Using web scraped data for consumer price indices Is there information and literature regarding comparative consumer price index methods? Specifically, the web scraping method of index construction?
Take a look at Billion Prices Project:


  The Billion Prices Project is an academic initiative that uses prices
  collected from hundreds of online retailers around the world on a
  daily basis to conduct economic research.


Also take a look at PriceStats


  PriceStats collects online prices to provide daily inflation updates
  for 22 economies.


Overview of the PiceStats approach

More broadly, price index construction is a huge literature full of pitfalls so it is difficult to point you to a generic but also advanced presentation of the issues. But you might start with Consumer Prices, the Consumer Price Index, and the Cost of Living (Boskin, Dulberger, Gordon, Griliches and Jorgenson (1998)), a Journal of Economic Perspectives piece on the subject.