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on Econometric Time Series |
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Issue of 2026–02–16
twelve papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Dezhbakhsh, Hashem; Levy, Daniel |
| Abstract: | It is well established that the U.S. prewar output was more volatile and less shock persistent than the postwar output. This is often attributed to the data interpolation employed to construct the prewar series. Our analytical results, however, indicate that commonly used linear interpolation has the opposite effect on shock persistence and volatility of a series-it increases shock persistence and reduces volatility. The surprising implication of this finding is that the actual differences between the volatility and shock persistence of the prewar and postwar output series are likely greater than the existing literature recognizes, and interpolation has dampened rather than magnified this difference. Consequently, the view that postwar output was more stable than prewar output because of the effectiveness of the postwar stabilization policies and institutional changes has considerable merit. Our results hold for parsimonious stationary and nonstationary time series commonly used to model macroeconomic time series. |
| Keywords: | Business Cycles, Output Volatility, Shock Persistence, Prewar US Output, Postwar US Output, Prewar vs Poswar US Output Series, Linear Interpolation, Variance Ratio, Stationary Time Series, Nonstationary Time Series, Periodicity, Periodic Nonstationarity, Missing Observations, Macroeconomic Stabilization, Economic Policy |
| JEL: | E32 E01 N10 C02 C18 C22 C82 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:336550 |
| By: | Yurui Wu; Qingying Deng; Wonou Chung; Mairui Li |
| Abstract: | Time series encountered in practice are rarely stationary. When the data distribution changes, a forecasting model trained on past observations can lose accuracy. We study a small-footprint test-time adaptation (TTA) framework for causal timeseries forecasting and direction classification. The backbone is frozen, and only normalization affine parameters are updated using recent unlabeled windows. For classification we minimize entropy and enforce temporal consistency; for regression we minimize prediction variance across weak time-preserving augmentations and optionally distill from an EMA teacher. A quadratic drift penalty and an uncertainty triggered fallback keep updates stable. We evaluate this framework in two stages: synthetic regime shifts on ETT benchmarks, and daily equity and FX series (SPY, QQQ, EUR/USD) across pandemic, high-inflation, and recovery regimes. On synthetic gradual drift, normalization-based TTA improves forecasting error, while in financial markets a simple batch-normalization statistics update is a robust default and more aggressive norm-only adaptation can even hurt. Our results provide practical guidance for deploying TTA on non-stationary time series. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.00073 |
| By: | Luis Ontaneda Mijares; Nick Firoozye |
| Abstract: | Overparameterized models have recently challenged conventional learning theory by exhibiting improved generalization beyond the interpolation limit, a phenomenon known as benign overfitting. This work introduces Adaptive Benign Overfitting (ABO), extending the recursive least-squares (RLS) framework to this regime through a numerically stable formulation based on orthogonal-triangular updates. A QR-based exponentially weighted RLS (QR-EWRLS) algorithm is introduced, combining random Fourier feature mappings with forgetting-factor regularization to enable online adaptation under non-stationary conditions. The orthogonal decomposition prevents the numerical divergence associated with covariance-form RLS while retaining adaptability to evolving data distributions. Experiments on nonlinear synthetic time series confirm that the proposed approach maintains bounded residuals and stable condition numbers while reproducing the double-descent behavior characteristic of overparameterized models. Applications to forecasting foreign exchange and electricity demand show that ABO is highly accurate (comparable to baseline kernel methods) while achieving speed improvements of between 20 and 40 percent. The results provide a unified view linking adaptive filtering, kernel approximation, and benign overfitting within a stable online learning framework. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.22200 |
| By: | Martin Bruns; Helmut Lütkepohl |
| Abstract: | In structural vector autoregressive analysis it has become quite popular to identify some structural shocks of interest by external instruments or proxies. This study points out a range of areas where such proxies have been used and sketches the way the proxies have been constructed. It reviews identification and estimation methods that have been considered in this context. Moreover, it points out some features such as heteroskedasticity, nonfundamentalness of the shocks and violations of the standard assumptions for proxies that may result in complications. |
| Keywords: | Structural vector autoregression, proxy VAR, local projection, weak instruments, internal instruments, external instruments, fundamental shocks |
| JEL: | C32 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:diw:diwwpp:dp2155 |
| By: | Samir Orujov (LMBA - Laboratoire de Mathématiques de Bretagne Atlantique - UBS - Université de Bretagne Sud - UBO EPE - Université de Brest - CNRS - Centre National de la Recherche Scientifique); Victor Elvira (The University of Edinburgh, Institut TELECOM/TELECOM Lille1 - IMT - Institut Mines-Télécom [Paris], CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 - Centrale Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique); Audrey Poterie (LMBA - Laboratoire de Mathématiques de Bretagne Atlantique - UBS - Université de Bretagne Sud - UBO EPE - Université de Brest - CNRS - Centre National de la Recherche Scientifique); Farid Rajabov (UCL - University College London [UCL]); Francois Septier (LMBA - Laboratoire de Mathématiques de Bretagne Atlantique - UBS - Université de Bretagne Sud - UBO EPE - Université de Brest - CNRS - Centre National de la Recherche Scientifique, UBS - Université de Bretagne Sud) |
| Abstract: | The log-TGARCHX model is less restrictive in terms of the inclusion of exogenous variables and asymmetry lags compared to the GARCHX model. Nevertheless, adding less (or more) covariates than necessary may lead to under- or overfitting, respectively. In this context, we propose a new algorithm, called VS-LTGARCHX, which incorporates a variable selection procedure into the log-TGARCHX estimation process. Furthermore, the VS-LTGARCHX algorithm is applied to extremely volatile BTC markets using 42 conditioning variables. Interestingly, our results show that the VS-LTGARCHX models outperform benchmark models, namely the log-GARCH(1, 1) and log-TGARCHX(1, 1) models, in one-step-ahead forecasting. |
| Keywords: | variable selection, Bitcoin volatility, log-GARCHX, GARCH |
| Date: | 2025–05–16 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04283159 |
| By: | Kevin Lee; Kalvinder Shields |
| Abstract: | The time series properties of output and price inflation can be accurately captured using VAR-E's, Vector-Autoregressive models of actual and expected measures of the series where the latter are provided by surveys. The paper proposes a method for estimating VAR-E's that accommodate individuals' real-time understanding of the macroeconomy and which deliver forecasts in a way that is useful to decision-makers. It notes the sort of statistics and figures that might be reported in a 'dashboard' to monitor the health of the macroeconomy, and this is illustrated using the actual and expected data produced by the Bank of England's Decision-Maker Panel. |
| Keywords: | learning, expectations, surveys, forecasts, decision-making |
| JEL: | C32 D84 E31 E32 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-10 |
| By: | Giovanni Bonaccolto (Department of Economics and Law, ``Kore" University of Enna, Piazza dell'Universita, 94100 Enna, Italy); Massimiliano Caporin (Department of Statistical Sciences, University of Padova, Via Cesare Battisti 241/243, Padova, Italy); Oguzhan Cepni (Ostim Technical University, Ankara, Turkiye; University of Edinburgh Business School, Centre for Business, Climate Change, and Sustainability; Department of Economics, Copenhagen Business School, Denmark); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa) |
| Abstract: | We investigate whether sentiment innovations help forecast realized volatility in U.S. state-level stock markets. We combine 5-minute intraday data for 50 U.S. states with a daily state-level Twitter-based sentiment index over the period August 2011 to August 2024. Realized variance, skewness, and kurtosis are constructed using intermittency-adjusted estimators that account for sparse trading and zero returns. We adopt a Heterogeneous Autoregressive framework and enrich it with higher-order realized moments and changes in state-level sentiment, estimating the models via weighted least squares to mitigate heteroskedasticity effects. Out-of-sample performance is assessed in a rolling-window forecasting design for daily, weekly, and monthly horizons, and formal forecast comparisons are conducted using Diebold-Mariano and Clark-West tests. Our results confirm that the Heterogeneous Autoregressive components remain the dominant drivers of realized volatility dynamics across all horizons. Importantly, tail-risk information, proxied by realized kurtosis, delivers the most systematic and economically meaningful improvements in predictive accuracy, particularly at short horizons. Sentiment changes exhibit an episodic but non-negligible predictive foot-print: while their average in-sample contribution is limited, they enhance forecast performance for a subset of states, especially when combined with higher-moment information in richer specifications. Overall, our findings highlight that integrating in-traday distributional characteristics and sentiment innovations can improve volatility forecasting at the regional level, albeit in a state- and horizon-dependent manner. |
| Keywords: | State-level stock markets, Sentiment, HAR-RV, Realized moments, Forecast evaluation |
| JEL: | C53 C58 G11 G17 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202603 |
| By: | Efrem Castelnuovo (University of Padua); Giovanni Pellegrino (University of Padua); Laust L. Saerkjaer (Aarhus University) |
| Abstract: | Imposing restrictions on policy rule coefficients in vector autoregressive (VAR) models enhances the identification of monetary policy shocks obtained with sign and narrative restrictions. Monte Carlo simulations and empirical analyses for the United States and the Euro area sup- port this result. For the U.S., adding policy coefficient restrictions yields a larger and more precise short-run output response and more stable Phillips multiplier estimates. Heterogeneity in output responses reflects variation in systematic policy reactions to output. In the Euro area, policy coefficient restrictions sharpen the identification of corporate bond spread responses to monetary policy shocks. |
| Keywords: | : Monetary policy shocks, narrative restrictions, policy coefficient restrictions, vector autoregressive models, Monte Carlo simulations, DSGE models. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:pad:wpaper:0328 |
| By: | Gary Koop; Stuart McIntyre; James Mitchell; Ping Wu |
| Abstract: | This paper develops a method to incorporate micro data, available as repeated cross-sections, into macro VAR models to understand the distributional effects of macroeconomic shocks at business cycle frequencies. The method extends existing functional VAR models by "looking within" the micro distribution to identify the degree to which specific types of micro units are affected by macro shocks. It does so by creating a pseudo-panel from the repeated cross-section and adding these pseudo individuals into the macro VAR. Jointly modeling the micro and macro data leads to a large (pseudo) VAR, and we use Bayesian methods to ensure shrinkage and parsimony. Our application revisits Chang et al. (2024) and compares their functional VAR-based distributional impulse response functions with our proposed pseudo VAR-based ones to identify what types of individuals' earnings are most affected by business-cycle-type shocks. We find that the individuals exhibiting the strongest positive cyclical sensitivity are those in the lower tail of the earnings distribution, particularly men and those without a college education, as well as young workers. |
| Keywords: | Functional VAR; pseudo panel; earnings distribution; business cycle shocks |
| JEL: | C32 C53 E37 |
| Date: | 2026–02–09 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedcwq:102417 |
| By: | Jiawen Luo (School of Business Administration, South China University of Technology, Guangzhou 510640, China); Jingyi Deng (School of Business Administration, South China University of Technology, Guangzhou 510640, China); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Oguzhan Cepni (Ostim Technical University, Ankara, Turkiye; University of Edinburgh Business School, Centre for Business, Climate Change, and Sustainability; Department of Economics, Copenhagen Business School, Denmark) |
| Abstract: | This paper provides a comparative, time-varying assessment of how macroeconomic skewness affects the business cycle in the US, Canada, and the UK. We construct novel aggregate skewness factors for Canada and the UK, alongside a US benchmark, and embed these indicators in country-specific time-varying parameter VAR models with stochastic volatility. Our results show that negative skewness shocks consistently depress output and equity prices, raise unemployment, and trigger monetary easing, while generating generally modest disinflationary effects. Crucially, the macroeconomic transmission of skewness is highly state-dependent: responses are markedly larger and more persistent during major downturns, particularly the global financial crisis and the COVID-19 episode, while remaining muted during tranquil expansions. |
| Keywords: | Skewness, Business Cycle, Time-Varying Vector Autoregressions |
| JEL: | C32 C36 E32 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202602 |
| By: | Tanique Schaffe-Odeleye; K\=osaku Takanashi; Vishesh Karwa; Edoardo M. Airoldi; Kenichiro McAlinn |
| Abstract: | We generalize the potential outcome framework to time series with an intervention by defining causal effects on stochastic processes. Interventions in dynamic systems alter not only outcome levels but also evolutionary dynamics -- changing persistence and transition laws. Our framework treats potential outcomes as entire trajectories, enabling causal estimands, identification conditions, and estimators to be formulated directly on path space. The resulting Dynamic Average Treatment Effect (DATE) characterizes how causal effects evolve through time and reduces to the classical average treatment effect under one period of time. For observational data, we derive a dynamic inverse-probability weighting estimator that is unbiased under dynamic ignorability and positivity. When treated units are scarce, we show that conditional mean trajectories underlying the DATE admit a linear state-space representation, yielding a dynamic linear model implementation. Simulations demonstrate that modeling time as intrinsic to the causal mechanism exposes dynamic effects that static methods systematically misestimate. An empirical study of COVID-19 lockdowns illustrates the framework's practical value for estimating and decomposing treatment effects. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.00836 |
| By: | Jamel Saadaoui |
| Abstract: | This paper constructs a new identification method to quantify bilateral geopolitical shocks-geopolitical turning points- i.e., abrupt, unforeseen state-to-state political turning points. Geopolitical shocks are captured by the second difference of the Political Relationship Index (Δ²PRI), a monthly narrative-based index constructed from Chinese government and media coverage. Unlike conventional global geopolitical risk indicators, Δ²PRI separates sudden departures from bilateral diplomatic paths so causal estimation is possible in a comparative cross-national context. Quantile instrumental variable local projections (IV-LP) are applied in the paper to estimate the dynamic and asymmetric geopolitical shock impact on world oil prices. It is estimated that US-China relational improvements lower oil prices by 0.2% in the short run and increase them by 0.3% in the medium run, with larger effects at the distribution boundaries of oil prices. Replication from Japan-China data establishes external validity. The paper adds a replicable analysis framework to explain how political shocks for dyads with heterogeneous institutional history and strategic rivalry spill over into global economic instability. |
| Keywords: | geopolitical risk, oil prices, quantile local projections, instrumental variables |
| JEL: | C26 C32 F51 Q41 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-08 |