A Design Concept of Forecasting Software for Normalized Vector Autoregressions with Fat Tails and Stochastic Volatility

Conditional projection methods for large-scale Bayesian VARs

We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. The scenarios are defined through separate distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it.

The Autoregressive Inverse‐Wishart Multivariate Stochastic Volatility Model and Its Factor Extension

Despite its conceptual appeal, the autoregressive inverse‐Wishart (AIW) multivariate stochastic volatility model has been hindered by inefficient sampling methods. The existing samplers for the latent covariance matrix severely suffer from the curse of dimensionality and only work when the dimension is very low. In this paper, we introduce a new proposal for the latent covariance matrix in the AIW model, which demonstrates far better scalability. We introduce different extensions to the basic AIW model that capture various stylized volatility features. We further fit the AIW model into a factor structure and provide an a posteriori identification procedure without introducing order dependence. When evaluated using real datasets ranging from 10 assets to 1000 assets, the new AIW‐based models, whether the standalone versions or the factor versions, are especially suited for multivariate volatility modeling in a wide range of dimensions.

Modelling of Regression with Non-Gaussian AR Errors

Volatility forecasting with econometric and machine learning models under capacity control

This study evaluates multiple forecasting models, ranging from HAR and GARCH to Tree-based and Neural architectures, across 14 Global Equity Indices and Horizons form 1 day to 100 Trading days within a strictly chronological and capacity-controlled framework, indicating that for strongly dependent time series, nominal sample size is a misleading measure of learnability, and model capacity must be constrained relative to effective information rather than observation count.

Testing the Impact of a Geometric Curvature Variable on the Accuracy of Econometric Forecasting Models

Classical financial econometric models often fail to capture the complex, nonlinear dynamics of stock price movements. This study addresses this limitation by investigating the predictive power of a financial time series' underlying geometric structure. We hypothesized that incorporating a geometric curvature metric—an exogenous variable derived from hyperbolic geometry to model hierarchical patterns—would significantly improve the forecasting accuracy of a standard econometric model. To test this hypothesis, we measured the effect of introducing this single variable into an autoregressive integrated moving average (ARIMA) model using daily stock data for Apple, Google, and Microsoft. The inclusion of the geometric curvature variable led to a substantial reduction in forecasting error, with root mean square errors (RMSEs) decreasing from 6.64 to 2.88 for Apple, 13.65 to 2.50 for Google, and 23.51 to 5.26 for Microsoft. This demonstrates that geometric curvature is a significant predictive factor in time-series analysis and suggests that incorporating geometric properties offers a powerful method for enhancing econometric forecasts, with broad implications for risk management.

Comparing the behaviors of some original short and long memory exponential volatility models