This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our approach demonstrates that matching the quantisation scheme to the real data distribution can reduce computational overhead while maintaining acceptable precision. Moreover, our approach is robust when applied to real-world data and mixed-precision quantisation, where most objects are quantised to 4 bits. Our findings inform model quantisation and deployment decisions while providing a foundation for advancing quantisation techniques.