Air fares can change between two searches hours apart. The mechanism is inventory management operating continuously in the background rather than anything responding to the individual searching.
Seats are sold in classes with separate allocations
A cabin is divided into booking classes, each carrying a price and a number of seats, and the cheapest class holds only a portion of the aircraft.
When that allocation is exhausted, the system offers the next class up, and the displayed price steps rather than drifts.
A single booking of several seats can therefore clear a class and move the price for everyone searching afterwards.
Forecasts are revised continuously
Revenue management systems predict how many passengers will book each flight and how many will be willing to pay higher fares closer to departure.
Those forecasts update as bookings arrive, and allocations are reopened or closed accordingly, which can move a price downward as well as upward.
A flight selling behind expectations may see cheap classes reopened, which is why fares do not rise monotonically as departure approaches.
Competitive positions change through the day
Carriers monitor each other's published fares on shared routes, and a change by one operator can prompt matching responses within hours.
Fare filings are processed at intervals rather than instantly, which is why prices sometimes appear to move in clusters at certain times.
Sales and promotions add another layer, with limited allocations that disappear once the promotional class sells out on a given flight.
Personal tracking is not the explanation
Searching repeatedly does not raise a fare for that user, because the price is attached to the seat inventory rather than to the person requesting it.
Differences between devices or browsers usually reflect cached results, different points of sale, or different currency and market settings rather than surveillance.
Comparison sites also cache aggressively, so a price shown in results may already have expired at the airline's own system by the time it is selected.
What this implies for booking behaviour
Watching a single flight over time reveals its own pattern, which is more informative than general advice about the best day to book.
Flexibility on date and airport affects the price far more than the timing of the search, since it accesses entirely different inventory.
Once a fare is acceptable, delaying carries the risk that a class closes, and that risk grows as the flight fills rather than as the date approaches.