Jagex's ways of detecting macros are very accurate so they rarely ban people by mistake. I'm more inclined to think that either you're account might have actually been hacked... or you're just lying.
Jagex have something to say for people who claim they didn't do the crime:I was hijacked
Please remember that players are responsible for the actions of any person to have accessed their account. We provide a number of tools and tips to help players keep their accounts secure. In instances where an account was hijacked at the time of the ban offence, the account owner will be held accountable. Further details can be found via our .
Ultimately the burden of responsibility is with our players, to ensure that their account is kept secure at all times. Further information on how to keep your account secure can be found via the & sections of our Wiki.
My brother/cousin/best friend/another person did it
We receive a large number of appeals daily which claim that a sibling, best friend, cousin or another person was responsible for the offence. This is often in the form of a claim of them using a macro to "help" or just accessing the account, whilst the account owner was away from their PC. In these situations there is no evidence to support this claim, so we're not going to remove the ban from the account.
You've probably seen this countless times. Sadly the longer a ban is applied for, the harder it becomes to overturn it. It's almost like cold-cases in police investigations.
I was in just the same position as you recently, only that my former ban was applied one or two years ago. If you aren't lying, what I'm about to say might help you.
Make. An. Appeal
Send a support ticket too. Jagex have made it very difficult to do just that. Luckily, someone found a link to the page to make an appeal(At the bottom of my answer).
If you aren't lying, good luck... I was VERY lucky to have my ban overturned.