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on Econometric Time Series |
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Issue of 2026–10–05
nineteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Han Xiao; Yuefeng Han; Rong Chen; Ama Ampadu-Kissi |
| Abstract: | Matrix time series is a series of matrix data observed over time. Analytical tools for such time series is needed in many applications in finance, economics, engineering and many other fields. To avoid the use of vectorization of the matrices which loses the column and row information, and the vector autoregression framework in traditional time series analysis, \cite{chen2021autoregressive} proposed the Matrix Autoregressive (MAR) Model. The model maintains and utilizes the matrix structure, leading to a substantial dimensional reduction and admitting explicit interpretations, comparing with the vector autoregressive model on the vectorized data. However, the MAR model still encounters difficulties in dealing with large dimensional matrix time series as the coefficient matrices in MAR models are also large. In this paper we propose to achieve further dimension reduction through reduced-rank constraints of the coefficient matrices in the MAR model. Estimation and rank determination procedures are studied. Theoretical investigation and empirical examples show that the reduced-rank constraint can achieve higher statistical efficiency than the MAR model. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.28841 |
| By: | Drew D. Creal; Marcelo C. Medeiros; Rodrigo Sarlo |
| Abstract: | We develop a class of linear state space models for matrix-valued time series data where the state is a latent matrix normal process. We derive matrix versions of the Kalman filter, log-likelihood, and smoother enabling estimation of the latent state matrix as well as the model's parameters. To conduct Bayesian inference, we provide algorithms that draw from the joint posterior distribution of the latent state matrices conditional on the observed data and parameters. We apply these methods to a large panel of U.S. macroeconomic time series across the 50 U.S. states. The proposed framework accommodates mixed-frequency data, heteroskedasticity, and outliers within a unified matrix-valued structure. Empirically, we find that a small number of latent factors captures the joint dynamics across states and variables, providing a parsimonious and scalable approach to modeling high-dimensional macroeconomic systems. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.18734 |
| By: | Lucas Harlaar (Maastricht University); Jan van den Brakel (Maastricht University); Siem Jan Koopman (Vrije Universiteit Amsterdam) |
| Abstract: | We develop a multivariate time series model for the complete national accounts dataset which typically consists of at least nine variables. The dynamic features of the variables are characterized by a set of unobserved components that evolve stochastically over time and may represent trend, cyclical, and seasonal effects. The components can be uniquely associated with a single variable or can be common to multiple variablesThe model treats expenditure and production variables jointly, subject to accounting-identity constraints, ensuring that their gross domestic product aggregates are consistent in both mean and variance by construction. The model constraints can be treated naturally within the Kalman filter. Parameter estimation is based on exact maximum likelihood which is feasible despite the high-dimensional parameter vector. This model-based framework allows for synchronized nowcasting, forecasting, seasonal adjustment, trend and cycle extraction for national accounts variables, including gross domestic product. We show that the statistical precision of signal extraction and forecasting improves when our framework is used instead of univariate and unconstrained model alternatives. When the model includes a common cycle component for all national accounts variables, it can be interpreted as a macroeconomic cycle indicator at current prices. We empirically illustrate our model-based methodology for data from national accounts of Germany, Italy, and the Netherlands, and show its significance for both official statistics and macroeconomic policy-making. |
| JEL: | C32 C54 |
| Date: | 2026–09–27 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260073 |
| By: | Bram Wouters; Cees Diks |
| Abstract: | We develop a model-agnostic framework for noise reduction in high-dimensional time series that explicitly targets optimal recovery of a low-dimensional latent dynamic component contaminated by observational white noise. Under the assumption that the latent dynamics live in a low-dimensional linear dynamic subspace, we characterize the optimal linear projection onto the dynamic subspace and provide a geometric description of the residual error in terms of the relative orientation of the signal and noise spaces. We propose estimators for the dynamic subspace and the optimal projection based on lagged covariance matrices, bootstrap dimension selection, and a low-rank representation of the structured noise. Under mild conditions, the resulting denoised series is shown to converge to its population target at the usual parametric rate. Simulations show that the proposed method can substantially improve subspace estimation, reconstruction error, and one-step-ahead forecast accuracy compared with both orthogonal projection-based denoising and the raw data. The approach is illustrated by empirical applications to high-dimensional stock returns and to a 20-variate time series of macroeconomic indicators. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.27614 |
| By: | Xinyu Song |
| Abstract: | We introduce a network realized GARCH-It\^o model in which volatility transmission is a dynamic relation among the latent daily integrated volatilities of multiple assets. An unknown directed and signed network is embedded in a continuous-time variance process and appears in the resulting exponential daily recursion. Intraday returns identify integrated volatility and hence the network that governs its propagation. For a fixed network template, feasible estimation based on realized volatility is first-order equivalent to estimation based on latent integrated volatility. For an unknown network, regularization selects the relevant structure, and, under oracle conditions, a fixed-rank local refit provides conditional inference for model-implied response-based connectedness. In an application to nine U.S. sector ETFs from 2007 to 2025, the model attains the lowest average out-of-sample QLIKE among the reported recursive forecasts, although its advantage over HAR is not statistically significant. In the full sample the weighted LASSO selects an empty sparse support, so inference concerns the rank-one projected factor component; this conditional analysis identifies Energy as a net volatility transmitter. Aggregate connectedness is more stable across volatility measures than individual sparse channels. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.29515 |
| By: | Oriol González-Casasús |
| Abstract: | Applied macroeconomists favor parsimonious VARs, which selection criteria and specification pre-tests routinely endorse. I show that weak, long-lived omitted dynamics escape those diagnostics and cannot be consistently estimated, yet the bias they induce in impulse responses and forecasts admits valid confidence intervals. Researchers can then keep the parsimonious VAR and state the direction and magnitude of the distortion it carries. In US data, the bias in the price response to a monetary contraction is significantly positive at several horizons, accounting for part of the price puzzle without expanding the cross-sectional information set. |
| Keywords: | dynamic mis-specification, price puzzle, robust inference, vector autoregression |
| JEL: | C12 C32 C52 E52 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:bge:wpaper:1595 |
| By: | Shuping Shi (Macquarie University); Jun Yu (University of Macau); Chen Zhang (Sun Yat-sen University) |
| Abstract: | Continuous time models provide a stronger benchmark for realized volatility forecasting than the discrete time models standard in empirical finance. Using 111 U.S. equities and ETFs, we compare continuous time fractional processes, ARFIMA, and HAR models on a common footing. Three families perform similarly at the daily horizon but separate at longer horizons, where continuous time models lead statistically and economically. The ranking reflects how each model balances recent volatility against its long run level. The continuous time advantage grows with volatility persistence and diminishes as jumps account for more variation. |
| Keywords: | Realized volatility, Continuous time models, Discrete time models, Forecasting, Economic utility |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202648 |
| By: | Micha{\l} Balcerek; Micha{\l} Wronka |
| Abstract: | We examine the conditional volatility dynamics of the USD 1Yx10Y forward swap rate using GARCH(1, 1), GJR-GARCH(1, 1), and a two-regime Markov-switching GARCH (MSGARCH) model. The analysis uses daily data from 2007 to 2023 and incorporates market-implied measures (ATM swaption volatility and the SRVIX in- dex) together with a broad set of diagnostic tests. Standard GARCH and GJR- GARCH models show stable short-run parameters, but the intercept {\omega} varies markedly across rolling windows, causing instability in the implied long-run vari- ance. This pattern, confirmed by the Nyblom test, motivates adopting a regime- switching specification. MSGARCH mitigates this issue by keeping regime-specific parameters stable and capturing time variation through filtered regime probabili- ties. It delivers the highest log-likelihood and lowest AIC, whereas BIC favours the more parsimonious GJR-GARCH. One-step-ahead backtesting indicates comparable short-horizon accuracy across models, but MSGARCH offers a clearer structural in- terpretation by isolating high- and low-volatility regimes aligned with major market events. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.25965 |
| By: | Hubeyb Gurdogan; Georg Menz |
| Abstract: | We establish a sharp pathwise signal-to-noise criterion for quasi-maximum-likelihood (QML) estimation of a dominant breakpoint in the second-moment structure of a multivariate time series: the QML estimator is consistent whenever the between-regime contrast exceeds the within-regime fluctuation by an explicit factor, and below this threshold global recovery can fail. Two innovations drive the result. First, the framework is pathwise: no stochastic model is imposed on the data. Second, the log-determinant objective carries an additive ridge regularization: it removes the endpoint boundary layers, so no trimming of the candidate set is required, and tuning the ridge weakens the consistency condition. As an application of the main theorem, we establish consistency of QML breakpoint estimation in pervasive factor models whose dimension diverges with the sample size, for completely general error terms -- not necessarily independent, idiosyncratic, or even random. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.12271 |
| By: | Zhiruo Zhang (Adelaide University); Firmin Doko Tchatoka (Adelaide University); Qazi Haque (Adelaide University) |
| Abstract: | We develop a Bayesian framework that combines adaptive shrinkage with variable selection to address over-parameterisation and sparsity in high-dimensional panel vector autoregressions (PVARs). The proposed approach employs Laplace-based spike-and-slab priors to enable flexible modelling of dynamic cross-sectional interdependencies and unit-specific heterogeneity. Monte Carlo evidence shows that the method delivers improvements in estimation accuracy and forecasting performance relative to existing regularisation approaches. We illustrate its empirical relevance in two applications. The first investigates financial contagion in euro area sovereign bond markets, while the second examines international forecasting performance in a multi-country macroeconomic panel. The results highlight the benefits of adaptive, component-specific shrinkage for capturing heterogeneous spillover structures in complex panel systems. |
| Keywords: | Dynamic Interdependency;Cross-sectional Heterogeneity;Bayesian Lasso;Variable Selection;Spike and Slab Prior;Financial Contagion |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:adl:wpaper:2026-05 |
| By: | Michela Eugenia Pasetto (Bank of Italy) |
| Abstract: | The accurate valuation of unquoted shares on the liability side of non-financial corporations' balance sheets is of primary importance, as equity issuance often constitutes a strategic choice for raising capital to finance investments. At macroeconomic level, quarterly data on equity issuance are published in financial accounts statistics and rely on estimation techniques. This paper proposes a new estimation method based on a Bayesian vector autoregression model to forecast unquoted equities issued by Italian non-financial corporations on a quarterly basis. The model is applied to both outstanding amounts and transactions. We compare the performance of the proposed model in its point forecasts and variability with five alternative econometric approaches, showing it performs very well in out-of-sample forecasting. |
| Keywords: | Bayesian VAR, forecasts, financial accounts, equity |
| JEL: | C32 C53 E27 E66 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:bdi:opques:qef_1037_26 |
| By: | Aidan Wardak (University of Florida); Sayar Karmakar (University of Florida) |
| Abstract: | We derive the limiting distributions of the $M$-test family of unit root statistics in the nearly integrated nearly white noise (NINW) framework introduced by Nabeya and Perron (1994) in the case of an unknown linear time trend. In the case of known long run variance (LRV), the limiting distributions of the $M^{GLS}$ tests are contaminated by additional noise terms as a result of quasi differencing whereas these terms are less present in the $M^{OLS}$ limiting distributions, both of which display conservative properties under conventional critical values. Furthermore, we prove the Gaussian power envelope in the NINW model is asymptotically equivalent to the standard envelope of Elliott, Rothenberg, and Stock (1996), and that the oracle $M$-tests have inefficient power relative to this benchmark. We then derive the limiting distributions of the feasible statistics and show that the autoregressive estimate of the LRV commonly used overestimates the LRV, creating altered limiting distributions. Finally, finite sample simulations illustrate that, of the procedures considered, no uniformly satisfactory solution exists for handling a series with a large negative moving average coefficient. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.30504 |
| By: | Frank, Luis |
| Abstract: | This paper evaluates different alternatives for nowcasting the year-on-year growth rate of Argentina’s Monthly Economic Activity Estimator (EMAE). A reduced set of high-frequency economic indicators - electricity demand, real tax revenue, automobile sales, and cement consumption - is used for the period from January 2015 to June 2026. An autoregressive distributed lag (ARDL) model, a dynamic factor model based on principal component analysis, and three regularization methods - LASSO, RIDGE, and Elastic Net - are compared. The results show that the ARDL model provides the best in-sample fit, with an R^2=0.92, and statistical evidence of a long-run relationship between EMAE and the indicators considered. The LASSO, RIDGE, and Elastic Net models achieve similar levels of fit, while offering advantages in dealing with multicollinearity and, in the case of LASSO and Elastic Net, allowing for variable selection. The dynamic factor model exhibits a lower fit (R^2=0.64), but provides a more parsimonious representation by summarizing the information contained in the indicators into a single factor. In terms of contemporaneous effects, cement consumption and electricity demand show the strongest associations with EMAE growth. The results should be interpreted with caution, since the high R^2 values obtained by the ARDL and regularized models reflect in-sample fit and, on their own, do not establish which methodology has greater predictive ability. |
| Keywords: | nowcasting; economic activity; EMAE; ARDL; LASSO; Elastic Net; principal component analysis |
| JEL: | C32 C53 |
| Date: | 2026–09–05 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:131074 |
| By: | Schröder, Maximilian |
| Abstract: | Macroeconomic policy increasingly requires assessments of risk rather than point forecasts alone. This paper develops a framework to compute impulse responses for scenario probabilities and the full predictive distribution of macroeconomic outcomes. The approach combines a regime-dependent mixture VAR with endogenous state probabilities and heteroskedastic shock identification, complemented by sparse sign and narrative restrictions. Applied to the euro area and U.S., the framework addresses a central policy question following the outbreak of the 2026 Iran war: do geopolitical shocks imply a return to the risk profile observed after Russia’s invasion of Ukraine, or is this time different? Results show that shocks differ not only in their effects on expected outcomes, but also in how they reshape scenario probabilities, tail risks, and transitions into high-volatility states. JEL Classification: C11, C32, C34, C53, E37 |
| Keywords: | Bayesian econometrics, density forecasting, macroeconomic risks, scenario analysis, state-dependent transmission |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263290 |
| By: | Nabeel Ahmad Saidd |
| Abstract: | Financial time series evolve across multiple temporal resolutions, challenging forecasting systems to incorporate newly available information without repeatedly recomputing unchanged representations. We introduce HARN, a Hierarchical Associative Resonance Network for event-driven multi-timeframe forecasting. HARN maintains persistent representations across temporal levels and updates each level only when its corresponding completed bar becomes available. The architecture combines causal multi-scale temporal encoding, gated associative memory, cross-level resonance, and hierarchical evidence aggregation, with forecasting performed in basis-point space and reconstructed to the original price scale. We evaluate HARN on four assets spanning equity, foreign exchange, and commodity markets using multiple random seeds and component ablations. HARN achieves competitive reconstructed-price forecasting errors against single-timeframe PatchTST and TimeXer baselines, while ablations reveal the effects of removing individual components across assets and timeframes. A code-level audit further examines consistency between the implementation and the defined event-driven causal protocol. The results position HARN as a persistent multi-timeframe forecasting framework rather than evidence of universal predictive superiority. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.26822 |
| By: | Aitor Ciarreta; Peru Muniain; Ainhoa Zarraga |
| Abstract: | The increasing volatility of electricity prices driven by renewable energy integration, market shocks, and regulatory changes has reinforced the need for forecasting methods that go beyond point predictions and accurately describe the full conditional price distribution. This paper applies the Generalised Additive Models for Location, Scale and Shape (GAMLSS) framework to forecast Spanish day-ahead electricity prices using hourly data from 2020 to 2024. Alternative specifications based on Normal, Johnson's SU (JSU), and Sinh-Arcsinh (SHASH) distributions are considered, allowing the location, scale, and shape parameters to vary with market fundamentals, including electricity demand, renewable generation, seasonal effects, and regulatory and geopolitical risk factors. Forecasts are generated using a rolling-window approach and evaluated through the mean absolute error (MAE), pinball loss, and Diebold-Mariano tests. The results show that flexible distributional specifications improve forecasting performance relative to a naive benchmark and the standard normal specification. While SHASH and JSU specifications provide the lowest point forecasting errors, the hourly analysis reveals substantial intraday variation in relative performance across specifications. JSU specification with all four parameters driven by covariates achieves the best probabilistic forecasting performance, particularly in the tails of the distribution. Diebold-Mariano tests confirm the statistical significance of these improvements. These findings highlight the importance of modelling time-varying shape distributional parameters and demonstrate the value of GAMLSS models for forecasting and risk management in increasingly volatile electricity markets. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.01465 |
| 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); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa) |
| Abstract: | We revisit Quantile-on-Quantile connectedness and argue that estimating the equations of a Quantile Vector AutoRegressive model at different quantile levels does not fully capture the conventional Quantile-on-Quantile mechanism. We propose a local, kernel-weighted QVAR approach that explicitly accounts for the quantile location of the conditioning variable. An empirical comparison using U.S. Treasury yields shows that this modification substantially affects estimated connectedness, producing a more homogeneous pattern across quantile pairs and markedly attenuating the differences between directly and reversely related quantiles. |
| Keywords: | Quantile-on-Quantile, Connectedness, Quantile VAR, Spillovers, Quantile Regression |
| JEL: | C22 C32 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202629 |
| By: | Andrzej Tokajuk; Jaros{\l}aw A. Chudziak |
| Abstract: | Volatility forecasts play a central role in financial risk management because their overall level and day-to-day movements affect downstream decisions. Most studies compare forecasting models while keeping the training loss fixed. Yet losses emphasise different errors and can target different properties of future volatility, so raw comparisons may combine persistent forecast-level differences with differences in daily forecast movements. This leaves unresolved whether the importance of loss choice comes mainly from the forecast level it targets or from differences that remain after level adjustment. We address this gap through a comparison of seven losses and five models across major cryptocurrencies. Validation-based alignment adjusts the forecast level before the raw and aligned forecasts are evaluated using statistical scores and one-day Value-at-Risk. Before alignment, marginal score variation is greater across losses. After alignment, model choice becomes the larger source of variation in the full five-model comparison, while cross-loss differences in VaR breach rates narrow substantially. Our contribution is a comprehensive evaluation of loss and model choice that shows why losses can appear so influential in raw comparisons and how this interpretation changes when forecast level and downstream risk are considered explicitly. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.27024 |
| By: | Farid Muradzada (Central Bank of Azerbaijan Republic); Khazan Bakhshaliyev (Central Bank of Azerbaijan Republic) |
| Abstract: | This study develops a forecasting framework for Brent crude oil prices based on the fundamental drivers of the global oil market, namely demand, supply, and market expectations. The estimation is conducted using quarterly time-series data covering the period 1994–2025 and employs a Vector Autoregressive (VAR) model. The results indicate that the proposed model demonstrates strong forecast performance under conditions of high oil price volatility. The forecasting error of the model is lower than that of benchmark models. Furthermore, the findings confirm that geopolitical tensions, regional conflicts, and uncertainty in global energy markets have a significant impact on oil price dynamics through oil futures prices. |
| Keywords: | Brent crude oil price, oil price forecasting, VAR model |
| JEL: | C53 Q43 Q47 |
| Date: | 2025–08–05 |
| URL: | https://d.repec.org/n?u=RePEc:aze:wpaper:2503 |