The short answer to this would be “not directly”.
However, the Flight Delay Prediction API makes it very easy to predict the future average delay of an airline, a specific route, or all flights of an airport within a certain period in the past – let’s say 1 year backward from the current day. Simply request the flights via the API on the targeted period and analyze how many times they operated and how many times of these were they delayed, and of course, for how long. This will give you a pretty clear understanding of the average delay rates from the current day forward and answer “how to predict flight delays with an API”.
You can always expand the data as the data expands over time too and build a more and more solid average delay rate for future flight delay prediction.
Tip: The date range you can request in 1 API call is normally 30 days at the most, but this can be shorter (down to 3-5 days) if the airport you requested is a busy one with higher traffic, and therefore the data the Flight Delay Prediction API is supposed to return.
In these cases, you may simply make multiple API calls covering shorter periods of time to complete your range.
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