I was on the way to the park. My friend called me and asked:
-What are you doing?
-I'm going jogging in the park.
Did it sound natural?
What is the difference between "I'm going to jog" and "I'm going jogging"?
I'm going jogging is definitely better. It's going+ing-form when you're concentrating on the action of the verb. I'm going jogging/swimming/shopping etc. The construction works with only a few verbs.
You could say I'm going to jog the last 100 yards to work, I'm going to swim in the river, I'm going to shop in Birmingham in future. You're not just saying what you're going to do. You're saying something else about it - the last 100 yards to work etc. So there's a difference in emphasis.