He's testing the wrong thing. It's not (just) the time of year, it's the time to flight that determines fare (which is why he's seeing the highest fares for flights in the upcoming week.
Airlines use complex loading systems to maximize both capacity utilization and total revenue. So when a flight is far off, the fare is moderate (because they still have a long time left until the flight). If there's extra capacity on a flight, they'll start lower the price to use up capacity as its date approaches. When you're in the last week or two before the flight, the fare may go way up (because there are only a few seats left and they are looking to maximize their price) or go down (because they have a lot of seats left and they're looking to fill them.)
Generally, if an airline is doing things right then a lot of flights will be fairly full, so you'll most often see prices rising in the last week or two before the flight date.
(An additional factor is that if you're looking for a ticket next week, you probably have less date flexibility than someone booking a month in advance.)
(Conversely someone once told me that the actual marginal cost of an empty seat on a commercial flight is around $35. In theory, if a flight is about to leave the gate and a seat is empty, the airline should be willing to sell a ticket for any price over $35... )
There are some other factors as well, such as trying to segregate business travelers from vacation travelers. Business travelers tend to book last-minute, want refundable fare and don't want their trip to extend over a weekend day. Hence the spike on traveling from LAX to the east on Thursdays - many flights from LAX to JFK or MIA on a Friday won't arrive until late Friday night at best.
I've spent time working with companies that do GDS systems (basically travel ticketing back-end infrastructure) and talked with a few startups in the affiliate/rewards space.
Load management is also used a lot in business schools as a case study of how more complex pricing schemes can be used to extract a higher average price than would be indicated by a traditional macro-economic demand curve approach. Basically you're segmenting customers and also varying pricing based on available inventory.
Airline seat inventory and hotel rooms as well are an interesting problem because they're essentially wasting inventory - if you don't sell a hotel room or airline seat before the day it's available, it becomes worthless. That's why airlines and hotels love to have reward systems where you're compensated with free travel/stays - it's a way to get value from something that might otherwise go to waste. (This is also why Priceline works - they are a way for hotels to get rid of excess inventory on a no-name basis.)
There's a presentation from ITA (a company that made one of the more known air travel search engines) about this topic, which covers pricing issues in much details:
Airlines use complex loading systems to maximize both capacity utilization and total revenue. So when a flight is far off, the fare is moderate (because they still have a long time left until the flight). If there's extra capacity on a flight, they'll start lower the price to use up capacity as its date approaches. When you're in the last week or two before the flight, the fare may go way up (because there are only a few seats left and they are looking to maximize their price) or go down (because they have a lot of seats left and they're looking to fill them.)
Generally, if an airline is doing things right then a lot of flights will be fairly full, so you'll most often see prices rising in the last week or two before the flight date.
(An additional factor is that if you're looking for a ticket next week, you probably have less date flexibility than someone booking a month in advance.)
(Conversely someone once told me that the actual marginal cost of an empty seat on a commercial flight is around $35. In theory, if a flight is about to leave the gate and a seat is empty, the airline should be willing to sell a ticket for any price over $35... )
There are some other factors as well, such as trying to segregate business travelers from vacation travelers. Business travelers tend to book last-minute, want refundable fare and don't want their trip to extend over a weekend day. Hence the spike on traveling from LAX to the east on Thursdays - many flights from LAX to JFK or MIA on a Friday won't arrive until late Friday night at best.