To do with the ARCH effects in explanatory variables, a new time-varying parameter regression is developed. The autoregressive conditional parameter (ACP) model with heteroskedastic regressors extends the ACP model of Lu and Wang (2016) by allowing explanatory variables to follow a multivariate GARCH process. The model is applied to examine time-varying causal effects of the daily United States (US) dollar exchange rate and S&P 500 stock index on WTI crude oil price. The empirical results show that the developed model outperforms the linear regression and ACP model. The casual effects of US dollar and S&P 500 stock indices on WTI are time-varying and become stronger after 2008.