The length of time that a moving violation stays on your record depends on the state you're living in.
In some states the moving violation stays on your driving record for 2 years and in some other states the moving violations stays on your driving record for 3 years.
In Indiana the moving violation stays on your driving record for 2 years and in Kansas the moving violation stays on your driving record for 3 years.
However in some states such as Iowa the moving violation stays on your record for as long as 6 years.
As long as you have no other moving violations and no more points go on your drivers license or driving record then those moving violations should no longer affect your auto insurance rates after 3 to 6 years depending on the state you're living in.