Fuli Yang
Published 30 October 2026 · Version 1.0 · pp. 66-87
Abstract
Applied volatility research routinely infers state dependence by estimating a model separately in subsamples defined by a conditioning variable and comparing slopes. This paper shows that in mixed-frequency volatility models such a comparison is not an interaction test, for two independent reasons. First, the conditioning variable typically enters the long-run variance component directly; omitting it makes each group-specific slope a pseudo-true quasi-maximum-likelihood parameter rather than a structural marginal effect. The resulting distortion does not diminish with sample size. Second, selecting non-contiguous daily observations by a monthly partition breaks the GJR-GARCH recursion at every omitted block, so the split-sample objective is not the likelihood of a valid GARCH process. We apply the argument to daily commodity futures returns, the New York Fed Global Supply Chain Pressure Index, and the Caldara-Iacoviello geopolitical-risk index. The consequences are not second-order. For copper, the conventional split reports a supply-chain slope 0.069 higher in high-geopolitical-risk months, but that positive difference exists only under the concatenation implementation used in applied work: re-initialising the recursion at each block gives −0.165 and filtering on the full daily sample gives −0.134. The reported amplification is a sign flip away from what coherent implementations deliver. In a unified specification with both direct effects and their monthly product under a shared Beta weight, the interaction is significantly negative for copper (θ3=−0.1002, p=0.005) and cocoa (−0.4635, p<0.001). A first-order decomposition attributes the split difference to the omitted direct effect: across copper, coffee, and cocoa the observed difference and its predicted omitted-variable component correlate at 0.997, and the largest, most threshold-stable apparent amplification occurs in soybeans, the one market where supply-chain pressure has no detectable effect on long-run volatility at all. In 1,000-replication placebo simulations with the true interaction fixed at zero throughout, the naive split-based Wald test rejects at 14 to 25 percent against a nominal 5 percent, and its rejection rate is nearly flat in the true interaction, whereas the unified likelihood-ratio test reaches 86 percent power at the estimated parameters. The same argument applies to splits on uncertainty, financial stress, liquidity, and policy states.
Cite this article
Fuli Yang (2026). Regime Splits Are Not Interaction Tests: Spurious Amplification in Mixed-Frequency Volatility Models. GARCH, 1(1), 66-87.
Versions and rights
This is the GARCH journal edition. The manuscript retains its original research-version date. Earlier working paper: SSRN 7254039.
Copyright © 2026 Fuli Yang. All rights reserved. Full text is freely available to read and download.