If this is the first correspondence, you should send them a letter demanding validation of the debt. Then do nothing. If this is not the first letter from them, do not respond. When you get the notice of arbitration, you should send a letter stating that the statute of limitations has passed and presenting your evidence. It should be in the form of a legal pleading.
You should also consult with an attorney about a FDCPA or Rosenthal Act case.
I agree with most of what Jon Stein posted. Validation can help you figure out if you really owe this debt.
But what you really need to know is whether you have actually passed the statute of limitations. The best way to find out is to contact a consumer lawyer. The NACA lawyer database is a great place to start, but you might want to call Ron Wilcox in San Jose. He has a lot of experience working with consumers on debt collection issues in California, and should be able to help.
To answer your question re the SOL: The statute runs anews each time you make a payment on the debt. The statute expires four years after the last payment. So, yes, the statute of limitations more than likely bars this claim. The collection agency is just trying to scare you. Write them a letter if you want but colelction agencies typically are going to keep harassing you unless and until you obtain an attorney.