Deep learning models have been shown to be a powerful solution for Time Series Classification (TSC). State-of-the-art architectures, while producing promising results on the UCR and the UEA archives , present a high number of trainable parameters. This can lead to long training with high CO2 emission, power consumption and possible increase in the number of FLoating-point Operation Per Second (FLOPS). In this paper, we present a new architecture for TSC, the Light Inception with boosTing tEchnique (LITE) with only 2.34% of the number of parameters of the state-of-the-art InceptionTime model, while preserving performance. This architecture, with only 9, 814 trainable parameters due to the usage of DepthWise Separable Convolutions (DWSC), is boosted by three techniques: multiplexing, custom filters, and dilated convolution. The LITE architecture, trained on the UCR, is 2.78 times faster than InceptionTime and consumes 2.79 times less CO2 and power. To evaluate the performance of the proposed architecture on multivariate time series data, we adapt LITE to handle multivariate time series, we call this version LITEMV. To bring theory into application, we also conducted experiments using LITEMV on multivariate time series representing human rehabilitation movements, showing that LITEMV not only is the most efficient model but also the best performing for this application on the Kimore dataset, a skeleton based human rehabilitation exercises dataset. Moreover, to address the interpretability of LITEMV, we present a study using Class Activation Maps to understand the classification decision taken by the model during evaluation.