Hey there! That's odd. Well, the servers should be on Defcon 5. - Call of Duty®: Ghosts || Game Status
There might be something going on your home network. I know a thread that might help you with this trouble.
Hope this should help you connect as well as know how NATs work. Cheers!
Try to sign out then reboot then relogin from XBox.
Also, try other accounts if you would be able to connect.
Try the following steps as well:
1. Shut down the Xbox
2. Switch off the modem/or the router and also unplug their power cables.
3. Wait for 30 seconds
4. Plug the power cords back into the modem and the router but don’t switch them on yet.
5. First turn on the modem and wait for it to initialize (let the lights become stable).
6. Then switch on the router and let the blinking lights stabilize.
7. Now turn on the gaming console/PC connected to the network. Test the Internet connection.
A support case was created for you and you should be contacted shortly by a Customer Support Representative, if you haven't been already. You can view and update your case at the Activision Support website. After logging in, go to "My Support" then "My Cases".