The authors test the statistical significance of Pindyck's (1999) suggested class of econometric equations that model the behaviour of long-run real energy prices. The models postulate mean-reverting prices with continuous and random changes in their level and trend, and are estimated using Kalman filtering. In such contexts, test statistics are typically non-standard and depend on nuisance parameters. The authors use simulation-based procedures to address this issue; namely, a standard Monte Carlo test and a maximized Monte Carlo test. They find statistically significant instabilities for coal and natural gas prices, but not for crude oil prices. Out-of-sample forecasts are calculated to differentiate between significant models.