Airline Fares - What analysis should be used to detect competitive price-setting behavior and price correlations?
Word of warning from a former airline Revenue Management analyst: you might be barking up the wrong tree with this approach. Apologies for the wall of text that follows, but this data is a lot more complex and noisy than might appear at first glance, so wanted to provide a short description of how it's generated; forewarned is forearmed.

Airline fares have two components to them: all the actual fares (complete with fare rules and what have you) that an airline has available for a certain route, most of which are published the Airline Tariff Publishing Company (a few special-use ones are not, but those are the exception rather than the rule) and the actual inventory management performed by the airline on a day-to-day basis.

Fares can be submitted to ATPCO four times a day, at set intervals, and when airlines do so, it will usually consist of a mixture of additions, deletions, and modifications of existing fares. When an airline initiates a pricing action (assuming their competitors aren't trying to make their own moves here), they usually have to wait until the next update to see if their competitors follow/respond. The converse goes when a competitor initiates a pricing action, as the airline has to wait until the next update before they can respond.

Now, this is all well and good with respect to fares, but the problem is that, because this is all getting published in ATPCO, fares are the next best thing to public information... all your competitors get to see what you've got in your arsenal, so attempts to obfuscate are not unheard of, such as publishing fares that will never actually be assigned any inventory, listing all the fares as day-of-departure, etc. 

In many ways, the secret sauce comes down to the actual inventory allocation, i.e. how many seats on each flight will you be willing to sell for a given fare, and this information is not publicly available. You can get some glimpses by scraping web info, but the potential combinations of departure time/date and fare rules are quite numerous and may quickly escalate beyond your ability to easily keep track of. 

Typically an airline will only be willing to sell a handful of seats for a very low fare and the people who snag those have to book quite far in advance lest the fare rules lock them out, or other travelers simply beat them to the punch. The airline will be willing to sell a few more seats for a higher fare, and so on and so forth. They will be quite happy to sell all of the seats for the highest fare they've got published, but this is not usually feasible.

What you're seeing with fares getting higher the closer you get to the day of departure is simply the natural process of having the cheap seats get booked farther out, while the remaining inventory gradually gets more expensive. Of course, there are some caveats here. The RM process is actively managed and human intervention is quite common as the RM team generally strives to meet its revenue goals and maximize revenue on each flight. As such, flights that fill up quickly may be "tightened up" by closing out low fares. Flights that are booking slowly may be "loosened up" by allocating more seats to lower fares.

There is a constant interplay and competition between airlines in this area, but you are not very likely to capture the actual dynamics just from scraping fares. Don't get me wrong, we had such tools at our disposal, and, despite their limitations, they were quite valuable, but they were just one data source that fed into the decision-making process. You'd need access to the hundreds, if not thousands of operational decisions made by RM teams on a daily basis, as well as state-of-the-world information as they see it at the time. If you cannot find an airline partner to work with in order to get this data, you might need to consider alternate data sources.

I'd recommend looking into getting access to O&amp;D fare data from the Official Airline Guide (or one of their competitors) and try to use that for your analysis. It's sample-based (about 10% of all tickets sold) and aggregated at a higher level than would be ideal so careful route selection is imperative (I'd recommend something with plenty of airlines, flying non-stop multiple times a day, with large aircraft), but you may be able to get a better picture of what was actually sold (average fare) and how much of it was sold (load factor), vs. merely what is available for sale at a given point in time. Using that information you might be in better position to at least explore the outcomes of the airlines' pricing strategy, and make your inferences from there.