We have found that a customer is kiting. We have closed the account so no further kiting activity can occur. Do I still need to file a SAR since we have closed the account?

if the dollar threshold has been breached a SAR is necessary even if the bank has lost no money.

Also consider that if it is addressed in your BSA/AML policy that you will file a SAR if kiting is detected, then you need to file as well.

If the amount involved exceeded $5,000, yes. The issue will be how to calculate the amount involved.

What is the best way to calculate the amount when researching the activity, such as how far back, should our research include?

Ken provided a link above to a discussion regarding how to calculate. Much depends on your procedures so make sure you are consistent in your application of the calculation. There is no guidance on how far back you go. if your program dictates a time period, use that as a starting point. If it is determined that the activity started before, feel free to go back and get it all. Be prepared to explain to regulators any situations where the activity went on for an extended period of time without being identified. Document any new systems, reviews or processes that may have identified the activity at this point and prompted the review going back.