Automation of file downloading calling a JavaScript function

I download lot of files from certain website regularly and I would like to automate the process. The problem is, that the website does not make any requests to the server (Network tab in Developer tools of Chrome stays empty when I click on the link to download file). So I suppose the website generates the files in JavaScript. Right?

How to easily automate the process?

I read something about JavaScript shells. Is this the way to go? Could you, please, provide detailed description how I could do it this way?