Stender

Hi guys. I have a question about my 99' Porsche Boxster 2.5. Im not 100% sure what the problem is, but I think it might be an air leak. When it has been sitting for at day or two and I start it up, it really runs bad until it gets to normal temp, Sometimes it even stalls. But as soon at it gets warm its fin. Its not perfect when it is warm, but acceptable. The rpm gage is not 100% steady, but again acceptable. But when I turn the car off, it makes this noise as you can hear. I think it sounds like and air leak, which would also explain that the craked hose would expand when the car gets warm and make run better. I dont know, but what do you guys think? Thanks for the help