In this paper we present the first results ever obtained by applying the autoregressive (AR) technique to the precipitable water vapour (PWV). The study is performed at the Very Large Telescope. The AR technique has been recently proposed to provide forecasts of atmospheric and astroclimatic parameters at short time scales (up to a few hours) by achieving much better performances with respect to the standard forecasts provided early afternoon for the coming night. The AR method uses the real-time measurements of the parameter of interest to improve the forecasts performed with atmospherical models. We used here measurements provided by LHATPRO, a radiometer measuring continuously the PWV at the VLT. When comparing the AR forecast at 1h to the standard forecast, we observe a gain factor of $sim$ 8 (i.e. $sim$ 800 per cent) in terms of forecast accuracy. In the PWV $leq$ 1 mm range, which is extremely critical for infrared astronomical applications, the RMSE of the predictions is of the order of just a few hundredth of millimetres (0.04 mm). We proved therefore that the AR technique provides an important benefit to VLT science operations for all the instruments sensitive to the PWV. Besides, we show how such an ability in predicting the PWV can be useful also to predict the sky background in the infrared range (extremely appealing for METIS). We quantify such an ability by applying this method to the NEAR project (New Earth in the Alpha Cen region) supported by ESO and Breakthrough Initiatives.
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