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on Econometric Time Series |
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Issue of 2026–06–29
fourteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Degui Li (Faculty of Business Administration, University of Macau); Yuying Sun (Chinese Academy of Sciences); Boyao Wu (University of International Business and Economics) |
| Abstract: | In this paper, we introduce a flexible time-varying multi-layer network vector autoregression (VAR) model framework for large-scale time series, allowing agents in dynamic systems to interact through multiple channels and incorporating multiple adjacency matrices to capture network spillover effects. We propose a penalized model averaging method to determine a time-varying optimal combination of multi-layer network VAR candidate models whose number may be divergent. Under some regularity conditions, the asymptotic properties such as asymptotic optimality and convergence rates of the proposed time-varying weight estimation are derived in the contexts of both the in-sample fitting and out-of-sample prediction. In addition, we extend the conformal prediction method to construct prediction bands for locally stationary time series. Monte-Carlo simulation studies and an empirical application to forecast CPI inflation by combining multiple network information are given to illustrate reliable finite-sample estimation and predictive performance of the developed methodology. |
| Keywords: | asymptotic optimality, conformal prediction, model averaging, multi-layer network, time-varying VAR |
| JEL: | C32 C38 C55 C58 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202640 |
| By: | Jinyuan Chang; Guanglin Huang; Qiwei Yao; Long Yu |
| Abstract: | We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08560 |
| By: | Ollech, Daniel |
| Abstract: | Official statistics routinely employs the X-13-ARIMA method to seasonally adjust economic time series. A key step is choosing the length of the seasonal moving av- erage. Traditionally, this choice relies on ad hoc criteria and expert judgement. We propose a cross-validation-based filter selection scheme that offers greater flexibility, including the possibility of incorporating novel filters. This approach is particularly promising for the seasonal adjustment of weekly, daily, and high-frequency time series. We demonstrate how to integrate cross-validation into the X-13-ARIMA method and discuss the advantages of various implementation options. Evaluation on monthly and quarterly time series demonstrates that this selection method performs at least as well as, and often better than, conventional selection criteria. |
| Keywords: | Seasonal adjustment, time series characteristics, non-parametric methods |
| JEL: | C13 C14 C22 C53 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:bubdps:341639 |
| By: | Andrea Bucci; Giulio Palomba; Eduardo Rossi |
| Abstract: | This paper proposes a Structural Matrix Autoregressive (SMAR) model for the joint analysis of asset returns, realized volatility, and trading volume in a large-dimensional setting. This framework simultaneously captures dynamic spillovers across financial variables and cross-sectional dependence across assets while preserving a parsimonious parameterization relative to conventional vector autoregressive models. The model is estimated on daily data for the constituents of the Dow Jones Industrial Average over the period 2021-2025 and is structurally identified through restrictions consistent with the Mixture of Distributions Hypothesis and efficient market theory. The empirical findings indicate that volatility is the primary driver of trading activity, suggesting that informational shocks are predominantly incorporated into markets through price variability. Forecast error variance decompositions further reveal that, although internal shocks dominate short-term volume dynamics, cross-asset spillovers account for more than 50% of trading volume variation at longer horizons. Finally, an event-study analysis around FOMC announcements supports the proposed decomposition by identifying significant increases in the informative component of trading activity on announcement days followed by rapid mean reversion. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08141 |
| By: | Hafner, Christian M. (Université catholique de Louvain, LIDAM/ISBA, Belgium); Preminger, Arie |
| Abstract: | This paper introduces a multivariate volatility model that is characterized by nonstationarity irrespective of the parameters. The model is motivated by the multivariate GARCH model in VEC form, setting the intercept term to zero. We first discuss the conditions required for a positive definite conditional variance matrix.For the special case of a diagonal parameter matrix, we derive the conditions for stability of trajectories, meaning that the processes do not diverge to infinity or to zero almost surely. We then develop the asymptotic theory for maximum likelihood estimation, and propose a test of the null hypothesis of a zero Lyapunov exponent, i.e. stability. In a simulation study we demonstrate the good performance of the estimator and the test in finite samples. |
| Keywords: | Volatility ; non-stationarity ; multivariate GARCH ; asymptotic theory ; maximum likelihood |
| Date: | 2026–03–28 |
| URL: | https://d.repec.org/n?u=RePEc:aiz:louvad:2026012 |
| By: | Roberto Baviera; Pietro Manzoni; Michele Domenico Massaria |
| Abstract: | Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, L\'evy copulas and zero-mixed models, often face practical difficulties in simulation and parameter calibration. In this paper, we introduce the Comb-Bernoulli model, a novel framework for capturing dependence between sparse time series of insurance risks, bridging the benefits of the two standard approaches. The (traditional) copula structure of the proposed model enables tractable: i) simulation, ii) likelihood evaluation, and iii) estimation of dependence parameters. We present the general properties of the model and analyze in detail the Gaussian copula case with lognormal marginals. Moreover, we illustrate an application using the Danish fire insurance dataset, highlighting both the modeling strengths and numerical efficiency of our approach in real-world risk management. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.25559 |
| By: | Marc Schmitt |
| Abstract: | In algorithmic markets, predictive models become part of the data-generating process they aim to forecast. Once their outputs are converted into trades, allocations, execution schedules, or risk controls, they change the future data on which they are evaluated. I introduce algometrics, a framework for time series whose evolution depends on the predictive algorithms forecasting them. The framework distinguishes historical risk, measured under passive forecasting, from deployment risk, measured when forecasts drive actions. I prove three results. First, deployment risk is not identifiable from passive historical data alone: even in a one-step linear feedback model, infinitely many algorithm-mediated environments induce the same historical law while implying different deployment risks for the same forecaster. Second, historical model rankings can invert under crowding, so a predictor with lower passive error can have higher deployment error once similar algorithms are adopted. Third, randomized or instrumented actions identify short-horizon linear feedback, and I derive a finite-sample bound for deployment-risk estimation. These results suggest that time-series benchmarks in algorithmic markets should report feedback sensitivity alongside predictive accuracy. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.23978 |
| By: | Miguel Sanchez-Martinez (International Labour Organization); Tomasz Wo\'zniak (University of Melbourne) |
| Abstract: | The R package bpvars was designed to forecast employment, unemployment, and labour market participation rates of 189 countries. However, it is generally applicable to dynamic panel data due to the flexibility of its modelling framework and robust coding. It includes a family of Bayesian hierarchical panel Vector Autoregressions (VARs) that are characterised by: (i) country-specific VAR models (ii) with their parameters' priors centred around their global counterparts, and (iii) featuring flexible multi-level hierarchical prior distributions (iv) with many variants of well-established in the literature benchmark choices, and (v) four alternative specifications including groupping of country-specific or global parameters. A~distinguishing feature is its implementation of missing observation treatment based on a model-coherent Bayesian approach. These models are accompanied by Bayesian prediction, offering a wide range of possible specifications that aim to increase forecasting precision and comply with various reporting standards. We also implement pseudo-out-of-sample recursive forecasting for evaluating point and density forecast performance. The package implements model specification, estimation, and forecasting routines, facilitating simple workflows and reproducibility, including estimation and forecasting results summaries and visualisations. It achieves extraordinary computational speed thanks to the employment of frontier econometric and numerical techniques, as well as algorithms written in C++. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.14143 |
| By: | Elton Beqiraj; Giovanni Di Bartolomeo; Marco Di Pietro; Carolina Serpieri |
| Abstract: | We propose a new approach to study the resilience to business cycle fluctuations of the Central Europe and Baltic macro-region. By individually estimating six open economy DSGE models within the macro-region, we identify the business-cycle-volatility drivers for each country. Then, we use the outcome of our six estimates to conduct a principal component analysis to determine structural common characteristics required to explain economic resilience in the Central Europe and Baltic macro-region. |
| Keywords: | Financial crisis, resilience, macroeconomic performance, emerging markets, Bayesian estimations, principal component analysis |
| JEL: | E02 E32 E58 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ter:wpaper:00194 |
| By: | Luis Rodrigo Asturias Schaub; Guglielmo Maria Caporale; Luis Alberiko Gil-Alana |
| Abstract: | This paper analyses the long-memory properties of sovereign bond spreads in 17 Latin American countries as well as two regional aggregates using daily EMBI (Emerging Markets Bond Index) data from April 2013 to January 2026 (3, 163 observations per series). Parametric methods show that all 19 series are characterized by fractional integration with estimated orders ranging from 0.97 (Uruguay) to 1.22 (Honduras) for the log-transformed spreads. Nine series have confidence bounds above unity, indicating that shocks have permanent effects; under autocorrelated errors (as in the Bloomfield model), Uruguay is the only country whose series exhibits mean reversion (as the confidence bands for the fractional parameter are below unity). The results are robust to making different assumptions about the error terms (white noise or autocorrelation) and to allowing for non-linear deterministic trends. |
| Keywords: | long memory, fractional integration, EMBI (Emerging Markets Bond Index), sovereign spreads, Latin America |
| JEL: | C22 F34 G15 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12731 |
| By: | Krzysztof Ozimek |
| Abstract: | Anomaly detection methods in financial time series score statistically unusual observations in observable data, not topologically misexpected persistent deviations in the latent structure of co-movement. This study constructs a stock-level topological anomaly score jointly conditioned on market-level topological structure and cross-sectional peer context, and tests whether its history carries predictive content for return curves. Intraday data for ten liquid S&P 500 constituents (April 2025--March 2026) are embedded via Takens delay embedding, graphed by BallMapper, and scored by three decoder-conditional variational autoencoder variants. Predictive content is assessed by penalised function-on-function regression and confirmed across all assets, intraday bar frequencies, and scoring variants, revealing a consistent temporal fingerprint -- gradual accumulation of return impact, a frequent early reversal of its direction, and broadly distributed predictive content weighted toward recent anomaly history. When the reversal occurs depends on market regime; how evenly the anomaly history contributes to prediction depends on bar frequency. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08586 |
| By: | Nicola Baldoni; Michele Sparviero; Lorenzo Viola |
| Abstract: | Generating stochastic trajectories for asset classes is an increasingly relevant task in quantitative finance. Traditional approaches, such as the stationary bootstrap, preserve by construction the empirical distribution of asset-class returns, but do not ensure that each individual simulated path is economically realistic: scenarios may be valid in distribution while single trajectories fail to represent plausible states of the world. To address this limitation, we review semiparametric simulation methodologies that combine a parametric structure, which enforces realistic dynamics, with the resampling of model residuals, which preserves the stochastic component observed in historical data. The issue is particularly acute for interest rates, where direct resampling of rate changes may produce implausible yield-curve evolutions despite correct distributional properties. Our empirical analysis shows the effectiveness of semiparametric bootstrap methods based on autoregressive or mean-reverting specifications. In the fixed-income setting, combining these methods with fully parametric term-structure models yields more coherent and realistic simulations of yield-curve dynamics. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.11859 |
| By: | Michele Sparviero; Lorenzo Viola |
| Abstract: | This paper develops a methodological framework for reverse stress testing (RST) in which a multivariate stress scenario, coherent with the empirical dependence structure of a market, is reconstructed from a single exogenous shock prescribed on one asset class. The problem is formulated as the maximisation of the conditional density given the imposed shock, and is solved under three progressively weaker distributional assumptions. In the parametric setting, joint Gaussianity of the returns yields a closed-form modal scenario coinciding with the conditional mean of the non-shocked components. In the semiparametric setting, the modal scenario is estimated nonparametrically through the empirical likelihood methodology and the surrounding stressed trajectories are generated via a Gaussian or Student-t local sampling scheme. In the fully nonparametric setting, stressed trajectories are obtained by inverse-distance resampling of the historical observations within a Mahalanobis neighbourhood of the estimated scenario. The three variants are validated on real market data. The simulated scenarios prove to be economically coherent and capable of reproducing the standard risk-reward asymmetry observed in stressed market regimes. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.09274 |
| By: | Amedeo Andriollo |
| Abstract: | This paper studies specification testing in dynamic linear models in the presence of omitted variables. The null hypothesis of interest is weak exogeneity: shocks have zero conditional expectation given their own past and the past of omitted variables. Existing tests based on quadratic forms of serial cross-correlations suffer from size distortions because their variance incorporates symmetric dependence in both directions, including causality from past shocks to present omitted variables (inverse causality). This paper proposes an asymmetric Portmanteau test that isolates violations of weak exogeneity from inverse causality, is asymptotically normal under the null, and does not require a parametric specification of the joint dynamics. An empirical application examines the Economic Policy Uncertainty shock series and rejects its weak exogeneity. Addressing this failure by controlling for omitted variables changes the estimated inflation response from negative to positive, suggesting a supply-side shock interpretation. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.07715 |