Unequal length observation sequences when training Hidden Markov model
No worries, length of observation would help in training of model. longer the length, training for Forward-backward Algo/baum Welch algo would be better. But length of observation is nothing to do with forecasting. read my blog below-   

http://machinelearningstories.blogspot.com/2017/02/hidden-markov-model-session-1.html

transition probabilities would give next hidden state. and from next hidden state you can get next observation.So number of observation would not matter as long as u have trained model( emission and transition probabilities). Also if are intrested to know in detail that how next state would be calculated, follow below article.

http://machinelearningstories.blogspot.com/2017_03_01_archive.html