remaining computationally tractable. An application to OECD inflation dynamics suggests asymmetric inflation propagation: under the structural IVQR interpretation, the response of current inflation to lagged inflation is substantially larger at the lower structural quantile than at the upper structural quantile. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12824 |
| By: | Pedro Picchetti |
| Abstract: | I study randomization inference for dynamic causal effects in panels with many units and few periods when treatment is endogenous and an instrument is as good as randomly assigned only through the innovations of a first-order autoregressive assignment mechanism with unknown persistence. The persistence is a nuisance parameter in two senses: it determines which weighted average of heterogeneous causal effects the instrumented local projection estimand measures, and it governs the randomization distribution of any statistic built from the instrument. I propose tests that never estimate it. For each candidate value the innovations are recovered, rerandomized under a group that leaves their joint law invariant, and a randomization p-value is formed; the reported p-value is the supremum over candidate values or over an exact confidence set. Under a sharp null on the path of lag-specific effects the tests have level at most $\alpha$ for every persistence in finite samples, including the unit root, and the supremum is a maximum over finitely many points. Under a weak null on the heterogeneity-weighted estimand a studentized version is uniformly asymptotically valid. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.19075 |
| By: | Andrey Itkin |
| Abstract: | We study a local stochastic volatility (LSV) model in which the variance factor follows a generalized Langevin equation (GLE) with colored noise, and past returns act on variance through a memory kernel with state-dependent amplitudes. For kernels given by finite sums of exponentials, we prove existence, uniqueness, and non-explosion under a growth condition linking the volatility map to the potential. In a one-mode family with a polynomial potential, feedback through log returns can cause explosion exactly when the squared volatility factor grows faster than the restoring force. Under structural and nondegeneracy conditions, an exact reduced Markovian state has a smooth density solving a deterministic forward equation. The Dupire conditional expectation therefore requires no stochastic partial differential equation. Under a bounded Sharpe ratio, exponential utility selects the minimal entropy martingale measure, whose premium solves a quadratic backward stochastic differential equation. Under a regularity hypothesis, which we verify in special cases with and without leverage, the premium depends only on the current state, and the squared VIX equals the expected average future local stochastic variance. Finally, a regularized calibration problem with bid--ask constraints admits a minimizer whenever a feasible point has finite objective value. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.18706 |
| By: | Shiqi Fang |
| Abstract: | Mortgage credit risk may exhibit dependence across economically connected areas, even when they are geographically distant. However, current models typically represent cross-area dependence through fixed geographical neighbourhoods, potentially overlooking economic connections that extend beyond physical proximity and evolve over time. These models may fail to capture shared risks among geographically distant but economically similar areas, and cannot describe a changing dependence of risk; it therefore risks retaining economically obsolete connections while omitting newly emerging ones. This paper uses similarities of industrial composition as a measure of economic proximity and develops a discrete-time survival model with dynamic industrial graphs to capture evolving cross-area dependence in mortgage default risk. The resulting graphs are reconstructed annually, allowing both their topology and edge weights to change as regional industrial compositions evolve. Jointly combining a proper conditional autoregressive process with a first-order autoregressive process governs the temporal cross-area dependence and the temporal persistence in latent risk simultaneously. The model is estimated using Integrated Nested Laplace Approximation and evaluated on U.S. mortgage loan-level data against the static industrial graph specifications. The results show that the proposed dynamic model achieves better in-sample fit and out-of-sample discrimination, while its estimated parameters indicate substantial graph-induced cross-area dependence and temporal persistence. These findings demonstrate the value of allowing economically defined neighbourhoods to evolve when modelling mortgage default risk. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.18795 |