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on Econometric Time Series |
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Issue of 2026–08–24
fifteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Qiao, Xinghao; Wang, Zihan; Yao, Qiwei; Zhang, Bo |
| Abstract: | The factor modeling for high-dimensional time series is powerful in discovering latent common components for dimension reduction and information extraction. Most available estimation methods can be divided into two categories: the covariance-based under asymptotically-identifiable assumption and the autocovariance-based with white idiosyncratic noise. This article follows the autocovariance-based framework and develops a novel weight-calibrated method to improve the estimation performance. It adopts a linear projection to tackle high-dimensionality, and employs a reduced-rank autoregression formulation. The asymptotic theory of the proposed method is established, relaxing the assumption on white noise. Additionally, we make the first attempt in the literature by providing a systematic theoretical comparison among the covariance-based, the standard autocovariance-based, and our proposed weight-calibrated autocovariance-based methods in the presence of factors with different strengths. Extensive simulations are conducted to showcase the superior finite-sample performance of our proposed method, as well as to validate the newly established theory. The superiority of our proposal is further illustrated through the analysis of one financial and one macroeconomic datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. |
| Keywords: | autocovariance;covariance;eigenanalysis;factor strength;reduced rank autoregression;weight matrix |
| JEL: | C1 |
| Date: | 2026–07–27 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:138585 |
| By: | Inoue, Atsushi; Jordà , Oscar; Kuersteiner, Guido |
| Abstract: | Inference for impulse responses estimated with local projections presents interesting challenges and opportunities. Analysts typically want to assess the precision of individual estimates, explore the dynamic evolution of the response over particular regions, and generally determine whether the impulse generates a response that is any different from the null of no effect. Each of these goals requires a different approach to inference. In this article, we provide an overview of results that have appeared in the literature in the past 20 years along with some new procedures that we introduce here. |
| JEL: | C11 C12 C22 C32 C44 E17 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19379 |
| By: | A. Monta\~n\'es; E. Ruiz |
| Abstract: | It is obvious to say that an adequate estimation of the autocorrelation function is central in time series analysis. In this paper, we propose three new robust estimators based on ratios of observations, which offer strong resistance against outliers. While the first estimator, which is based on the median, is not efficient, the second is a Quasi Maximum Likelihood (QML) estimator with better efficiency properties. The third estimator is a plug-in estimator, which does not require numerical optimization and, consequently, is extremely simple from a computationally point of view, having similar efficiency to that of the ML estimator. We derive the asymptotic distribution of the first two estimators, when the true autocorrelations are zero. Furthermore, we also show that the asymptotic distribution of the plug-in estimator is rather close to that of the QML estimator, allowing for inference and, in particular, for the construction of point-wise significance bands for the autocorrelations. Using Monte Carlo simulations, we analyse the finite sample properties of the proposed estimators and compare them with those of the sample autocorrelations and alternative extant robust estimators based on ranks. Although the proposed estimators have larger dispersion than the sample autocorrelations in uncontaminated time series, they are highly robust in the presence of outliers. Also, they have better properties than popular alternative robust estimators based on ranks when estimating autocorrelations of order larger than one. The results are illustrated by estimating the correlogram of daily IBEX35 returns, quarterly US economic growth and monthly US inflation. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.23744 |
| By: | Hauzenberger, Niko; Huber, Florian; Klieber, Karin; Marcellino, Massimiliano |
| Abstract: | Macroeconomic data is characterized by a limited number of observations (small T), many time series (big K) but also by featuring temporal dependence. Neural networks, by contrast, are designed for datasets with millions of observations and covariates. In this paper, we develop Bayesian neural networks (BNNs) that are well-suited for handling datasets commonly used for macroeconomic analysis in policy institutions. Our approach avoids extensive specification searches through a novel mixture specification for the activation function that appropriately selects the form of nonlinearities. Shrinkage priors are used to prune the network and force irrelevant neurons to zero. To cope with heteroskedasticity, the BNN is augmented with a stochastic volatility model for the error term. We illustrate how the model can be used in a policy institution through simulations and by showing that BNNs produce more accurate point and density forecasts compared to other machine learning methods. |
| Keywords: | Bayesian neural networks; Model selection; Shrinkage priors; Macro forecasting |
| JEL: | C11 C30 C45 C53 E3 E44 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19381 |
| By: | Jordà , Oscar; Taylor, Alan M. |
| Abstract: | A central question in applied research is to estimate the effect of an exogenous intervention or shock on an outcome. The intervention can affect the outcome and controls on impact and over time. Moreover, there can be subsequent feedback between outcomes, controls and the intervention. Many of these interactions can be untangled using local projections. This method’s simplicity makes it a convenient and versatile tool in the empiricist’s kit, one that is generalizable to complex settings. This article reviews the state-of-the art for the practitioner, discusses best practices and possible extensions of local projections methods, along with their limitations. |
| Keywords: | Local projections; Impulse responses; Multipliers; Instrumental variables; indirect inference |
| JEL: | C01 C14 C22 C26 C32 C54 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19378 |
| By: | Kasun Dewage; Suranadi De Silva; Shankhadeep Mondal |
| Abstract: | Foundation models for time series forecasting demonstrate impressive zero-shot generalization but often underperform on specialized domains such as high-frequency finance. We present a comprehensive study of hybrid neural-classical correction for adapting frozen TimesFM (200M parameters) to stock return prediction during the volatile opening trading hour. We compare two neural correction architectures - AttnCorrect (multi-head self-attention, approximately 471K parameters) and GatedLinear (low-rank bilinear projection with gating, approximately 49K parameters) - each augmented with Random Forest residual learning. Through systematic ablation across 10 major technology stocks (NVDA, MSFT, AAPL, GOOG, GOOGL, AMZN, META, AVGO, TSLA, NFLX) spanning 2 million data points, we reveal critical insights: (1) The hybrid neural-classical approach achieves 0.597 pooled correlation and 6.4x mean per-day correlation improvement over frozen TimesFM; (2) Classical residual learning (Random Forest) provides the largest single-component contribution, matching or exceeding the neural correction component; (3) Simpler neural architectures surprisingly outperform complex ones when classical residual learning is removed; (4) Self-attention provides the largest neural-only contribution. GatedLinear+RF achieves best overall performance with 9x fewer neural parameters than AttnCorrect+RF. We report three complementary correlation metrics - mean per-day, cross-day cumulative, and pooled - to provide a complete picture of predictive quality. Our results provide practical guidance: effective foundation model adaptation requires careful integration of neural and classical components, with classical methods playing a crucial complementary role. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.08825 |
| By: | Xiaoyu Huang; Lulu Wang |
| Abstract: | Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models observe only returns while the ground-truth latent volatility state is known to the researcher. This setting provides a useful benchmark for mechanistic interpretability under partial observability: the latent state is hidden from the model but directly available for evaluation. Across architectures, losses, and output heads, we find evidence for a two-stage computation. Hidden representations encode substantial information about the next latent volatility state, and the output head maps this representation to squared return forecasts. Furthermore, in Transformers, latent-state decodability emerges at identifiable architectural stages whose location depends on the volatility period. In long-cycle regimes, this computation simplifies into an explicit latent-state filter consisting of a learned linear projection followed by $\ell^2$ normalization. Output-head replacement further shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure. These results suggest that stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.25459 |
| By: | Alexandre Alouadi; Charles-Albert Lehalle |
| Abstract: | Estimating the covariance structure of financial assets typically relies on historical returns, making risk models dependent on noisy and asset-specific time series. We propose the Characteristic-Driven Dynamic Factor Model (CD-DFM), a non-linear latent factor model that instead constructs a representation of the asset cross-section directly from observable firm characteristics, primarily company fundamentals. The learned latent space jointly determines interpretable factor exposures and a forward covariance estimator, and is trained end to end on an objective that combines a Stein covariance loss with a factor reconstruction term, targeting the out-of-sample second moments used in risk management. Because the latent representation, i.e. the encoder depends only on characteristics, previously unseen assets can be embedded at inference time without retraining. Experiments on S&P 500 equities show that CD-DFM produces economically structured latent representations, interpretable factor portfolios, and competitive covariance forecasts despite relying on substantially lower-frequency information than return-based approaches. Among the benchmarked methods, it is the only model that simultaneously combines characteristic-driven representations, factor interpretability, competitive covariance calibration, and zero-shot onboarding of unseen assets. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.24410 |
| By: | Andrea Bastianin (University of Milan, Italy and Fondazione Eni Enrico Mattei (FEEM)); Elisabetta Mirto (Study Center Gerzensee); Yan Qin (ClearBlue Markets); Luca Rossini (University of Milan, Italy and Fondazione Eni Enrico Mattei (FEEM)) |
| Abstract: | We tackle the issue of producing point, sign, and density forecasts for the monthly real price of carbon within the European carbon market, EU ETS. We show that a Bayesian Vector Autoregressive (BVAR) model, augmented with factors based on macroeconomic and financial variables, yields accuracy gains over a set of benchmark forecasts in both point and density forecasts. We also provide a qualitative comparison of model-based forecasts with survey expectations and forecasts released by data providers. Moreover, we consider verified emissions and demonstrate that adding stochastic volatility can further improve the forecasting performance of a single-factor BVAR model. Lastly, we rely on forecasts to build market monitoring tools that track demand and price pressure in the EU ETS. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:szg:worpap:2603 |
| By: | Miguel D. Ramirez (Department of Economics, Trinity College) |
| Keywords: | Autoregressive Distributed Lag (ARDL) model, Block-Granger causality test, Bounds cointegration test, Complementarity hypothesis, Error correction term (ECT), Foreign Direct Investment (FDI), gross and net foreign capital stock, Hannan-Quinn criterion (HQ), Johansen methodology, labor productivity, Ramsey Reset test, unit root tests. |
| JEL: | O10 O40 O57 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:tri:wpaper:2602 |
| By: | Junyi Ye; Gargi Vijay Borde |
| Abstract: | Financial volatility is regime dependent, yet incorporating regime information into neural networks can also destabilize training. This paper asks where such information should enter a neural cross-sectional volatility forecasting model. We study five-day realized-volatility forecasts for 1, 027 U.S. equities using a rolling walk-forward evaluation framework in which information, model capacity, hyperparameter tuning, and random seeds are matched across architectures. We propose RG-ResMoE, a regime-gated residual mixture-of-experts architecture in which regime information is used only for expert routing rather than for direct forecasting. The base predictor models volatility from stock features, while a gating network uses regime state variables to route residual corrections. RG-ResMoE consistently outperforms a capacity-matched MLP in both forecasting accuracy and training stability in the main U.S. study. Similar gains are observed on an independent Japanese panel. The integration pathway is decisive: appending the same regime variables directly to the forecasting input degrades both predictive performance and training stability, whereas restricting them to the routing gate improves accuracy and Value-at-Risk calibration. Hard routing consistently underperforms soft routing. The results suggest that, in compact neural volatility forecasting models, the primary value of mixture-of-experts models lies less in increasing model capacity than in controlling how nonstationary regime information influences prediction. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.12251 |
| By: | Xiaozhen Wang; Ana\"is Despr\'es; Martin Dureau; Francois Buet-Golfouse |
| Abstract: | Local-stochastic volatility (LSV) combines vanilla marginals with richer smile dynamics, but calibration requires a slow, noisy and sequential McKean--Vlasov fixed point. We learn a projection-consistent operator for the calibration triple. Given finite quotes and a stochastic-volatility (SV) backbone, it jointly returns an implied-volatility surface subject to static-arbitrage constraints, its Dupire local volatility, LSV leverage and the conditional moment required by the projection identity. Starting from option-price marginals, we derive a division-free Dupire residual in log-implied-variance coordinates and a quotient Fokker--Planck equation after Gy\"ongy projection. Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO) implementations enforce quote fit, static-arbitrage, Dupire and projection constraints. For the witness-augmented residual system, we prove conditional identification and empirical consistency under LSV existence and inverse residual stability. In controlled synthetic tests, forward-start and cliquet errors differ from a particle method by 0.1 and 0.2 percentage points, while calibration latency falls from 98.5 to 0.6 ms. Compared with the tested baselines, local-volatility root-mean-square error (RMSE) falls by 36% and leverage RMSE by 7-16%. These results support amortizing the LSV fixed point: the expensive solve moves offline, while online calibration reduces to a single projection-consistent operator evaluation. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.01217 |
| By: | Igor Halperin |
| Abstract: | The Observable Matrix Dynamics (OMD) approach monitors the time development of complex non-linear systems through the trajectory of a fixed-size distance matrix and its spectrum. We apply it to the S\&P 500 cross section over three crisis decades, the 2001 dot-com bust, the 2007--2008 financial crisis, and the 2020 Covid crash, with three fixed-size observables on a fixed universe. The arccos distance matrix of the rolling return correlations reads the correlation geometry: its effective dimension collapses at the 2008 and 2020 crises, while the 2001 bust is a dispersed unwind. Read against machine-learning distance matrices, its spectrum stays in the un-relaxed, pre-learning regime with no low-dimensional manifold, so the market never learns its correlation structure or relaxes to a stationary geometry. Subtracting the market factor exposes a coherent sector rotation, whose name-level attribution identifies which stocks drive each crisis and in what order. At a short lookback these signals resolve precursors and forecast the endogenous 2008 crisis, though not the exogenous 2020 shock. The other two observables model the daily return and volatility rankings as Markov chains on their ranking spaces. The return chain has persistent, defensive-led bellwethers and near-reversible dynamics. The volatility chain is far more persistent, led by the financial sector, and is the only one to carry a weak, episodic arrow of time, flaring at market stress and matching volatility clustering and the Zumbach effect. All three matrices show coherent changes during market crashes. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.19005 |
| By: | Runyao Yu; Yuchen Tao; Yujie Chen; Wentao Wang; Derek W. Bunn |
| Abstract: | Probabilistic K-line forecasting describes uncertainty in four complementary prices, namely open--high--low--close (OHLC). However, it introduces two consistency problems: quantile crossing and K-line crossing. Quantile crossing occurs when a higher-quantile forecast falls below a lower-quantile forecast, while K-line crossing occurs when the forecast low exceeds the open or close, or the forecast high falls below the open or close. Existing solutions generally address only one problem through output reordering, specialized architectures, or penalized training objectives. We propose K-line--Quantile Sequential Projection (KQSP), a parameter-free and training-free reconciliation method applicable to forecasts produced by any model. Compared with other crossing solutions, KQSP preserves predictive accuracy while producing substantially smaller corrections to the original forecasts. To mitigate model bias, we evaluate KQSP using various models, including pretrained foundation models. KQSP reduces both quantile and K-line crossing rates to zero for all test data undertaken. These results show that probabilistic K-line consistency can be enforced independently of forecast generation and without retraining. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.26792 |
| By: | Nader Karimi; Foad Shokrollahi |
| Abstract: | This paper develops a unit-consistent actuarial framework for pricing capped cumulative temperature-index insurance under long-range dependence and stochastic variability. Daily temperature anomalies are modeled as increments of fractional Brownian motion evaluated at an operational time generated by the integral of a stationary normalized Cox--Ingersoll--Ross process. We show that the stochastic time change preserves stationarity and the long-memory covariance decay of the increments while introducing additional variability through the random operational clock. The cumulative temperature index admits a conditionally Gaussian representation, which leads to an exact conditional exponential kernel for capped stop-loss contracts and ensures existence of the entropic premium for every positive risk-aversion parameter. Consequently, valuation reduces to an outer Monte Carlo expectation over the accumulated CIR time, avoiding fractional Brownian path simulation and covariance-matrix construction. We further establish monotonicity properties of the premium with respect to risk aversion and conditional volatility. An empirical illustration based on Chicago temperature data shows that both long memory and stochastic time change can materially affect insurance premiums relative to conventional Brownian and fractional Brownian benchmarks, with the Hurst parameter playing an important role in valuation uncertainty. The proposed framework therefore provides a tractable approach for incorporating persistent dependence, stochastic variability, and bounded insurance losses into climate-index pricing. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.15097 |