You will be hard-pressed to find any scientific data on this question. Psychology in humans is already a difficult study, at times failing to demonstrate results with real scientific rigor. When studying animal psychology, you face another substantial barrier - language. Although some primates have been taught to communicate with sign language, the best of them are still far from the level of proficiency of a human. We can measure brain activity and observe behavior, which can lead us to strong suspicions about what is going on in an animal's mind, but very little can actually be proven.
Mostly, all we can do is speculate about such questions. You will find some veterinarians out there who treat pets for mental conditions, but you will find at least as many people calling them quacks as those who believe in the validity of their work. And certainly, they can't prove to you that a treatment has helped an animal. It's subjective.
If we see an animal do something which in a human might reliably be interpreted as a sign of depression, it's possible that this interpretation is appropriate for the animal as well. It's also possible that there is some totally foreign unrelated explanation. The problem we find when trying to scientifically discuss matters which cannot be proven scientifically is that scientists must be careful to state what they know and nothing more. So they might say "We cannot prove that the porpoise is depressed", or "Science cannot prove the existence of a God." This is often misinterpreted as evidence against the finding - that the porpoise is not depressed; that there is no God. This is a fallacy. Rather, we should recognize that we have different ways of exploring questions like these.
I can't prove it to you, but I know that my Beagle had a rich emotional life. I know this because I spent huge amounts of time with him. He was a close friend of mine. I would just as soon question whether my wife has real emotions as my dog. I can't prove that my wife's emotions are real either, but I don't have to. It would be silly to assume that everything she shares with me is some sort of evolutionary programming, and not real emotion. Now, when I extend this to cetaceans, I must admit that I don't have any friends in those circles. So I can only guess.