|
on Econometric Time Series |
|
Issue of 2026–10–19
sixteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Alain Hecq; Ivan Ricardo; Ines Wilms |
| Abstract: | Matrix autoregressive (MAR) models offer a parsimonious framework for modeling matrix-valued time series, yet tools for estimation and inference for their impulse response functions are lacking. We develop asymptotic and bootstrap-based inference for impulse responses of stable MAR($p$) models. We derive the joint asymptotic distribution of the coefficient and covariance estimators, which permits closed-form delta-method standard errors. To address finite-sample bias, we propose ProBAB-MAR, a bias-corrected bootstrap that projects the corrected coefficients back onto the Kronecker parameter space, and prove that it attains asymptotically correct coverage. Monte Carlo simulations show that delta-method intervals undercover in small samples, while ProBAB-MAR achieves near-nominal coverage with intervals considerably narrower than those from an unrestricted VAR. An application to euro area inflation illustrates how shocks transmit across countries and inflation categories. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05405 |
| By: | Lennart Empting; Saskia \"Ozt\"urk; Simone Maxand; Konstantin Wagner |
| Abstract: | We develop inference for heterogeneous panel vector autoregressive (VAR) models and their structural impulse response functions, where the error terms are dependent in the cross-sectional and time dimensions (two-way dependence). For proxy-identified structural VARs, we first adapt mean-group estimation and construct a closed-form pooled identification. Considering the reduced-form VAR dynamics, residual covariances, and structural parameters, we derive a joint central limit theorem under joint limits in the cross-sectional and time dimensions. We then propose a recursive-design panel moving-block bootstrap that resamples the estimated error terms in (i) the temporal, (ii) the cross-sectional, or (iii) both dimensions jointly, and prove consistency of the joint panel-block scheme under two-way dependence. Simulations show coverage close to the nominal level for the joint scheme but severe undercoverage for cross-sectional resampling. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11898 |
| By: | Yu, Xuewen |
| Abstract: | Individual-level time series data, such as longitudinal survey data, are increasingly used for policy evaluation. To infer the impact of a policy given such data, we propose a hierarchical Bayesian structural time series (HBSTS) model that extends the existing Bayesian structural time series model. Hierarchical Bayesian structural time series can accommodate multiple observations per time point by adding an extra layer to capture individual-level variation. It also uses a regularized horseshoe prior with a signal-adaptive variable selection algorithm. These extensions provide a more flexible and realistic framework for policy evaluation, and make inference less sensitive to the prior specification of the expected model size (i.e. the expected number of covariates included in the model that are predictive of outcomes). In simulation studies, HBSTS demonstrated greater robustness to misspecification of the expected model size and was more powerful in detecting putative intervention effects compared with BSTS. We apply our model to the UK Household Longitudinal Study to investigate the impact of a UK immigration policy reform. Our findings indicated that the policy led to psychological distress among individuals from Black Caribbean backgrounds, which was also observed in an earlier Bayesian interrupted time series analysis, though derived by comparing them with people from White backgrounds. |
| Keywords: | Bayesian structural time series;causal inference;synthetic control method |
| JEL: | C1 |
| Date: | 2026–10–06 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:141174 |
| By: | Hong Kiat Tan; Isaac-Neil Zanoria; James Chen; Haoyang Lyu; Mihai Cucuringu |
| Abstract: | Finding which variables cause which others in multivariate time series, and at what lags, is central to science and policy, yet existing methods force a choice between flexible confounder adjustment, data-driven lag selection, and inference that controls the false discovery rate (FDR). ORACLE-VARX does all three in one pipeline. First, double/debiased machine learning (DML) removes nonlinear confounder effects from the outcomes and the lagged series. Second, adaptive causal lag estimation (ACLE) picks the lag order at each time step by sequential significance tests, tracking regime changes. Third, entry-wise $z$-tests with Benjamini--Hochberg correction select directed edges at a target FDR. We prove that in each rolling window, the debiased coefficients are asymptotically normal around a window-averaged target, so their $z$-tests are asymptotically valid. On a synthetic benchmark with time-varying structure and nonlinear confounding, ORACLE-VARX (LightGBM) tracks the true lag order best (RMSE $0.96$ vs $1.1$--$1.5$), has edge FDR $0.047$, close to PCMCI ($0.045$) and below VAR ($0.129$) and VAR-LiNGAM ($0.187$), and forecasts better than all three. On nine U.S. sector ETFs with macroeconomic confounders, it yields interpretable causal graphs whose lag order rises in high-volatility regimes. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05618 |
| By: | Hunter Ng; Yubo Tao |
| Abstract: | Joint-event forecasts often combine a dependence estimate based on past forecast errors with newly estimated marginal distributions. When each historical error retains the marginal fit available at its issue date, inference must account for an overlapping sequence of estimation errors. We derive their joint influence with the terminal forecast estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical correction to harmonically weighted innovation moments, while terminal slope uncertainty remains. The resulting covariance estimator gives asymptotically valid repeated-sample intervals for fixed one-sided event probabilities at the realized forecast state. In the Gaussian submodel, retaining issued transforms adds a positive semidefinite covariance term relative to refitting margins on the same observations. Monte Carlo simulations show that terminal-margin uncertainty is quantitatively more important than this additional term and that logit intervals improve lower-tail coverage in the designs studied. A real-time forecasting application to U.S. macroeconomic releases shows how marginal estimation contributes to uncertainty in predicted probabilities of joint contractions and identifies limitations of the stationary marginal model. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.07589 |
| By: | Shiyao Huang; Xiaojun Song |
| Abstract: | This paper develops novel smooth tests for structural changes in the innovation copula of multivariate dynamic models. We characterize deviations from copula constancy through a collection of generalized Fourier coefficients and test their joint significance. Under the null hypothesis, estimation of the dynamic parameters and the unknown marginals has no first-order estimation effect on the proposed statistics. Consequently, the feasible tests based on estimated residuals are asymptotically equivalent to their infeasible counterparts based on the unobserved innovations, yielding a desirable oracle property. Our proposed tests are asymptotically $\chi^2$-distributed and possess nontrivial power against local alternatives that approach the null at the parametric rate. To enhance the practicability of our methods, we further develop a data-driven procedure that automatically selects the truncation orders of the basis expansions. Unlike existing methods based on empirical copula processes or kernel smoothing, our tests require neither computationally intensive bootstrap procedures nor bandwidth selection. Extensive simulations demonstrate the satisfactory empirical size and power of our proposed tests. In particular, the data-driven test delivers substantial power gains under sparse alternatives, while remaining competitive under dense alternatives. Applications to exchange rates and stock returns further illustrate the practical usefulness of the proposed methods. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.09351 |
| By: | Kit Baum (Boston College); Jesús Otero (Universidad del Rosario, Colombia) |
| Abstract: | We present the community-contributed blockboot command to bootstrap time-dependent stationary processes using four schemes that preserve the processes' dependence structure by resampling blocks of observations. These schemes include the nonoverlapping block bootstrap of Carlstein (1986, Annals of Statistics 14: 1171–1179); the moving block bootstrap of Künsch (1989, Annals of Statistics 17: 1217–1241) and Liu and Singh (1992, in Exploring the Limits of Bootstrap, ed. LePage and Billard: Wiley); the circular block bootstrap of Politis and Romano (1992, also in Exploring the Limits of Bootstrap); and the stationary block bootstrap of Politis and Romano (1994, Journal of the American Statistical Association 89: 1303–1313). An illustration of these four block bootstrap schemes for time-series data in the context of computing the size of unit-root tests extends and updates the findings of Schwert, "Tests for Unit Roots: A Monte Carlo Investigation" (1989, Journal of Business and Economic Statistics 7: 147–159). We find that the results are most sensitive to the choice of block length, which can be specified in the command or computed automatically. |
| Date: | 2026–10–03 |
| URL: | https://d.repec.org/n?u=RePEc:boc:usug26:25 |
| By: | Antoine A. Djogbenou |
| Abstract: | The paper develops a theory for selecting the rolling window when generating out-of-sample forecasts with factor-augmented regression (FAR) models in the presence of structural instabilities. It shows how to select a rolling window by minimizing the conditional mean squared forecast error (MSFE) while accounting for uncertainty in factor estimation. Because the conditional MSFE is unobserved and the factors are latent, this paper proposes a feasible version of the criterion and derives conditions under which the new method is asymptotically loss-efficient. A simulation experiment documents the procedure's performance. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12025 |
| By: | Stephen Snudden (Wilfrid Laurier University); Quinlan Lee (Erasmus University Rotterdam) |
| Abstract: | Many economic forecasts are constructed for temporally aggregated variables, such as monthly averages or quarterly sums, even when high-frequency data are available. Recent work on temporal aggregation shows that using only monthly or quarterly data can substantially reduce forecast accuracy and distort forecast evaluation. This presentation shows how Stata users can exploit high-frequency information using mixed-data sampling (MIDAS) methods. I first demonstrate how unrestricted MIDAS and restricted MIDAS can be implemented in Stata using existing data-management and time-series commands. These methods are straightforward to code and produce large gains relative to monthly or quarterly benchmarks, but they recover only part of the efficiency available from high-frequency information. I then show how to implement bottom-up MIDAS (BUMIDAS) methods. BUMIDAS reduces the number of parameters by up to a factor equal to the aggregation frequency and is the direct-forecast equivalent of optimal recursive bottom-up approaches. In the applications, daily recursive methods and bottom-up MIDAS reduce forecast errors by roughly half relative to standard monthly or quarterly approaches, and BUMIDAS often outperforms recursive methods in practice. Prototype Stata code is provided to automate aggregation, lag construction, estimation, forecasting, and forecast comparison across low-frequency, UMIDAS, RMIDAS, recursive bottom-up, and bottom-up MIDAS methods. |
| Date: | 2026–10–03 |
| URL: | https://d.repec.org/n?u=RePEc:boc:usug26:23 |
| By: | Szymon P. Chudziak |
| Abstract: | A new form of the fiscal multiplier suited to data expressed as gross growth rates is proposed, together with a structural vector autoregression that isolates discretionary fiscal policy from regime and rule-based components. Because cumulating growth-rate responses over a horizon involves a product rather than a sum, the proposed multiplier is multiplicative: both numerator and denominator are polynomials in the size of the fiscal impulse, so the multiplier varies nonlinearly with the scale of the expenditure programme -- a dependence that conventional additive multipliers cannot capture. The multiplier requires no discounting, no ad hoc conversion factor, and no auxiliary estimate of an average expenditure share of output, and it is computed directly from nominal, non-seasonally-adjusted data, matching the terms in which government budgets are actually expressed. A version of the narrative approach to identification is introduced. It allows to decompose the influence of fiscal policy into a regime component, a standard policy rule embedded in the autoregressive structure, and discretionary shocks. Removing the regime component from the residuals yields smaller identified shocks, and correspondingly smaller multipliers, than found in SVARs not controlling for regime changes -- closing much of the gap between SVAR- and DSGE-based estimates. It is found that multipliers vary substantially across countries and across types of government expenditure, that regime volatility itself differs markedly by country, and that several economies display cyclicality in spending and multiplier paths that only becomes visible once responses are cumulated multiplicatively. The resulting multipliers are nominal, derived from unadjusted data, proven to be sensitive to shock size, and purged of regime effects, offering a tool with direct relevance for budget planning and fiscal policy evaluation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.04982 |
| By: | Christophe Barrette; Philippe Goulet Coulombe; Tim Reinicke |
| Abstract: | What should a macroeconomically relevant climate index contain? The composition is inherently ambiguous, and aggregation choices affect structural inference. We introduce the Assemblage VAR, which jointly estimates nonnegative aggregation weights and VAR parameters by maximizing the system likelihood-gain criterion, effectively outsourcing aggregation to observed macroeconomic dynamics. Two variants operate in component-space and rank-space, reweighting named subcomponents or emphasizing regions of the cross-sectional distribution. Applied to disaggregated U.S. climate data from the Actuaries Climate Index and NOAA, VARs using the assembled climate measures yield contractionary impulse responses that are substantially larger than those estimated using fixed-weight benchmarks. Weights emphasize high-wind variables and distributional tails over slow-moving components such as sea level. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10043 |
| By: | Aashish Bohra; Lokendra Vishwakarm |
| Abstract: | Wavelet-based financial forecasters typically use the transform only to denoise, or reduce it to a single spectral snapshot at the forecast origin, and the convolution that produces the coefficients is usually bilateral, so it can read past the forecast origin. DSTNet instead retains the recent evolution of filter-bank magnitudes as a causal Dynamic Spectral Trajectory, built from seven trailing technical indicators over a twenty-day lookback with a one-sided Morlet-derived filter bank and an explicit burn-in for the left-boundary transient. A factorized Scale-Temporal Spectral Transformer attends along the time and filter-bank axes separately, a learned gate fuses the spectral branch with a CNN-BiLSTM, and horizon-specific gates emit one, three, five, and ten day forecasts in a single pass. We evaluate seven equity indices and gold under a common expanding-window protocol and an untouched one-year hold-out, against nine learned baselines and a random-walk persistence benchmark. Under MAE and MAPE, persistence is the strongest of the ten fixed competitors in 29 of the 32 series-horizon cells and DSTNet is the only model below it in every cell, by 0.7 to 0.9 percent at one day and 3.4 to 4.5 percent at ten days. At one day, paired testing favours DSTNet against the weaker learned baselines but is inconclusive against persistence and the strongest learned forecasters. A downstream allocation diagnostic does not support an equity-timing advantage on any of the seven indices. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.09654 |
| By: | Samuel N. Cohen; Giulia Mantoan; Lars Nesheim; Ã ureo de Paula; Arthur Turrell; Lingyi Yang |
| Abstract: | We introduce a new method of nowcasting using regression on path signatures. Path signatures capture the geometric properties of sequential data. Because signatures embed observations in continuous time, they naturally handle mixed frequencies and missing data. We prove theoretically, and demonstrate with simulations, that regression on signatures both subsumes the linear Kalman filter and has desirable consistency properties. Nowcasting with signatures is more robust to disruptions in data series than previous methods, making it useful in stressed times (for example, during COVID-19). This approach is performant in nowcasting US GDP growth, and in nowcasting UK unemployment. |
| Date: | 2026–10–06 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:17/26 |
| By: | Diego R. Känzig; James H. Stock; Luca Zanotti |
| Abstract: | We study how the shale revolution and the U.S. transition from petroleum importer to net exporter have changed the macroeconomic effects of oil shocks. Using oil supply news shocks identified from OPEC announcements, a time-varying model of the U.S. macroeconomy shows that the contractionary effects weakened over time and eventually became expansionary. State-dependent local projections link this change to the U.S. petroleum trade balance. The improvement goes beyond mechanical net export effects: as the terms-of-trade response turns more favorable, consumption, equity valuations, and activity strengthen broadly across sectors and regions, pointing to general-equilibrium income and wealth effects. A counterfactual analysis of the 2022 oil price surge implies sharply different paths for U.S. activity, prices, and monetary policy under the propagation mechanisms prevailing before the shale boom vs. the early 2020s. |
| JEL: | C32 E31 E32 F41 Q43 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35864 |
| By: | Rok Spruk |
| Abstract: | Synthetic control relies on pre-treatment fit to balance the unobserved factors that drive untreated outcomes. The argument fails when an observed common shock, such as a commodity price, moves with the latent factors before treatment and departs from them afterwards and pre-treatment fit then says almost nothing about the synthetic unit's exposure to the shock. I derive a period-specific bound that links the post-treatment bias of any weighting estimator to pre-treatment misfit through a leverage statistic, and show that the statistic decomposes exactly into a latent-factor component and the partial leverage of the observed shock. The decomposition yields a diagnostic for such silent factor that uses no post-treatment outcome of the treated unit. Balancing an observed exposure index removes the problem, but simplex weights can achieve balance only when the treated unit lies inside the donors' exposure hull. Outside the hull, every simplex-weighted estimator carries an exposure imbalance with an explicit lower bound. For that case I propose an exposure-augmented synthetic control that corrects the remaining imbalance with a cross-donor regression, characterise what the correction identifies and when it fails, and derive bias-aware confidence intervals with a breakdown value. Monte Carlo experiments, including designs in which the correction's assumptions fail, map its gains and its limits. Iran's 2012 sanctions coincided with the 2014 oil collapse, and Iran is more oil-dependent than any of its natural comparators. The 2012-15 output loss of about 12 percent survives every adjustment. The persistent loss that standard synthetic control reports after 2016 does not. Any adjustment for oil exposure removes it, and the long-run effect is not identified with these comparators. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05535 |
| By: | Cheng Zhenghao (Nanchang University) |
| Abstract: | Export controls and economic sanctions have become increasingly frequent and covert, yet existing measurements either record de jure measures without observing enforcement, or presume known events at annual frequency. This paper transplants the monitoring paradigm of statistical process control (SPC) onto bilateral trade data and constructs the Rolling-Baseline Trade Suppression (RBTS) index, which relies solely on monthly customs records. A rolling baseline with selective updating identifies the in-control regime; idiosyncratic residuals from factor decomposition are calibrated and smoothed, yielding restriction readings in σ units that are comparable across commodity-partner pairs and over time. Two classified case studies and a blind test covering 120 sanction pairs on the full U.S. export matrix show that explicitly restricted pairs respond at the event or announcement month, pairs listed on paper but not actually restricted stay flat, and covert restrictions without formal texts are quantified; in the blind test, readings rise strictly monotonically with the ex-ante verified severity of measures (median shares of above-threshold cells 0.58%, 3.26% and 5.47% across three severity tiers). Simulations delineate the effective working zone of the index, with a minimum detectable effect of about 50% sustained suppression. The index complements list-based measures and provides a new statistical tool for monitoring trade restrictions. |
| Keywords: | trade restriction index; statistical process control; principal component residuals; export controls; mirror trade data |
| JEL: | F1 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:drx:wpaper:202619 |