Hidden Markov Model for regime detection

Project Assignment:

Hidden Markov Models for regime detection.

Fit an Hidden Markov Model with Gaussian emissions to the data in DSET1; it is sufficient to focus on the “Appliances” and “Lights” columns of the dataset which measure the energy consumption of appliances and lights, respectively, across a period of 4.5 months. Consider the two columns in isolation, i.e. train two separate HMM, one for appliances and one for light. Experiment with HMMs with a varying number of hidden states (e.g. at least 2, 3 and 4). Once trained the HMMs, perform Viterbi on a reasonably sized subsequence (e.g. 1 month of data) and plot the timeseries data highlighting (e.g. with different colours) the hidden state assigned to each timepoint by the Viterbi algorithm. Then, try sampling a sequence of at least 100 points from the trained HMMs and show it on a plot discussing similarities and differences w.r.t. the ground truth data.