This study develops time varying parameter (TVP) linear almost ideal demand system (LAIDS) models in both long-run (LR) static and short-run error correction (EC) forms. The superiority of TVP-LAIDS models over the original static version and the fixed-parameter EC counterparts is examined in an empirical study of modelling and forecasting the demand for tourism in Western European destinations by UK residents. Both the long-run static and the short-run EC-LAIDS models are estimated using the Kalman filter algorithm. The evolution of demand elasticities over time is illustrated using the Kalman filter estimation results. The remarkably improved forecasting performance of the TVP-LAIDS relative to the fixed-parameter LAIDS is illustrated by a one-year- to four-years-ahead forecasting performance assessment. Both the unrestricted TVP-LR-LAIDS and TVP-EC-LAIDS outperform the fixed-parameter counterparts in the overall evaluation of demand level forecasts, and the TVP-EC-LAIDS is also ranked ahead of most other competitors when demand changes are concerned.