Regime Splits are not Interaction Tests: Spurious Amplification in Mixed-frequency Volatility Models

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 mixedfrequency 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 secondorder. For copper, the conventional split reports a supply-chain slope 0.069 higher in high-geopoliticalrisk 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 (θ^ 3 = − 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 commodities 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.

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