The growing disintegration between the natural gas and oil prices, together with shale revolution and market financialization, lead to continued fundamental changes in the natural gas markets. To capture these structural changes, this paper considers a wide set of highly flexible time-varying parameter models to evaluate the out-of-sample forecasting performance of the natural gas spot prices across the US, European and Japanese markets. The results show that for both Japan and EU markets, the best forecasting performance is found when the model allows for drastic changes in the conditional mean and gradual changes in the conditional volatility. For the US market, however, no model performs systematically better than the simple autoregressive model. Full sample estimation results further confirm that allowing t-distributed error is important in modelling the natural gas prices, especially for EU markets.