In this installment of my series on the Exponential Moving Average, I point out the relationships between the EMA and simple analog RC circuits. Electronics really isn’t my thing, but I found this to be interesting and kinda beautiful.
In the last post, we went over how well EMAs track straight lines in detail. Now, it’s natural to wonder how EMAs do with sources modeled after:
s[t] = m t^2
It turns out, they don’t do very well at all. Here’s our standard 20-ema of the basic parabola with ‘m’ = 1:
As you can [...]
We know from a couple posts ago that the EMA of a constant is equal to that constant. In other words, EMA’s track a DC signal perfectly. It might be natural to wonder how well they do against a straight line.
Recall that a line has a slope ‘m’ and an offset ‘b’ at [...]
I never noticed this until today, but the EMA filter is 100% invertible. That means, if you give me an ema-smoothed dataset, I can tell you what the original dataset was. You would think, as a low-pass filter, that it would be throwing away the high-frequency data, but it’s not. It’s just [...]
Here are a few algebraic properties of EMAs:
ema(constant) = constant
ema(s + t) = ema(s) + ema(t)
ema(s + constant) = ema(s) + constant
ema(s * constant) = ema(s) * constant
ema1(ema2(s)) = ema2(ema1(s))
Also, recall that the standard ‘bar form’ of an EMA, such as when we say “20-ema,” is actually specifying the ema [...]
The definition of an EMA:
ema[t] = (1-alpha)*ema[t-1] + alpha*data[t]
… tells you what to do with the last EMA you had and the current data sample. That’s all fine and good, but how do you get started? In other words, how do you get your first EMA value? The formula above is no [...]
My EMA article will be as comprehensive as I can manage. I’m going to try to cover every facet of the EMA that I’ve heard of. If there are any topics you’d like to see covered, write them in as comments so I will be sure to include them. Here’s another [...]
In case you can’t tell, I’m working on the mother of all EMA articles. A couple parts have been posted here so far. As I pointed out, my plan is to post bits on the blog prior to the article, for two reasons:
it keeps me moving forward, without the pressure of polishing the [...]
Over the weekend, Jeppetto asked:
“Why do EMA’s require fewer resources to calculate?”
The SMA Case
An SMA is a moving sample mean. So lets consider the 12 SMA and the 100 SMA for examples. In the 12 SMA, the naive calculation on each new bar is to add up the last 12 closes and divide [...]
You know, EMA’s are pretty attractive compared to SMA’s. They look smoother, they require fewer resources to calculate, they aren’t restricted to a smoothing amount based on a bar count, etc. One might look at the evidence, and ask: Why would I ever use an SMA over an EMA?
Here are a couple scenarios:
If [...]