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on Econometric Time Series |
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Issue of 2025–09–01
fifteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Jialing Han; Yu-Ning Li |
| Abstract: | We propose a novel framework for approximate factor models that integrates an S-vine copula structure to capture complex dependencies among common factors. Our estimation procedure proceeds in two steps: first, we apply principal component analysis (PCA) to extract the factors; second, we employ maximum likelihood estimation that combines kernel density estimation for the margins with an S-vine copula to model the dependence structure. Jointly fitting the S-vine copula with the margins yields an oblique factor rotation without resorting to ad hoc restrictions or traditional projection pursuit methods. Our theoretical contributions include establishing the consistency of the rotation and copula parameter estimators, developing asymptotic theory for the factor-projected empirical process under dependent data, and proving the uniform consistency of the projected entropy estimators. Simulation studies demonstrate convergence with respect to both the dimensionality and the sample size. We further assess model performance through Value-at-Risk (VaR) estimation via Monte Carlo methods and apply our methodology to the daily returns of S&P 500 Index constituents to forecast the VaR of S&P 500 index. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.11619 |
| By: | Bruno E. Holtz; Ricardo S. Ehlers; Adriano K. Suzuki; Francisco Louzada |
| Abstract: | Financial time series often exhibit skewness and heavy tails, making it essential to use models that incorporate these characteristics to ensure greater reliability in the results. Furthermore, allowing temporal variation in the skewness parameter can bring significant gains in the analysis of this type of series. However, for more robustness, it is crucial to develop models that balance flexibility and parsimony. In this paper, we propose dynamic skewness stochastic volatility models in the SMSN family (DynSSV-SMSN), using priors that penalize model complexity. Parameter estimation was carried out using the Hamiltonian Monte Carlo (HMC) method via the \texttt{RStan} package. Simulation results demonstrated that penalizing priors present superior performance in several scenarios compared to the classical choices. In the empirical application to returns of cryptocurrencies, models with heavy tails and dynamic skewness provided a better fit to the data according to the DIC, WAIC, and LOO-CV information criteria. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10778 |
| By: | Edward P. Herbst; Benjamin K. Johannsen |
| Abstract: | This comment discusses Kolesár and Plagborg-Møller's (2025) finding that the standard linear local projection (LP) estimator recovers the average marginal effect (AME) even in nonlinear settings. We apply and discuss a subset their results using a simple nonlinear time series model, emphasizing the role of the weighting function and the impact of nonlinearities on small-sample properties. |
| Keywords: | Local projections; Average marginal effect; Nonlinear time series; Small-sample properties; Weighting function |
| JEL: | C32 C52 E32 |
| Date: | 2025–08–05 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2025-58 |
| By: | Bahaa Aly, Tarek |
| Abstract: | This paper introduced a novel methodology for measuring nonlinear Granger causality in macroeconomic time series by combining Multivariate Singular Spectrum Analysis (MSSA) for data denoising with Artificial Neural Network (ANN) input occlusion for causal inference. We applied this framework to five countries, analyzing key macro-financial variables, including yield curve latent factors, equity indices, exchange rates, inflation, GDP, and policy rates. MSSA enhanced data quality by maximizing signal-to-noise ratios while preserving structural patterns, resulting in more stable ΔMSE values and reduced error variability. ANNs were trained on MSSA-denoised data to predict each target variable using lagged inputs, with input occlusion evaluating the marginal predictive contribution of each input to derive causality p-values. This approach outperformed traditional VAR-based Granger causality tests, identifying 38 significant causal relationships compared to 24 for VAR. Cross-country analysis of variables revealed differences in transmission mechanisms, monetary policy effectiveness, and growth-inflation dynamics. Notably, feature importance rankings showed that policy rates and stock market indices predominantly drove macroeconomic outcomes across countries, underscoring their critical role in economic dynamics. These findings demonstrated that combining MSSA and ANN input occlusion offered a robust framework for analyzing nonlinear causality in complex macroeconomic systems. |
| Keywords: | Nonlinear Granger causality, Input Occlusion, Multiple Singular Spectrum Analysis, p-values |
| JEL: | C45 |
| Date: | 2025–07–26 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:125453 |
| By: | Zheng Fan; Worapree Maneesoonthorn; Yong Song |
| Abstract: | We propose the Markov Switching Dynamic Shrinkage process (MSDSP), nesting the Dynamic Shrinkage Process (DSP) of Kowal et al. (2019). We revisit the Meese-Rogoff puzzle (Meese and Rogoff, 1983a, b, 1988) by applying the MSDSP to the economic models deemed inferior to the random walk model for exchange rate predictions. The flexibility of the MSDSP model captures the possibility of zero coefficients (sparsity), constant coefficient (dynamic shrinkage), as well as sudden and gradual parameter movements (structural change) in the time-varying parameter model setting. We also apply MSDSP in the context of Bayesian predictive synthesis (BPS) (McAlinn and West, 2019), where dynamic combination schemes exploit the information from the alternative economic models. Our analysis provide a new perspective to the Meese-Rogoff puzzle, illustrating that the economic models, enhanced with the parameter flexibility of the MSDSP, produce predictive distributions that are superior to the random walk model, even when stochastic volatility is considered. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.14408 |
| By: | Atsushi Inoue; \`Oscar Jord\`a; Guido M. Kuersteiner |
| Abstract: | We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of distributions that include moment restrictions with general forms of heteroskedasticity. We show that the AR based tests have correct asymptotic size when parameters are unidentified, partially identified, weakly or strongly identified. We obtain these results by constructing an upper bound that is using a novel perturbation and regularization approach applied to the first order conditions of the CUE. Our theory applies to both cross-sections and time series data and does not assume stationarity in time series settings or homogeneity in cross-sectional settings. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.01167 |
| By: | Fay\c{c}al Djebari; Kahina Mehidi; Khelifa Mazouz; Philipp Otto |
| Abstract: | This paper examines several network-based volatility models for oil prices, capturing spillovers among OPEC oil-exporting countries by embedding novel network structures into ARCH-type models. We apply a network-based log-ARCH framework that incorporates weight matrices derived from time-series clustering and model-implied distances into the conditional variance equation. These weight matrices are constructed from return data and standard multivariate GARCH model outputs (CCC, DCC, and GO-GARCH), enabling a comparative analysis of volatility transmission across specifications. Through a rolling-window forecast evaluation, the network-based models demonstrate competitive forecasting performance relative to traditional specifications and uncover intricate spillover effects. These results provide a deeper understanding of the interconnectedness within the OPEC network, with important implications for financial risk assessment, market integration, and coordinated policy among oil-producing economies. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.15046 |
| By: | Zhongyuan Lyu; Ming Yuan |
| Abstract: | Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the noise has complex dependence structure. We argue that the inconsistency often stems from bias and introduce a general approach to restore consistency. Specifically, we propose a general weighting scheme for PCA and show that with a suitable choice of weighting matrices, it is possible to deduce consistent and asymptotic normal estimators under much weaker conditions than the usual PCA. While the optimal weight matrix may require knowledge about the factors and covariance of the idiosyncratic noise that are not known a priori, we develop an agnostic approach to adaptively choose from a large class of weighting matrices that can be viewed as PCA for weighted linear combinations of auto-covariances among the observations. Theoretical and numerical results demonstrate the merits of our methodology over the usual PCA and other recently developed techniques for large-dimensional approximate factor models. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.15675 |
| By: | Gregorio Impavido |
| Abstract: | This paper proposes a “quasi-agnostic” sign restriction procedure to identify structural shocks in frequentist structural vector autoregression (SVAR) models. It argues that low acceptance rates, inherent to agnostic sign restriction procedures, are not necessarily an indication of model misspecification. They can be low because agnostic procedures fail to exploit the ex ante priors on the sign of responses of macro variables to structural shocks. |
| Keywords: | VARs; SVARs; parametric restrictions; sign restrictions |
| Date: | 2025–08–15 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2025/162 |
| By: | Victor Chernozhukov; Christian B. Hansen; Lingwei Kong; Weining Wang |
| Abstract: | Structural estimation in economics often makes use of models formulated in terms of moment conditions. While these moment conditions are generally well-motivated, it is often unknown whether the moment restrictions hold exactly. We consider a framework where researchers model their belief about the potential degree of misspecification via a prior distribution and adopt a quasi-Bayesian approach for performing inference on structural parameters. We provide quasi-posterior concentration results, verify that quasi-posteriors can be used to obtain approximately optimal Bayesian decision rules under the maintained prior structure over misspecification, and provide a form of frequentist coverage results. We illustrate the approach through empirical examples where we obtain informative inference for structural objects allowing for substantial relaxations of the requirement that moment conditions hold exactly. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.00555 |
| By: | Grzegorz Dudek; Witold Orzeszko; Piotr Fiszeder |
| Abstract: | Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. To address this limitation, this paper introduces probabilistic forecasting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryptocurrency realized variance. To the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, particularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a significant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.15922 |
| By: | Matthias Eckardt; Philipp Otto |
| Abstract: | Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate autoregressive model tailored for panel data with composition-valued responses at each areal unit and time point. The proposed framework enables the joint modelling of temporal dynamics and spatial dependence under compositional constraints and is estimated via a quasi maximum likelihood approach. We build on recent theoretical advances to establish identifiability and asymptotic properties of the estimator when both the number of regions and time points grow. The utility and flexibility of the model are demonstrated through two applications: analysing property transaction compositions in an intra-city housing market (Berlin), and regional sectoral compositions in Spain's economy. These case studies highlight how the proposed framework captures key features of spatiotemporal economic processes that are often missed by conventional methods. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.14389 |
| By: | Paolo Foschi |
| Abstract: | A multi-factor extension of the Hobson and Rogers (HR) model, incorporating a quadratic variance function (QHR model), is proposed and analysed. The QHR model allows for greater flexibility in defining the moving average filter while maintaining the Markovian property of the original HR model. The use of a quadratic variance function permits the characterisation of weak-stationarity conditions for the variance process and allows for explicit expressions for forward variance. Under the assumption of stationarity, both the variance and the squared increment processes exhibit an ARMA autocorrelation structure. The stationary distribution of the prototypical scalar QHR model is that of a translated and rescaled Pearson type IV random variable. A numerical exercise illustrates the qualitative properties of the QHR model, including the implied volatility surface and the term structures of forward variance, at-the-money (ATM) volatility, and ATM skew. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08773 |
| By: | Rehim Kılıç |
| Abstract: | This paper fills an important gap in the volatility forecasting literature by comparing a broad suite of machine learning (ML) methods with both linear and nonlinear econometric models using high-frequency realized volatility (RV) data for the S&P 500. We evaluate ARFIMA, HAR, regime-switching HAR models (THAR, STHAR, MSHAR), and ML methods including Extreme Gradient Boosting, deep feed-forward neural networks, and recurrent networks (BRNN, LSTM, LSTM-A, GRU). Using rolling forecasts from 2006 onward, we find that regime-switching models—particularly THAR and STHAR—consistently outperform ML and linear models, especially when predictors are limited. These models also deliver more accurate risk forecasts and higher realized utility. While ML models capture some nonlinear patterns, they offer no consistent advantage over simpler, interpretable alternatives. Our findings highlight the importance of modeling regime changes through transparent econometric tools, especially in real-world applications where predictor availability is sparse and model interpretability is critical for risk management and portfolio allocation. |
| Keywords: | Realized volatility; Machine learning; Regime-switching; Nonlinearity; VaR; forecasting |
| JEL: | C10 C50 G11 G15 |
| Date: | 2025–08–08 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2025-61 |
| By: | Antonio F. Galvao; Gabriel Montes-Rojas |
| Abstract: | This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles, vector quantile regression, or copula-based methods--MQR defines quantiles through the conditional probability structure of the joint conditional distribution function. The method constructs multivariate quantile curves using sequential univariate quantile regressions derived from conditioning mechanisms, allowing for an intuitive interpretation and flexible estimation of marginal effects. The paper develops theoretical foundations of MQR, including asymptotic properties of the estimators. Through simulation exercises, the estimator demonstrates robust finite sample performance across different dependence structures. As an empirical application, the MQR framework is applied to the analysis of exchange rate pass-through in Argentina from 2004 to 2024. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.15749 |