Apple ID and iCloud on Macbook Air

I changed my Apple ID and I'm having issues connecting my new Apple ID with my iCloud on my Macbook. I have tried going to system preferences, iCloud and then "sign out". But when I do this, it prompts me to give the password for my old Apple ID. When I go to type in the password for my old Apple ID, it then tells me that my old ID does not exist. How do I put in my password and sign out of my previous Apple ID, if its telling me that my old ID does not exist? (My operating system is High Sierra 10.13.2). Any help is appreciated, thank you!