Predict next event occurrence, based on past occurrences

Question

I'm looking for an algorithm or example material to study for predicting future events based on known patterns. Perhaps there is a name for this, and I just don't know/remember it. Something this general may not exist, but I'm not a master of math or algorithms, so I'm here asking for direction.

An example, as I understand it would be something like this:

A static event occurs on January 1st, February 1st, March 3rd, April 4th. A simple solution would be to average the days/hours/minutes/something between each occurrence, add that number to the last known occurrence, and have the prediction.

What am I asking for, or what should I study?

There is no particular goal in mind, or any specific variables to account for. This is simply a personal thought, and an opportunity for me to learn something new.

Answer 1

I think some topics that might be worth looking into include numerical analysis, specifically interpolation, extrapolation, and regression.

Answer 2

This could be overkill, but Markov chains can lead to some pretty cool pattern recognition stuff. It's better suited to, well, chains of events: the idea is, based on the last N steps in a chain of events, what will happen next?

This is well suited to text: process a large sample of Shakespeare, and you can generate paragraphs full of Shakespeare-like nonsense! Unfortunately, it takes a good deal more data to figure out sparsely-populated events. (Detecting patterns with a period of a month or more would require you to track a chain of at least a full month of data.)

In pseudo-python, here's a rough sketch of a Markov chain builder/prediction script:

n = how_big_a_chain_you_want
def build_map(eventChain):
    map = defaultdict(list)
    for events in get_all_n_plus_1_item_slices_of(eventChain):
        slice = events[:n]
        last = events[-1]
        map[slice].append(last)

def predict_next_event(whatsHappenedSoFar, map):
    slice = whatsHappenedSoFar[-n:]
    return random_choice(map[slice])