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This seems like a rather ignorant question but some searching has proven fruitless. When looking at any EMA lines in a small timeframe (1-minute or 5-minute bars), I noticed the EMA changes across those periods (as expected given the name).

My noob understanding of something like 9EMA is factoring the close value of the previous 9 days. That makes sense.

What is the formula for that concept but using minute bars?

  • Is it comparing the current minute close value to the same minute the previous 9 days?
  • Or is it a simple average of all the closing values from the day so far and the final close of the previous 8 days?
  • Or even more complex... the average of each minute close, each day.

This feels laughable... I'm sure I'm overcomplicating this.

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My noob understanding of something like 9EMA is factoring the close value of the previous 9 days. That makes sense.

You're close. This is true for a 9-day SMA specifically. The 9 in a 9 S/EMA can be 9 of any time unit. Whatever unit a single bar is in your chart (the "Period"), that's what will be used. So if you want a 9-day EMA, you'd choose a:

  • Length = 9 and
  • set your Period to be Days

Length = 9

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Period = Day

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What is the formula for that concept but using minute bars?

It's exactly the same, except discrete close data is taken every minute instead of every day.

 EMA(t) = Price(t)×k – EMA(t–1)×(1 – k)

 where k = 2 / (N+1)

 N = 9 in your example

Notice that this is weighted more heavily toward the most recent time data compared to prior time data. This makes the EMA more of a leading indicator than the SMA (or, rather, less of a lagging indicator).

Also note that it's recursive in nature.

Is it comparing the current minute close value to the same minute the previous 9 days?

No. If you're looking at the minute chart, your Period is a Minute. A 9 EMA would most strongly be influenced by the price 1 minute ago, 2 min ago, 3 min ago, and with each minute before having less and less impact. Price from 2 days ago, let alone 9, has no bearing on a 9 1min EMA.

Or is it a simple average of all the closing values from the day so far and the final close of the previous 8 days?

You're overcomplicating it. The previous days have no significance on a 9 1min EMA. The last 8-9 minutes are the only things that are important.

In the event that you want the last several days to be relevant, you should switch to a 9 Day EMA or a 50 4hr EMA.

Or even more complex... the average of each minute close, each day.

If your Period is a Minute, then in order to account for every minute of the last 9 trading days, your length would have to be:

  • Length = 4050, because there are 7.5 hrs / day and 60 min / hr

But no one trades like this.

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The formula for calculating an EMA is:

EMA = Price(t) * k + EMA(y) * (1 – k)

t = today, y = yesterday, N = number of days in EMA, k = 2/(N+1)

To calculate a 9 day EMA:

  1. Determine k: 2/(9 + 1) = 0.20

  2. Add the prices for first 9 days and divide by 9 (9 day SMA)

  3. On day 10, multiply the day 10 value by k and multiply the previous day’s moving average by (1-k). Adding the two values gives you the EMA for period 10.

  4. Repeat step 3 for every subsequent value.

This formula is the same for whatever periodicity of data your are using (one minute, five minute, daily, etc.).

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