Time-lapse hyperspectral image (HSI) data has an enormous size and demands lossless compression for most of the high fidelity applications. In literature, spatial and spectral correlations in HSI are widely studied and used for compression. We propose a novel adaptive switched prediction-based scheme, which efficiently exploits temporal correlations in addition to spatial, and spectral correlations. The predictor switching uses a threshold, which is chosen based on the residual error distribution of already encoded band. Hence, our method does not need any overhead to be transmitted. The proposed scheme outperforms other state-of-the-art methods in bit-rate, and the method is computationally efficient too.