I've never been bothered by an advertisement since ages because of my ruthless choice of using a full-fledged ad blocker like AdAway. You may try it if the device is rooted, or try adblock-plus for non-rooted devices.
Let's come to the issue. If that advertisement is indeed a notification, then you can tap and hold that notification → App info, and you would be shown the app's info which generated that notification. If the app's notifications or toasts are not important to you, uncheck Show notifications and you won't be bothered again by the app through notification or toasts. This also implies that you would receive no notification at all from that app. It's take it or leave it approach. Check Show notification by going into Settings → Apps → and things would come back to where they previously were.
For Android 4.2.1 and 4.4.2:
(Click image to enlarge; hover to know details)
For Android 5.0.2:
An alternate way to find out which app owns the current notification is to issue the command (after setting up adb of course) :-
adb shell dumpsys notification
(Android 4.2.1 needs root access for
It will give detailed output for each of the current notification. Under each record, look for entries like
contentIntent=. You can see the package name of the app. See the corresponding app name using App Browser (Lollipop already shows package name below an app name in Settings → Apps).