The large number of pixels to be processed and stored for digital holographic techniques necessitates the development of effective lossless compression techniques. Use cases for such techniques are archiving holograms, especially sensitive biomedical data, and improving the data transmission capacity of bandwidth-limited data transport channels where quality loss cannot be tolerated, like display interfaces. Only a few lossless compression techniques exist for holography, and the search for an efficient technique well suited for processing the large amounts of pixels typically encountered is ongoing. We demonstrate the suitability of autoregressive modeling for compressing signals with limited spatial bandwidth content, like holographic images. The applicability of such schemes for any such bandlimited signal is motivated by a mathematical insight that is novel to our knowledge. The devised compression scheme is lossless and enables decoding architecture that essentially has only two steps. It is also highly scalable, with smaller model sizes providing an effective, low-complexity mechanism to transmit holographic data, while larger models obtain significantly higher compression ratios when compared to state-of-the-art lossless image compression solutions, for a wide selection of both computer-generated and optically-acquired holograms. We also provide a detailed analysis of the various methods that can be used for determining the autoregressive model in the context of compression.