Hypotheses testing in mixed–frequency volatility models: a bootstrap approach

It is widely recognized that standard likelihood–based inference suffers from the presence of nuisance parameters. This problem is particularly relevant in the context of Mixing–Data Sampling (MIDAS) models, when volatility forecasting is the research topic and where often covariates’ data are sampled at a different (usually lower) frequency than the asset returns. In this framework, testing the significance of the MIDAS terms brings together the presence of nuisance parameters that under the null hypothesis are not identifiable. This circumstance interferes with the asymptotic distribution of the common statistical tests employed in this framework. In particular, the asymptotic distribution is no more a χ2 distribution. The present paper proposes a bootstrap likelihood ratio (BLR) test to overcome this problem, simulating the likelihood ratio test distribution. Using a Monte Carlo experiment, the proposed BLR test presents quite good performances in terms of the test’s size and power.