Testing for local covariate trend effects in volatility models (Q2192311)

This article proposes a new nonparametric local covariate trend testing approach to statistically test the significance of an exogeneous covariate in the autoregressive conditional heteroscedastic volatility model, where the effect of the covariate can be nonlinear. The test statistic is based on an artificial high-dimensional one-way ANOVA where the number of factor levels increases with the sample size. The key idea is to measure the local effect of the covariate on the residuals of the null model in small neighborhoods of time, so that, if different neighborhoods exhibit significantly different average effects, then an overall covariate effect may be expected to exist. Asymptotic properties of the new test statistic are derived. As for the finite sample performance of the test, simulation studies are presented which indicate a competitive performance of the new method both in terms of size and power of the test. An application to volatility analysis of three major cryptoassets and their relationship with the prices of gold and the S\&P500 index is presented