We test for the presence of time-varying parameters (TVP) in the long-run dynamics of energy prices for oil, natural gas and coal, within a standard class of mean-reverting models. We also propose residual-based diagnostic tests and examine out-of-sample forecasts. In-sample LR tests support the TVP model for coal and gas but not for oil, though companion diagnostics suggest that the model is too restrictive to conclusively fit the data. Out-of-sample analysis suggests a random-walk specification for oil price, and TVP models for both real-time forecasting in the case of gas and long-run forecasting in the case of coal.