This paper proposes a new method for conformal inference in time series forecasting that works under any changes in the data generation process. It can be used with any black box forecasting models that predict the future values of a time series. Unlike existing methods, the proposed method adapts to changes in the distribution faster and in a more predictable way. We achieve this by modifying the adaptive conformal inference (ACI) algorithm of Gibbs and Candès (2021) by replacing the constant learning rate parameter with the one that adapts to changes in the data generation process. We tested our method on real datasets and showed the absence of sharp explosions in the width of intervals common for other adaptive conformal prediction approaches.