  We introduce a multivariate hidden Markov model to jointly cluster
time-series observations with different support, i.e. circular and linear.
Relying on the general projected normal distribution, our approach allows for
bimodal and/or skewed cluster-specific distributions for the circular variable.
Furthermore, we relax the independence assumption between the circular and
linear components observed at the same time. Such an assumption is generally
used to alleviate the computational burden involved in the parameter estimation
step, but it is hard to justify in empirical applications. We carry out a
simulation study using different data-generation schemes to investigate model
behavior, focusing on well recovering the hidden structure. Finally, the model
is used to fit a real data example on a bivariate time series of wind speed and
direction.
