That seems fine, but I think computation of empirical joint distribution requires enormous amount of data and is generally not feasible.The joint probability is approximated with the product of conditional probabilities based on first order Markov Chain assumption p(xi+n|xi+n-1)p(xi+n-1|xi+n-2)…p(xi+1|xi).

You can explore how I have used Markov Chain model to detect anomalies in time series sequence with ECG data.