With the large amounts of modern financial and econometric data available from disparate informational sources, it becomes increasingly critical to develop inferential tools for the impact of exogenous factors on volatility of financial time series. We develop a new Local Covariate Trend test (LOCOT) for the significance of an exogenous covariate in the autoregressive conditional heteroscedastic volatility model, where the covariate effect can be nonlinear. The new LOCOT statistic is based on an artificial high-dimensional one-way ANOVA where the number of factor levels increases with the sample size. We derive asymptotic properties of the new LOCOT statistic and show its competitive finite sample performance in a broad range of simulation studies. We illustrate utility of the new testing approach in application to volatility analysis of three major cryptoassets and their relationship with the prices of gold and the S&P500 index.
"Testing for local covariate trend effects in volatility models." Electron. J. Statist. 14 (2) 2529 - 2550, 2020. https://doi.org/10.1214/20-EJS1722