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on Econometric Time Series |
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Issue of 2026–08–17
fifteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Guo, Hongfei; Marín Díazaraque, Juan Miguel; Veiga, Helena |
| Abstract: | Adding flexibility to a multivariate volatility model can worsen covariance forecasts; we show when, and how to detect it. We decompose the multivariate QLIKE loss into trace, marginal-scale, and correlation log-determinant components; counterfactual block substitutions attribute gains or losses to either part. In Bayesian dynamic-correlation stochastic volatility, the diagnostic yields a sequence: diffuse dynamic correlations can underperform a constant-correlation baseline; a stabilizing prior repairs the correlation component; once stabilized, lagged realized-volatility inputs are the strongest remaining lever, with neural corrections competitive but not dominant. Under a rolling protocol, the stabilized realized-augmented family rivals realized-covariance benchmarks while retaining full predictive densities. |
| Keywords: | Covariance forecasting; Dynamic correlations; Forecast-object diagnostics; Neural networks; Prior regularization; Realized volatility; Stochastic volatility |
| JEL: | C11 C32 C53 C58 G17 |
| Date: | 2026–07–28 |
| URL: | https://d.repec.org/n?u=RePEc:cte:wsrepe:50561 |
| By: | Gabriel Rodriguez Rondon; Jean-Marie Dufour |
| Abstract: | Markov switching models are widely used to capture nonlinearities arising from regime shifts. Most existing tests for the number of regimes focus on one versus two regimes. Even in such simple cases, this type of problem raises issues of non-standard asymptotic distributions, identification failure, and nuisance parameters. We address these difficulties by applying the technique of Monte Carlo tests, which yields both finite-sample and asymptotically valid procedures, without the need to establish an asymptotic distributional theory, nor the existence of an asymptotic distribution. Monte Carlo likelihood-ratio tests are developed for testing M_0 regimes against M_0+m regimes, for any M_0≥1 and m≥1. The proposed tests apply to nonstationary processes, non-Gaussian errors, and multivariate models. A key contribution is the Maximized Monte Carlo likelihood-ratio test (MMC-LRT), an identification-robust procedure with both finite-sample and asymptotic validity. The framework also accommodates tests for regime synchronization and Markov switching GARCH models. Simulations show accurate size control and strong power. An empirical application using Markov switching VAR models finds weakened U.S.-Canada business cycle synchronization when COVID-period data are included, while applications to U.S. output growth support a three-regime specification consistent with previous empirical studies. |
| Keywords: | Models and tools, Econometric, statistical and computational methods, Economic models, Monetary policy, Real economy and forecasting |
| JEL: | C12 C15 C22 C32 C46 C52 E32 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:bca:bocawp:26-23 |
| By: | Afees A. Salisu (Centre for Econometrics and Applied Research, Ibadan, Nigeria; Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Ahamuefula E. Ogbonna (Centre for Econometrics and Applied Research, Ibadan, Nigeria); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Elie Bouri (School of Business, Lebanese American University, Lebanon) |
| Abstract: | This paper employs the generalized autoregressive conditional heteroscedasticity-mixed data sampling (GARCH-MIDAS) framework to forecast monthly and daily stock return volatility in the United States (US), based on a quarterly news-based Price Conflict Index (PCI) that signals “bad macroeconomic news†. An analysis of historical monthly (1860-2023) and daily (1885-2023) data demonstrates that the GARCH-MIDAS model incorporating PCI outperforms both the benchmark GARCH-MIDAS model with realized volatility (GARCH-MIDAS-RV) and models with macroeconomic variables such as output growth, inflation, unemployment, and interest rates. Furthermore, the inclusion of the PCI in modeling stock return volatility provides higher utility gains compared to models that exclude it. These findings have important implications for both investors and policymakers. |
| Keywords: | Price Conflict, Stock Returns Volatility, Forecasting, GARCH-MIDAS |
| JEL: | C32 C53 E31 G12 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202620 |
| By: | Goncalves, Silvia; Herrera, Ana Maria; Kilian, Lutz; Pesavento, Elena |
| Abstract: | Nonlinearities play an increasingly important role in applied work when studying the responses of macroeconomic aggregates to policy shocks. Seemingly natural adaptations of the popular local linear projection estimator to nonlinear settings may fail to recover the population responses of interest. In this paper we study the properties of an alternative nonparametric local projection estimator of the conditional and unconditional responses of an outcome variable to an observed identified shock. We discuss alternative ways of implementing this estimator and how to allow for data-dependent tuning parameters. Our results are based on data generating processes that involve, respectively, nonlinearly transformed regressors, state-dependent coefficients, and nonlinear interactions between shocks and state variables. Monte Carlo simulations show that a local-linear specification of the estimator tends to work well in reasonably large samples and is robust to nonlinearities of unknown form. |
| Keywords: | Impulse response; Local projection; Nonparametric estimation; Nonlinear structural model; Potential outcomes |
| JEL: | C14 C32 E52 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19684 |
| By: | Christopoulos, Dimitris; McAdam, Peter; Tzavalis, Elias |
| Abstract: | We develop an endogenous threshold VAR that addresses contemporaneous dependence between the threshold variable and reduced-form innovations— a pervasive issue when regime indicators are jointly determined with system dynamics. A regime-specific copula-based control function removes this dependence instrument-free, without parametric assumptions on the threshold’s marginal distribution, while preserving the linear regime-wise least-squares structure. We characterize the resulting misspecification through excess sensitivity and excess propagation errors in impulse responses, clarify structural and proxy-SVAR identification under endogenous regimes, and establish conditions under which Chan-type threshold asymptotics remain valid with generated controls. A Hermite sieve extension accommodates tail-dependent and asymmetric dependence. Monte Carlo evidence documents large distortions from ignoring endogeneity. Applied to monetary transmission, the framework avoids the price and persistence puzzles displayed by the linear VAR, delivers regime-dependent sacrifice ratios, and aligns estimated regimes with historical inflation episodes. JEL Classification: C32, C34, E52 |
| Keywords: | copula, impulse response, monetary policy, Monte Carlo |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263263 |
| By: | Paritosh Shankarrao Junare |
| Abstract: | Standard pre-tests of normality on reduced-form innovations are insufficient to detect two or more Gaussian shocks and hence, the failure of identification in non-Gaussian SVARs. We instead propose a bootstrap-based approach to evaluate the asymptotic validity of this condition by measuring the divergence between the conditional bootstrap distribution of a maximum likelihood estimator and its limiting distribution under valid identification. We show that, under valid identification and certain regularity conditions, the conditional bootstrap distribution of the impact matrix is asymptotically normal, so the diagnostic reduces to a test of normality of the bootstrap replications. The diagnostic remains valid in the single-Gaussian case, where the shape parameter of the Gaussian shock lies on the boundary, and the full-parameter information is singular; this establishes its validity across the entire null. Under the null of valid identification, the diagnostic induces no pre-testing bias as bootstrap replications and sample size diverge jointly at an appropriate rate. The joint divergence ensures that the test statistic, conditional on the data, is asymptotically pivotal, so conditioning on the diagnostic does not distort subsequent inference. Monte Carlo simulations with Normal-Inverse Gaussian shocks show that the diagnostic attains near-exact nominal size under valid identification and detects the failure due to multiple Gaussian shocks with power increasing in the sample size. Under weak identification with a near-Gaussian shock, conditioning on the bootstrap diagnostic, unlike on residual-based normality pre-tests, preserves the probability coverage of the estimates. Based on estimates of a SVAR model in the macroeconomic and financial uncertainty literature, we demonstrate its potential as a practical, robust tool for validating non-Gaussian identification without pre-testing bias. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.17275 |
| By: | Gabriel Rodriguez Rondon; Jean-Marie Dufour |
| Abstract: | We present the R package MSTest, which implements hypothesis testing procedures to determine the number of regimes in Markov switching models. These models have wide ranging applications in economics, finance, and many other fields. MSTest provides several testing frameworks, including Monte Carlo likelihood ratio tests (Rodriguez-Rondon and Dufour (2025)), moment-based tests (Dufour and Luger (2017)), parameter stability tests (Carrasco et al. (2014)), and classical likelihood ratio procedures (Hansen (1992)). In addition, the package offers tools for simulating and estimating univariate and multivariate Markov switching and hidden Markov models using either the expectation–maximization algorithm or maximum likelihood estimation. The functionality of the package is demonstrated through simulation-based examples. |
| Keywords: | Models and tools, Econometric, statistical and computational methods, Economic models, Monetary policy, Real economy and forecasting |
| JEL: | C12 C15 C18 C63 C87 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:bca:bocawp:26-7 |
| By: | Gabriel Rodriguez Rondon; Jean-Marie Dufour; Md. Nazmul Ahsan |
| Abstract: | Statistical inference--both estimation and testing--for stochastic volatility (SV) models is known to be challenging and computationally demanding. We propose simple and efficient estimators for SV models with conditionally heavy-tailed error distributions, particularly the Student’s t and Generalized Exponential Distributions (GED). The estimators rely on a small set of moment conditions derived from ARMA-type representations of SV models, with an option to apply “winsorization” to improve stability and finite-sample performance. Except for the degrees-of-freedom parameter, closed-form expressions are available for all other parameters, extending Ahsan and Dufour (2019, 2021), thus eliminating the need for numerical optimization or initial values. We derive the estimators’ asymptotic distribution and show that, due to their analytical tractability, they support reliable, and even exact, simulation-based inference via Monte Carlo or bootstrap methods. We assess their performance through extensive simulations and demonstrate their practical relevance in financial return data, which strongly reject the normality assumption in favor of heavy-tailed models. |
| Keywords: | Financial markets and funds management, International markets and currencies, Models and tools, Econometric, statistical and computational methods, Economic models |
| JEL: | C15 C22 C53 C58 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:bca:bocawp:26-8 |
| By: | Padhyoti, Yadav; Mugera, Amin; White, Benedict |
| Abstract: | Price transmission between distant markets is a measure of market performance, weighing the fairness of the distribution of market surplus among producers, traders, and consumers. We estimate price transmission from global wheat futures (CBOT and Euronext) to Australian regional wheat spot markets (Kwinana and Newcastle) using the Non-Linear Autoregressive Distributed Lag (NARDL) model. The NARDL captures non-linearity and asymmetric adjustments when price series are stationary or of mixed order at the level. The model is further extended into the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) framework to account for time-varying volatility. The results reveal that price transmission from CBOT and Euronext futures to Kwinana is negatively asymmetric in both the short and long run, while it is symmetric to the Newcastle spot market. The export-oriented Kwinana market is highly concentrated, with a single major buyer, whereas the Newcastle market has multiple buyers and significant domestic demand. This study adds to the existing spatial price transmission literature, especially in the underexplored context of Australian grain markets. It also advances the econometric practices by integrating the NARDL framework with a GARCH specification to account for time-varying volatility in high-frequency time series data. |
| Keywords: | Marketing |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea26:404540 |
| By: | Artur Sepp; Vladimir Lucic |
| Abstract: | We present a unified approach to designing trend-following (TF) systems and classify them into European, American, and Time Series Momentum categories. For European TF systems, we derive an exact relationship between profit-and-loss, autocorrelation, and drift in volatility-normalized returns. We analyze the expected return under fractional ARFIMA processes and show that TF systems are profitable when the long-term autocorrelation is positive, even under short-term mean reversion. In the frequency domain, the expected return is represented as a Poisson-kernel reading of the analytical or empirical spectrum of the volatility-normalized returns: the system profits at zero drift when the kernel-weighted spectral mass exceeds one, so trend-following alpha is excess spectral mass at low frequencies. Longer lookbacks benefit in addition from the squared drift of the return process. We derive the closed-form Sharpe ratio, with the excess kurtosis of the innovations entering through a single loading, and the net Sharpe ratio and cost-optimal span under trading costs. Under white noise, we derive the closed-form skewness of aggregated TF returns, which is positive at every horizon and peaks near half the filter span. Monte Carlo experiments confirm the analytical results. We show that the positive skewness of TF returns is structural under various model assumptions. Empirically, we evaluate the systems on liquid contracts, and show that all TF systems are strongly correlated and our analytical results can be applied for their performance attribution. Our results enable design, simulation, and performance attribution of TF systems from trend persistence, mean reversion, drift, and skewness. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.19497 |
| By: | Özer, Yeliz; del Barrio Castro, Tomás; Escribano, Álvaro; Sibbertsen, Philipp |
| Abstract: | Deep-time climate records contain deterministic orbital signals and persistent stochastic variation, but how these components jointly affect predictability across climate states remains unclear. We analyze the Cenozoic Global Reference benthic foraminifer oxygen and carbon isotope record spanning 67.1 million years. This very long period is divided into seven climate-state segments. For each segment, we estimate deterministic contemporaneous long-run components combining linear trends, eccentricity, obliquity, climatic precession, and identified harmonic frequencies. The remaining variation is modeled with a bivariate vector autoregressive forecasting framework conditioned on astronomical forcing. The selected deterministic and dynamic structures differ substantially across climate states. Obliquity is the most recurrent orbital predictor, whereas squared obliquity, eccentricity, climatic precession, and harmonic components contribute only in particular segments and differ between the two proxies. Forecast accuracy likewise varies across the record, although observed and predicted values agree closely in several segments. A projection for the next 100, 000 years provides a baseline implied by natural astronomical forcing and continued Icehouse dynamics. Overall, the results show that orbital responsiveness, proxy interactions, and statistical predictability are state dependent. Deep-time climate variability therefore cannot be represented by a single common combination of deterministic forcing and stochastic dynamics across the complete Cenozoic. |
| Keywords: | CENOGRID, Deep-Time Paleoclimate, Forecasting Climate Data. |
| JEL: | C22 C32 C53 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-751 |
| By: | Andrade, Philippe; Ferroni, Filippo; Melosi, Leonardo |
| Abstract: | We develop a robust and tractable method to identify SVARs using non-Gaussian features of structural shocks. The approach combines inequality restrictions on higher-order moments with standard set-identifying constraints such as sign restrictions. To benchmark its performance, we apply it to the identification of monetary policy shocks. Combining standard minimal sign restrictions with a constraint that monetary policy shocks be leptokurtic, we recover several key properties documented in earlier work: a correct output response to policy tightening, salient policy narrative episodes, and a plausible central bank reaction function. We then identify sovereign and geopolitical risk shocks, assuming they are skewed and leptokurtic, and uncover sizable macroeconomic effects that remain hidden under conventional identification schemes. |
| Keywords: | Shock identification |
| JEL: | C32 E27 E32 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19813 |
| By: | Weiye Xi; Ciamac C. Moallemi; Mallesh Pai; Shouqiao Want |
| Abstract: | Forward-looking volatility forecasts are central inputs to derivatives pricing, market making, risk management, and volatility-linked trading strategies, with ARCH and GARCH models serving as the canonical workhorses. Such models are natural in standard asset markets, where prices are positive-valued stochastic processes and volatility is typically inferred from return dynamics. Prediction markets have a different structure: prices are bounded probabilities, payoffs are binary, and contracts resolve at known deadlines. We develop and estimate a volatility model tailored to binary prediction markets. The model combines two economic mechanisms: a Wright-Fisher deadline-resolution component, capturing how remaining binary uncertainty is forced to resolve over time, and a Glosten-Milgrom order-flow component, capturing volatility from informed trading as reflected in spreads and volume. Using a large panel of Kalshi contracts, we show that these structural variables carry substantial forecasting power. Plain ARCH/GARCH benchmarks are dominated by structural specifications; combining the structural model with residual GARCH dynamics gives the best overall forecasts. The model also provides an interpretable measurement framework: volatility is highest near fifty-fifty prices, rises near resolution, and varies across categories with the timing and discreteness of information arrival. Economics contracts are closer to smooth deadline-resolution dynamics, while sports contracts exhibit more event-concentrated, jump-like behavior. Across major categories, category-specific fitting does not systematically improve out-of-sample performance, suggesting that the structural specification transfers beyond the pooled headline result. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.08199 |
| By: | Koop, Gary; McIntyre, Stuart; Mitchell, James; Poon, Aubrey; Wu, Ping |
| Abstract: | Bayesian mixed-frequency vector autoregressions (MF-VARs) are commonly used to produce timely and high-frequency estimates of low-frequency variables. A typical application uses quarterly data on output, for a given country, and monthly indicator data to produce monthly estimates of national output. But, when working at sub-national levels, data limitations preclude the use of standard MF-VARs. The frequency mismatch is more complicated, key variables can have missing data, and release delays can be substantial. In this paper, we develop a novel MF-VAR which addresses all these issues and use it to produce historical estimates of sub-regional output growth in the UK. The model combines information in the annual sub-regional data (when available) with data from the UK regions and the UK as a whole. The model is estimated using variational Bayesian methods with shrinkage priors, reflecting the “big data” setup. We use our model to produce a new database of quarterly estimates of sub-regional GVA growth back to the 1960s, that importantly, because the MFVAR imposes temporal and cross-sectional restrictions, is consistent with those official data that do exist. We illustrate the use of these new estimates by showing how they can used to characterize the considerable heterogeneity in sub-regional business cycle dynamics in the UK and contribute to our understanding of regional economic resilience. |
| Keywords: | regional resilience; vector autoregressions; mixed-frequency data; sub-national |
| JEL: | C32 R1 |
| Date: | 2024–09–30 |
| URL: | https://d.repec.org/n?u=RePEc:eoe:escoed:escoe-dp-2024-11 |
| By: | Chris Angstmann; Tim Gebbie |
| Abstract: | We derive an operational-time variance kernel for a latent-order-book reaction boundary and use it to separate three objects usually collapsed in calendar-time volatility models: a structural boundary cumulant, a clock projection, and a pricing-measure choice. The reaction boundary is the zero of a bid--ask imbalance field. For a locally linear book, signed order-flow perturbations displace this zero through a damped Abel response kernel, so the variance of boundary increments is obtained as a finite-scale Green-function cumulant rather than introduced as a primitive diffusion coefficient. For long-memory forcing with exponent $0 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.05011 |