Hidden Markov models are among the most important machine learning methods for the statistical analysis of sequential data, but they struggle when applied to big data. Their relative inefficiency has been addressed several times by the use of some compression techniques, either for the computation or for the data. This thesis explores the latter, with the application of a data compression technique based on wavelets and the subsequent adaptation of the main HMMs algorithms from the literature: the forward, Viterbi and Baum-Welch algorithms used to solve the evaluation, decoding and training problem respectively. The testing phase shows that this new technique generally yields equal or better results, obtaining some extremely high speedups in the training problem, making it even thousands of times faster; this enables the training of a HMM with big data on a commodity laptop..