New score-driven scale and shape interactions: an application to international stock indices

Szabolcs Blazsek and Morgan Hall

Applied Economics, 2026, vol. 58, issue 2, 293-313

Abstract: This paper introduces a score-driven volatility model for the $t$t distribution, the Beta-$t$t-QVAR (quasi-vector autoregressive) model, in which the scale and degrees of freedom parameters interact through a multivariate score-driven filter. Both components of the filter influence the conditional volatility of returns. This paper aims to improve the statistical and forecasting performances of Beta-$t$t-EGARCH (exponential generalized AR conditional heteroscedasticity). The Beta-$t$t-QVAR model and the conditions of its maximum likelihood (ML) estimation are presented. Beta-$t$t-QVAR is applied to 15 international stock indices using data from December 1997 to April 2024. The in-sample statistical and out-of-sample density forecasting performances of Beta-$t$t-QVAR, normal-GARCH (NGARCH), asymmetric power-ARCH (APARCH), and Beta-$t$t-EGARCH are compared. Beta-$t$t-QVAR is superior to NGARCH, APARCH, and Beta-$t$t-EGARCH, motivating its practical use for financial forecasting.

Date: 2026
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DOI: 10.1080/00036846.2025.2452536

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