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on Econometric Time Series |
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Issue of 2026–05–25
nineteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Safira, Dinda Ayu; Kuswanto, Heri; Ahsan, Muhammad; Sibbertsen, Philipp |
| Abstract: | This study proposes an optimized estimation approach for Self-Exciting Threshold Autoregressive (SETAR) models by integrating the Majorization-Minimization Group Least Absolute Shrinkage and Selection Operator (MM-gLASSO) algorithm, with a primary focus on improving forecasting performance in complex regime-switching environments. While SETAR models are powerful in capturing non-linear regimes and asymmetric dynamics in time series data, they often suffer from high-dimensional parameter spaces. This typically leads to high-dimensional parameter spaces that cause overfitting and reduced forecasting stability. We address this by employing the MM algorithm to simplify the complex, non-differentiable gLASSO penalty into a more manageable surrogate function. This ensures stable convergence and allows for simultaneous variable selection and parameter estimation across multiple regimes. The gLASSO penalty is specifically utilized to ensure that irrelevant lags are excluded consistently across the threshold structure. We provide a detailed derivation of the estimation procedure and evaluate its performance through extensive simulation studies. The results indicate that the MM-gLASSO framework significantly outperforms traditional methods, particularly in terms of sparsity recognition and parameter consistency. Finally, an empirical application on PM2.5 concentration demonstrates the model's superior forecasting capability and its effectiveness in identifying structural transitions in real-world time series data. |
| Keywords: | gLASSO, MM algorithm, nonlinear time series, regime detection, SETAR model |
| JEL: | C13 C32 C53 Q53 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-746 |
| By: | OBIDAJU, INNOCENT |
| Abstract: | This study examined the trend, behaviour, and forecasting of TETFund allocation to universities, polytechnics, and colleges of education in Nigeria using a quantitative time series approach based on ARIMA modeling. The findings revealed that allocations across all categories exhibit a consistent upward trend and are stationary in levels around a deterministic trend which indicates that they are trend-stationary processes. Model estimation showed that the autoregressive and moving average components are statistically insignificant, leading to the adoption of a parsimonious ARIMA (0, 0, 0) model with a deterministic trend for all categories. Diagnostic tests, including checks for serial correlation and heteroskedasticity, confirmed that the models are statistically adequate, with residuals behaving as white noise and exhibiting constant variance. Forecast results projected a steady increase in TETFund allocations up to 2036, following a smooth linear trajectory; however, these projections are purely trend-driven and do not capture potential structural breaks or external shocks. Overall, the study concludes that TETFund disbursement is largely policy-driven and influenced by fiscal and macroeconomic conditions rather than historical allocation patterns, underscoring the importance of stable fiscal policy, effective planning, and adaptive funding strategies in sustaining tertiary education development in Nigeria. |
| Keywords: | Budgetary Allocation, Funding gap, Tertiary Education Funding (TETFund), ARIMA Modeling, Forecasting, Time Series |
| JEL: | H30 |
| Date: | 2026–05–08 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129024 |
| By: | Patrick Woitschig; Mike West |
| Abstract: | We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian dynamic linear models (DLMs) for asset price series. This represents reduced-form volatility leverage and feedback effects through use of realized volatility proxies in conditional DLMs for prices or returns, coupled with the synthesis of higher frequency data to track and anticipate volatility fluctuations. Analysis is computationally straightforward, extending conjugate-form Bayesian analyses for sequential filtering and model monitoring with simple and direct simulation for forecasting. A main applied setting is equity return forecasting with daily prices and realized volatility from high-frequency, intraday data. Detailed empirical studies of multiple S&P sector ETFs highlight the improvements achievable in asset price forecasting relative to standard models and deliver contextual insights on the nature and practical relevance of volatility leverage and feedback effects. The analytic structure and negligible extra computational cost will enable scaling to higher dimensions for multivariate price series forecasting for decouple/recouple portfolio construction and risk management applications. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.12099 |
| By: | Sanjiv R Das; Taranag Goyal; Mohini Yadav |
| Abstract: | Using Chronos-2, an open-source time-series foundation model, we evaluate pretrained time-series models for economic and financial forecasting with an emphasis on whether multivariate (MV) inputs improve accuracy relative to univariate (UV) baselines. The study covers two panels -- the Magnificent-7 equities and U.S. Treasury interest rates -- as well as a combined panel, using rolling monthly evaluations from 2000--2025. We vary input window lengths and forecast horizons and report RMSE and MAPE. Across datasets, MV forecasts consistently outperform UV forecasts, with especially strong gains for interest rates and meaningful improvements for equities. Series-level comparisons show MV improvements in every case, and error dispersion is generally lower under MV inputs. We also provide parameter-heatmap and time-series visualizations. However, mixing time series across equity and interest rate markets reduces forecast accuracy, indicating that adding noisy context degrades model performance. Overall, the results indicate that foundation models can leverage cross-series information to improve forecast accuracy in finance, and that the benefits are strongest when related series are modeled jointly under disciplined rolling protocols. Other than using an open-source foundation model, this paper also showcases how AI may be used for financial research. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.21504 |
| By: | Jonas F. Frederiksen; Muneya Matsui; Rasmus S. Pedersen |
| Abstract: | We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test statistic converges to a nonstandard limit involving non-Gaussian stable random variables. As a consequence, conventional critical values can yield severely distorted inference: a nominal 5$\%$ test may reject a true null as often as 70$\%$ of the time. To establish these results, we develop a new stable limit theorem for strongly mixing, infinite-variance time series processes. Building on this theory, we consider sub-sampling-based inference that remains valid irrespective of tail-heaviness and requires no estimation of long-run variances or tail indices. An application to risk forecasts for emerging-market exchange rates shows that accounting for heavy tails can substantially alter conclusions about predictive performance relative to standard procedures. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.16866 |
| By: | Yasumasa Matsuda; Michel F. C. Haddad |
| Abstract: | We propose a density-valued vector autoregressive model with latent factors for multivariate time series of density functions. Motivated by weekly regional distributions of SARS-CoV-2 cycle threshold (Ct) values in Brazil, we study their distributional dynamics across regions. The Ct value is the number of amplification cycles required for the viral signal to cross a detection threshold (lower Ct values correspond to higher viral load). We estimate each regional density by a B-spline mixture, mapping the mixture weights to a Euclidean space by a generalized logit transform equipped with an isometric inner product, and model the transformed series by a crossregional VAR with latent factors. This decomposition allows for the separation between strong common movements and directed idiosyncratic dynamics. Directed edges are identified from the idiosyncratic VAR component using one-sided tests with Benjamini–Yekutieli false discovery rate control. Simulations show that increasing the number of estimated factors does not mechanically eliminate genuine idiosyncratic dependence; rather, it mainly removes spuriously detected edges driven by common factor movements. In the real-world data application, the full sample yields only a weak directed network, whereas a substantial network emerges once the first six months are excluded and the density prior is kept weak. The estimated links suggest directed predictive relations from the northern region toward southeastern metropolitan areas. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:toh:dssraa:150 |
| By: | Philippe Goulet Coulombe |
| Abstract: | Needless to say, linear dynamics are pervasive in economic time series, particularly autoregressive ones. While gradient boosting with trees excels at capturing nonlinearities, it is inefficient in small samples when much of the predictive content is linear, expending splits to approximate relationships better captured by simple linear terms. This paper proposes LGB+, a boosting procedure operating on a more inclusive set of basis functions. The idea comes in two flavors. LGB+ evaluates a tree and a linear candidate at each step against out-of-bag data; only the winner advances. The simpler variant, LGB^A+, alternates on a fixed schedule: a block of tree updates, then a greedy linear correction, repeat. Both designs avoid ex ante commitments to any particular functional form or predictor selection. Because the prediction is the sum of a linear and a tree component, forecasts decompose natively into linear and nonlinear contributions, and so does permutation-based variable importance and historical proximity weights. In a quarterly U.S. macroeconomic forecasting exercise, LGB+ delivers strong gains for targets with pronounced autoregressive dynamics or mixed linear-nonlinear signals. Variables dominating the linear channel are those operating through autoregressive persistence or near-accounting relationships to the target (e.g., initial claims for unemployment and building permits for housing starts). |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.09740 |
| By: | Peter Reinhard Hansen; Chen Tong |
| Abstract: | Score-driven models update time-varying parameters using conditional likelihood scores. This paper gives a Bayesian interpretation based on Tweedie's formula. In Gaussian signal extraction, Tweedie's formula expresses the posterior correction as a scaled score of the marginal predictive density; in natural exponential families, the corresponding identity includes a base-measure adjustment. For general conditional densities, we show that inverse-Fisher-scaled conditional scores arise as local Gaussian posterior corrections based on Fisher scoring and precision discounting. For conjugate natural exponential families, the classical discounted Bayesian recursion has an exact score-driven representation: with steady-state precision discounting and expectation-space inverse-Fisher scaling, the score-driven correction equals the Bayesian posterior mean before transition dynamics are imposed. Tweedie's variance-function index further clarifies how conditional scores normalize forecast errors. The results link empirical Bayes, approximate filtering, dynamic generalized linear models, and score-driven models while distinguishing exact Bayesian updating from local score-based approximation. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15902 |
| By: | Martin Bruns (School of Economics, University of East Anglia); Helmut Lütkepohl (DIW Berlin & FU Berlin); James McNeil (Department of Economics, Dalhousie University) |
| Abstract: | Several recent studies consider a set of proxies to identify different monetary policy shocks for different regions in the world. We show that the way the proxies are used to identify the monetary policy shocks may lead to correlated shocks and dubious structural analysis and we demonstrate how to overcome the problem of correlated shocks. We illustrate that, if correlated shocks are used in applied studies, key statistics of interest such as impulse responses and forecast error variance decompositions can be severely distorted and we consider bench mark studies on monetary policy in the euro area (EA), the US and the UK to demonstrate the problems. |
| Keywords: | Structural vector autoregression, proxy VAR, GMM, correlated structural shocks |
| JEL: | C32 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:uea:ueaeco:2026-02 |
| By: | Yuan Liao; Xin Tong; Wanjie Wang; Dacheng Xiu |
| Abstract: | We develop asymptotic theory for principal component analysis (PCA) of a high-dimensional factor model in which the working dimension $R$ is fixed and only required to satisfy $R \ge r$, where $r$ is the true number of factors. Building on anisotropic local laws from random matrix theory, we show that the ``extra'' empirical eigencomponents beyond the $r$-th are asymptotically noise-governed, incoherent, and nearly orthogonal to the factor loadings. We introduce two rotations, an expanded $r\times R$ map $H'$ and a compressed $R\times r$ map $H^{+}$, and establish consistency of the estimated factors under both. As an application, we analyze a factor-augmented regression for treatment-effect inference and prove $\sqrt{T}$-asymptotic normality for every fixed $R \ge r$. These results provide a theoretical underpinning for the common empirical practice of adopting a conservative upper bound on the number of factors, and shift the analytical burden from consistent dimension selection to the milder requirement of bounding $r$ from above. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.18448 |
| By: | Stanis{\l}aw M. S. Halkiewicz |
| Abstract: | We propose and analyse rolling-origin conformal prediction for time-series forecasting. The method calibrates the conformal quantile against the $m$ most recent pseudo-out-of-sample forecast errors, adapting to serial dependence, volatility clustering, and distributional drift that invalidate classical conformal guarantees. Under H\"{o}lder-$\beta$ local stationarity and $\alpha$-mixing, we establish a four-term coverage-error decomposition and derive the optimal calibration window $m^{\star} \asymp T^{2\beta/(2\beta+1)}$ with coverage-error rate $O(T^{-\beta/(2\beta+1)})$. A Le Cam two-point construction shows this rate is minimax-optimal over the H\"{o}lder-$\beta$ model class. The Bahadur representation is proved under both $\alpha$-mixing and the physical-dependence framework of Wu (2005). An oracle inequality formalises Winkler cross-validation as an adaptive window selector; the required uniform concentration condition is established in an appendix. Validation on six real series and 93 M4 competition series confirms the theory: rolling-origin calibration outperforms full-history calibration in 86\% of comparisons (median Winkler improvement 12.3\%), maintains coverage within $\pm2\%$ of the 90\% target at short and medium horizons, and the cross-frequency log-log regression slope $0.614$ ($95\%$ CI $[0.424, 0.805]$) is consistent with the theoretical $2/3$ after controlling for frequency fixed effects. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.08422 |
| By: | Marco Gregnanin; Johannes De Smedt; Giorgio Gnecco; Maurizio Parton |
| Abstract: | Generating synthetic data for financial time series poses challenges, especially considering their non-stationary nature. Traditional statistical time series models normally assume weak stationarity. However, this assumption can constrain their effectiveness. Deep learning models, particularly Generative Adversarial Networks (GANs), have exhibited considerable potential in emulating complex probability distributions. GANs employ a generator-discriminator framework, where the generator creates data samples, while the discriminator distinguishes real from generated data. In this research, we introduce the Sig-Graph GAN model, which integrates the time-series signature, offering a structured summary of its temporal evolution; the Long Short-Term Memory network, capturing its inherent autoregressive structure; and Graph Neural Networks (GNNs), leveraging geometric patterns within the time-series data. To employ GNNs optimally, we use the visibility graph algorithm to derive a graph-based representation of the underlying time series. Numerical evaluations demonstrate that the Sig-Graph GAN model outperforms baseline methods in replicating the distribution of logarithmic returns across different stock exchanges. The integration of the graph structure with the autoregressive component effectively captures both geometric and temporal patterns embedded in time-series data. This research advances the field of GAN models for time series by introducing a model capable of leveraging both autoregressive properties and geometric structures for synthetic data generation. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.22215 |
| By: | Andrea Carriero; Florian Huber; Davide Pettenuzzo |
| Abstract: | We study double descent and benign overfitting in macroeconomic forecasting. We document that double-descent risk curves arise in standard macroeconomic datasets that are driven by a small number of latent factors, and we characterize when the underlying benign-overfitting mechanism holds. The conditions of Bartlett et al. (2020) are satisfied under the exact factor model and can also hold under the more realistic approximate factor model, provided idiosyncratic variances are not too dispersed across series. Because macroeconomic panels have only moderate dimensions, the overparameterization ratio N/T required by the theory is not naturally available. Our solution is to augment the data with synthetic copies from an estimated factor model and we prove that this strategy converges to a kernel ridge regression with a factor-structured kernel. Using monthly (FRED-MD) and quarterly (FRED-QD) US data, the resulting estimator consistently outperforms the Stock-Watson factor model for point forecasting across all series and horizons, with gains that are pervasive, statistically significant, and increasing with the forecast horizon. Our results suggest that benign overfitting, when it works, succeeds because overparameterization implicitly constructs a well-behaved kernel, not because overparameterization is intrinsically desirable. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15358 |
| By: | Marco Gregnanin; Johannes De Smedt; Giorgio Gnecco; Maurizio Parton |
| Abstract: | Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing temporal patterns within the time series data. In this research, we study the statistical significance of the inclusion of geometric patterns in enhancing forecasting accuracy within the context of time series analysis. We introduce the Time-Geometric model, a combination of models designed to exploit both geometric and temporal patterns. The contribution of this research lies in advancing the domain of univariate time series prediction, as demonstrated through extensive empirical evaluations. Our findings underscore that leveraging geometric patterns, captured through Graph Neural Networks, yields statistically significant improvements in forecasting accuracy. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.21192 |
| By: | Masahiro Tanaka |
| Abstract: | This paper introduces a quasi-Bayesian approach for local projection instrumental-variables (LP-IV) estimation. It builds a moment-based quasi-posterior using the generalized method of moments (GMM) objective and applies a roughness-penalty prior to smooth impulse responses over different horizons. The approach maintains the key first-order features of traditional LP-IV methods, while enhancing stability in finite samples and allowing for joint inference through simultaneous bands. Simulations indicate that this regularization decreases root mean squared error compared to standard GMM, especially at medium and longer horizons. An application to Danish electricity markets highlights the method's practical usefulness. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15966 |
| By: | Domagoj Ćorić (Dr. Franjo Tuđman Defense and Security University, Department of Statistics); Matej Kožnjak (Faculty of science – Department of Mathematics, University of Zagreb); Dražen Smiljanić (Dr. Franjo Tuđman Defense and Security University) |
| Abstract: | This paper examines the long-run cointegration between the German DAX and the US S&P 500 from January 2021 to December 2025, using daily closing prices expressed as natural logarithms. The central argument is that methodological choices prevalent in the existing literature systematically fail to detect genuine long-run equilibrium relationships due to the econometric costs of over-differencing and firststep OLS bias amplification. Drawing on the theoretical contributions of Granger and Newbold (1974), Granger (1981), Granger and Joyeux (1980), Engle and Granger (1987), and Phillips (1988), the paper reconstructs the conditions under which differencing destroys low-frequency spectral dynamics and renders standard cointegration tests unreliable. With this conclusion in mind, the paper tests two models that encompass long-term cointegration: ARDL and ECM models. The empirical analysis confirms that the ARDL model outperforms its competitor, making it the best-fit methodology for modelling cross-Atlantic equity market integration and carrying direct implications for portfolio diversification, financial stability monitoring, and applied econometric practice. |
| Keywords: | cointegration, ARDL, error correction model, DAX, S&P 500, spurious regression, fractional integration, capital market integration |
| JEL: | C22 C51 G17 |
| Date: | 2026–04–14 |
| URL: | https://d.repec.org/n?u=RePEc:zag:wpaper:2603 |
| By: | Sahaj Raj Malla |
| Abstract: | This study investigates the macroeconomic determinants and dynamic behaviour of personal remittances as a share of Gross Domestic Product (GDP) in Nepal, emphasizing external demand in major destination countries and domestic monetary policy. Using annual data (1993-2024), we construct composite indices via Principal Component Analysis (PCA) for multi-country external demand and a domestic Monetary Conditions Index (MCI). Our small-sample econometric pipeline includes Autoregressive Distributed Lag (ARDL) bounds testing, Engle-Granger cointegration, Dynamic OLS (DOLS), and a two-step Error Correction Model (ECM). We also employ Granger causality tests and multi-model forecasting using machine learning and ECM scenarios. The analysis reveals a strong positive long-run effect of external demand on remittances and a significant negative impact of tighter domestic monetary conditions. The ECM confirms a stable cointegrating relationship, correcting approximately 26% of disequilibria annually. Medium-term projections indicate remittances will remain structurally important, reaching around 28.3% of GDP by 2030 under baseline conditions, while exhibiting high sensitivity to external demand shocks. This study advances the literature by integrating PCA-derived external demand and monetary conditions indices within a unified ARDL-ECM framework for small samples. Focusing on one of the world's most remittance-dependent economies, it offers actionable insights for monetary policy calibration, migration diversification, and the productive utilization of remittance inflows. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.19401 |
| By: | Philippe Goulet Coulombe |
| Abstract: | Average forecast accuracy is not the same as forecast reliability. I treat forecast loss differentials relative to a benchmark as a return series. I then evaluate these returns using risk-adjusted performance measures from finance, including the Sharpe ratio, Sortino ratio, Omega ratio, and drawdown-based metrics. I also introduce the Edge Ratio capturing a model's propensity to deliver uniquely informative predictions relative to the forecasting frontier. I apply this framework to U.S. macroeconomic forecasting, comparing econometric benchmarks, machine learning models, a foundation model (TabPFN), and the Survey of Professional Forecasters. While it is often feasible to beat professional forecasters in terms of average accuracy, it is much harder to beat them on a risk-adjusted basis. They rarely exhibit catastrophic failures and often achieve high Edge Ratios, plausibly reflecting the value of contextual judgment. Nonetheless, selected machine learning methods deliver attractive risk profiles for specific targets. The framework naturally extends to meta-analyses across targets, horizons, and samples, illustrated with a density forecast evaluation and the M4 competition. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.09712 |
| By: | Ziyi Liu; Yiqing Xu |
| Abstract: | Synthetic control methods can produce misleading counterfactual predictions when outcome series contain unit-specific stochastic trends, a common feature of nonstationary macroeconomic data. Existing remedies, such as pre-filtering or differencing, reduce spurious matching but may discard shared nonstationary variation that helps estimate donor weights. We propose Harmonic Synthetic Control (HSC), which replaces this binary choice with a soft allocation mechanism. HSC jointly estimates donor weights and a treated-unit-specific smooth residual component, then extrapolates this component into post-treatment periods using a time-series forecaster. A tuning parameter, selected by rolling-origin cross-validation, governs the division between donor matching and forecasting. As it varies, HSC continuously interpolates between synthetic control applied to differenced outcomes and synthetic control applied to raw outcomes with an intercept or trend. We provide a spectral interpretation showing how HSC downweights low-frequency residual components in donor matching and assigns them to the forecasting branch. A prediction-error decomposition separates weight-estimation distortion from residual-forecasting error. Monte Carlo exercises show that HSC adapts across regimes, performing well when stochastic trends are predominantly common or idiosyncratic, while estimators fixed to one regime can fail in the other. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.20359 |