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on Econometric Time Series |
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Issue of 2025–09–22
nine papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Silvia Goncalves; Michael W. McCracken; Yongxu Yao |
| Abstract: | This paper examines the properties of out-of-sample predictability tests evaluated with real-time data subject to annual benchmark revisions. The presence of both regular and annual revisions can create time heterogeneity in the moments of the real-time forecast evaluation function, which is not compatible with the standard covariance stationarity assumption used to derive the asymptotic theory of these tests. To cover both regular and annual revisions, we replace this standard assumption with a periodic covariance stationarity assumption that allows for periodic patterns of time heterogeneity. Despite the lack of stationarity, we show that the Clark and McCracken (2009) test statistic is robust to the presence of annual benchmark revisions. A similar robustness property is shared by the bootstrap test of Goncalves, McCracken, and Yao (2025). Monte Carlo experiments indicate that both tests provide satisfactory finite sample size and power properties even in modest sample sizes. We conclude with an application to U.S. employment forecasting in the presence of real-time data. |
| Keywords: | real-time data; bootstrap; prediction; forecast evaluation |
| JEL: | C53 C12 C52 |
| Date: | 2025–09–11 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedlwp:101742 |
| By: | Anna Bykhovskaya; Vadim Gorin; Eszter Kiss |
| Abstract: | Cointegration is a property of multivariate time series that determines whether its non-stationary, growing components have a stationary linear combination. Largevars R package conducts a cointegration test for high-dimensional vector autoregressions of order k based on the large N, T asymptotics of Bykhovskaya and Gorin (2022, 2025). The implemented test is a modification of the Johansen likelihood ratio test. In the absence of cointegration the test converges to the partial sum of the Airy_1 point process, an object arising in random matrix theory. The package and this article contain simulated quantiles of the first ten partial sums of the Airy_1 point process that are precise up to the first 3 digits. We also include two examples using Largevars: an empirical example on S&P100 stocks and a simulated VAR(2) example. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.06295 |
| By: | Tony Chernis; Niko Hauzenberger; Haroon Mumtaz; Michael Pfarrhofer |
| Abstract: | We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation equation, specified via Gaussian Process (GP) priors for each series. Factor dynamics are modeled with a standard vector autoregression (VAR), which facilitates computation and interpretation. We discuss a computationally efficient estimation algorithm and consider two empirical applications. First, we forecast key series from the FRED-QD dataset and show that the model yields improvements in predictive accuracy relative to linear benchmarks. Second, we extract driving factors of global inflation dynamics with the GP-DFM, which allows for capturing international asymmetries. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.04928 |
| By: | Guo, Hongfei; Marín Díazaraque, Juan Miguel; Veiga, Helena |
| Abstract: | Accurately forecasting volatility is central to risk management, portfolio allocation, and asset pricing. While high-frequency realised measures have been shown to improve predictive accuracy, their value is not uniform across markets or horizons. This paper introduces a class of Bayesian neural network stochastic volatility (NN-SV) models that combine the flexibility of machine learning with the structure of stochastic volatility models. The specifications incorporate realised variance, jump variation, and semivariance from daily and intraday data, and model uncertainty is addressed through a Bayesian stacking ensemble that adaptively aggregates predictive distributions. Using data from the DAX, FTSE 100, and S&P 500 indices, the models are evaluated against classical GARCH and parametric SV benchmarks. The results show that the predictive content of high-frequency measures is horizon- and market-specific. The Bayesian ensemble further enhances robustness by exploiting complementary model strengths. Overall, NN-SV models not only outperform established benchmarks in many settings but also provide new insights into market-specific drivers of volatility dynamics. |
| Keywords: | Ensemble forecasts; GARCH; Neural networks; Realised volatility; Stochastic volatility |
| JEL: | C11 C32 C45 C53 C58 |
| Date: | 2025–09–16 |
| URL: | https://d.repec.org/n?u=RePEc:cte:wsrepe:47944 |
| By: | Tanujit Chakraborty; Donia Besher; Madhurima Panja; Shovon Sengupta |
| Abstract: | Accurate forecasting of exchange rates remains a persistent challenge, particularly for emerging economies such as Brazil, Russia, India, and China (BRIC). These series exhibit long memory, nonlinearity, and non-stationarity properties that conventional time series models struggle to capture. Additionally, there exist several key drivers of exchange rate dynamics, including global economic policy uncertainty, US equity market volatility, US monetary policy uncertainty, oil price growth rates, and country-specific short-term interest rate differentials. These empirical complexities underscore the need for a flexible modeling framework that can jointly accommodate long memory, nonlinearity, and the influence of external drivers. To address these challenges, we propose a Neural AutoRegressive Fractionally Integrated Moving Average (NARFIMA) model that combines the long-memory representation of ARFIMA with the nonlinear learning capacity of neural networks, while flexibly incorporating exogenous causal variables. We establish theoretical properties of the model, including asymptotic stationarity of the NARFIMA process using Markov chains and nonlinear time series techniques. We quantify forecast uncertainty using conformal prediction intervals within the NARFIMA framework. Empirical results across six forecast horizons show that NARFIMA consistently outperforms various state-of-the-art statistical and machine learning models in forecasting BRIC exchange rates. These findings provide new insights for policymakers and market participants navigating volatile financial conditions. The \texttt{narfima} \textbf{R} package provides an implementation of our approach. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.06697 |
| By: | MD Nazmul Ahsan; Jean-Marie Dufour; Gabriel Rodriguez |
| Abstract: | Stochastic covariances are critical for macroeconomic and financial modelling, particularly in capturing uncertainty and dynamic interdependencies. This study introduces the Dynamic Factor Augmented VAR with Higher-order Multivariate Stochastic Volatility (DFAVAR-HMSV) framework, along with a computationally efficient estimation methodology. The proposed model captures complex dynamic interdependencies, leverage effects, and higher-order persistence in volatility structures. Applying this framework to construct uncertainty indices for Canada and Québec, the study provides critical insights into regional and national macroeconomic dynamics. Les covariances stochastiques sont essentielles pour la modélisation macroéconomique et financière, en particulier pour capturer l’incertitude et les interdépendances dynamiques. Cette étude introduit le cadre VAR avec facteurs dynamiques et volatilité multivariée stochastique d’ordre supérieur (DFAVAR-HMSV) et propose une méthodologie d’estimation computationnellement efficace. Le modèle proposé capture des interdépendances dynamiques complexes, des effets de levier et une persistance d’ordre supérieur dans les structures de volatilité. En appliquant ce cadre à la construction des indices d’incertitude pour le Canada et le Québec, cette étude fournit des informations critiques sur les dynamiques macroéconomiques régionales et nationales. |
| Keywords: | Macroeconomic uncertainty, multivariate stochastic volatility, dynamic factor models, high-dimensional econometrics, forecasting, policy analysis, Incertitude macroéconomique, volatilité stochastique multivariée, modèles factoriels dynamiques, économétrie à haute dimension, prévision, analyse politique |
| JEL: | C32 C53 C55 E37 |
| Date: | 2025–09–08 |
| URL: | https://d.repec.org/n?u=RePEc:cir:cirpro:2025rp-19 |
| By: | Niklas Ahlgren; Alexander Back; Timo Ter\"asvirta |
| Abstract: | We develop misspecification tests for building additive time-varying (ATV-)GARCH models. In the model, the volatility equation of the GARCH model is augmented by a deterministic time-varying intercept modeled as a linear combination of logistic transition functions. The intercept is specified by a sequence of tests, moving from specific to general. The first test is the test of the standard stationary GARCH model against an ATV-GARCH model with one transition. The alternative model is unidentified under the null hypothesis, which makes the usual LM test invalid. To overcome this problem, we use the standard method of approximating the transition function by a Taylor expansion around the null hypothesis. Testing proceeds until the first non-rejection. We investigate the small-sample properties of the tests in a comprehensive simulation study. An application to the VIX index indicates that the volatility of the index is not constant over time but begins a slow increase around the 2007-2008 financial crisis. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.23821 |
| By: | Pablo A. Guerron-Quintana; James M. Nason |
| Abstract: | This chapter surveys Bayesian methods for estimating dynamic stochastic general equilibrium (DSGE) models. We focus on New Keynesian (NK)DSGE models because of the ongoing interest shown in this class of models by economists in academic and policy-making institutions. Their interest stems from the ability of this class of DSGE model to transmit monetary policy shocks into endogenous fluctuations at business cycle frequencies. Intuition about this propagation mechanism is developed by reviewing the structure of a canonical NKDSGE model. Estimation and evaluation of the NKDSGE model rests on detrending its optimality and equilibrium conditions to construct a linear approximation of the model from which we solve for its linear decision rules. This solution is mapped into a linear state space model. It allows us to run the Kalman filter generating predictions and updates of the detrended state and control variables and the predictive likelihood of the linear approximate NKDSGE model. The predictions, updates, and likelihood are inputs needed to operate the Metropolis-Hastings Markov chain Monte Carlo sampler from which we draw the posterior distribution of the NKDSGE model. The sampler also requires the analyst to pick priors for the NKDSGE model parameters and initial conditions to start the sampler. We review pseudo-code that implements this sampler before reporting estimates of a canonical NKDSGE model across samples that begin in 1982Q1 and end in 2019Q4, 2020Q4, 2021Q4, and 2022Q4. The estimates are compared across the four samples. This survey also gives a short history of DSGE model estimation as well as pointing to issues that are at the frontier of this research agenda. |
| Keywords: | dynamic stochastic general equilibrium, Bayesian, Metropolis-Hastings, Markov Chain Monte Carlo, Kalman filter, likelihood |
| JEL: | C32 E10 E32 |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2025-52 |
| By: | Crystal Rust |
| Abstract: | We introduce a new risk modeling framework where chaotic attractors shape the geometry of Bayesian inference. By combining heavy-tailed priors with Lorenz and Rossler dynamics, the models naturally generate volatility clustering, fat tails, and extreme events. We compare two complementary approaches: Model A, which emphasizes geometric stability, and Model B, which highlights rare bursts using Fibonacci diagnostics. Together, they provide a dual perspective for systemic risk analysis, linking Black Swan theory to practical tools for stress testing and volatility monitoring. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.08183 |