Cfrtjryk

I'm wanting to calculate exponential moving averages of a variable, distance. Is the logic (and math) correct in the below code?

time and lastTime are millisecond-precise timestamps in seconds – the former is the current time, the latter is the time of the last calculations.

lastA etc are the exponential moving averages from the last calculations.

a etc will be left with the calculated exponential moving averages.

var distance = ...;

var a = Math.pow(1.16, -(time-lastTime)),

    b = Math.pow(1.19, -(time-lastTime)),

    c = Math.pow(1.22, -(time-lastTime)),

    d = Math.pow(1.26, -(time-lastTime)),

    e = Math.pow(1.30, -(time-lastTime)),

    f = Math.pow(1.35, -(time-lastTime)),

    g = Math.pow(1.40, -(time-lastTime));

a = a*lastA + (1-a)*distance;

b = b*lastB + (1-b)*distance;

c = c*lastC + (1-c)*distance;

d = d*lastD + (1-d)*distance;

e = e*lastE + (1-e)*distance;

f = f*lastF + (1-f)*distance;

g = g*lastG + (1-g)*distance;

This is border line a bad question, as not enough code is given to properly review it.

The variables a -> g look terrible, I would create an array with the numbers you need:

var dataPoints = [1.16,1.19,1.22,1.26,1.30,1.35,1.40];

Then I would would loop over those points and create an averages object

var averages = {},

    value, x;

for(var i = 0, length = dataPoints.length ; i < length ; i++ ){

  value = dataPoints[i];

  x = Math.pow(value, -(time-lastTime));

  averages[value] = x * lastAverages[value] + (1-x) * distance;

}

I cannot tell whether the math is correct, if it is not correct, then this question does not belong here :)

Either I'm confused by your notation, or you may have implemented something completely different from an exponential moving average, which is traditionally defined as

$S_{t} = alpha Y_{t-1} + (1-alpha) S_{t-1}$

where

• $alpha$ is the decay rate


• $Y_{t}$ is the value at time $t$


• $S_{t}$ is the exponential moving average at time $t$.

How do your variables correspond to those in the definition? Let's just consider one of your letters instead of all seven:

var distance = ...;

var a = Math.pow(1.16, -(time-lastTime));

a = a*lastA + (1-a)*distance;

I'm guessing

• 
  a corresponds to $alpha$, and you adjust the decay per timeslice based on the duration of the timeslice


• 
  lastA corresponds to $Y_{t-1}$


• 
  distance corresponds to $S_{t-1}$

But then, I'm confused:

1. What's the purpose of the seven letters a … g? To track the results using multiple decay rates? If so, wouldn't the different decay rates result in a different series S_t for each decay rate?


2. Why do all seven cases all share the same distance — isn't it the point to have a different distance series for each case?


3. Why do you assign the final result to a (= the decay rate) rather than to distance or something?