Exponential moving average of a tick stream

Question

An exponential moving average (EMA) smooths a series by weighting recent prices more heavily than old ones. Each new EMA blends the latest price with the previous EMA using a smoothing factor alpha (between 0 and 1): higher alpha reacts faster.

prices = [10, 20, 30], alpha = 0.5
-> [10, 15.0, 22.5]     # seed with first price, then blend

Return the EMA at each step, seeding the first value with the first price.

Accepted Answer

Seed the EMA with the first price (there is nothing earlier to blend). For every subsequent price, the new EMA is alpha price + (1 - alpha) previousema, a weighted average of the fresh tick and the accumulated history. This needs only the running EMA, so it is O(1) memory per step. Tracing [10, 20, 30] with alpha = 0.5: start at 10, then 0.520 + 0.510 = 15, then 0.530 + 0.515 = 22.5. Time O(n), space O(n) for the output (O(1) if you only keep the latest EMA). Edge cases: an empty input returns []; alpha = 1 reproduces the raw prices; alpha = 0 freezes at the seed; the seeding choice matters m…

Exponential moving average of a tick stream

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