The R package HMMt provides a modified Baum-Welch algorithm that supports multi-dimensional Student's t emission. It also handles NA and provides a 'bridge()' function to uniformize sampling rate.

Please do not copy-paste the code. Instead, use 'git clone git@github.com:gui11aume/HMMt.git' to have the full version history.

The code is here for reproducibility and mistake-tracking purposes, but feel free to copy, reuse and modify it in any way you like.

After installing the package, you can run the following lines of code in R to get started.

library(HMMt)
x <- c(rt(1000, df=3), rt(1000, df=3)+1)

# x has a t distribution with a jump at position 1001.
plot(x, type = 'l')

# Check the output of BaumWelchT. 
BaumWelchT(x)

# See that it usually finds the transition.
lines(BaumWelchT(x)$ViterbiPath-1, col=2)