I am creating a program to collect and analyze prices for goods and alert the user when the price decreases so that they can buy it on "sale." I know a little statistics (e.g. standard deviation) but am looking for the best way to determine if a price drop is significant compared to historical prices - i.e. if I should bother alerting the user to the price decrease.
Let's say, for example, that my program is collecting prices for books. It searches the web, say, on a daily or weekly basis for prices for the book (both used and new), and stores this data in a database. I can make a graph of the prices over time (both lowest price, mean price, etc.) and visually determine when the price drops a significant amount - this is easy for a person to do. But what is the best statistical algorithm to determine this?
I can think of a few cases in which a person would buy a product when the price drops:
- If the price drops below a certain static barrier. For example, if the customer determines that they would buy the product at < 15, then whenever the price dips below that amount they should be alerted to that. This scenario is based on the idea that the customer believes that the price will actually eventually get that low, at some point in the future.
- If the price drops a significant amount below the current price. This is more realistic in some scenarios. For example, if there is a rare and relatively expensive book (for example, it was printed by an academic publisher with only a few thousand copies, all in hardcover, which sold for 150 when new and there are only a few copies on the market) - the book may be available (used) at the current time for an average price of 85. The price may never drop to 15, because the supply is so low. However, it may drop to a significantly lower price (40 or 50), but the customer doesn't have a specific price where they will buy the book.
- If the price of the book drops very low. A book may go today for 20, but the customer may want to wait and see if a bookseller is going to put it on sale for 5-8, because they don't need this book right now - but it's on their "wish list."
I am interested in this second and third scenario. Essentially I want to be able to determine when an item is available for a price that is "notable." I will store all of the historic prices in a database, and can compare this week's prices with historic prices.
What are your suggestions for statistical analytic tools which can be used to study this type of data and make automated recommendations?