Exponentially Weighted Moving Average (EWMA)

Hello community, kindly let me ask for your help one more time.

I'm trying to apply this EWMA formula to my data:

EWMA(t) = a * x(t) + (1-a) * EWMA(t-1)

where :

a = the weight decided by the user

x = value of the series in current period

My data is:

EWMA(initial value) = 0.3

a = 0.3

x = [ .15 .11 .11 .1 .09 .12 .11 .09];

using the formula and above values I will get this:

EWMA = 0.3 * 0.15 + (1 - 0.3) * EWMA(initial value) 0.3 = 0.255

then I need to apply the formula to all my data but now using previous EWMA value EWMA(t-1), calculated above

EWMA = 0.3 * 0.11 + (1 - 0.3) * 0.255 = 0.2115

EWMA = 0.3 * 0.11 + (1 - 0.3) * 0.2115 = 0.18105

EWMA = 0.3 * 0.1 + (1 - 0.3) * 0.18105 = 0.1516735

EWMA = 0.3 * 0.09 + (1 - 0.3) * 0.156735 = 0.136714

EWMA = 0.3 * 0.12 + (1 - 0.3) * 0.136714 = 0.131700

EWMA = 0.3 * 0.11 + (1 - 0.3) * 0.131700 = 0.125190

EWMA = 0.3 * 0.09 + (1 - 0.3) * 0.125190 = 0.114633

any recomendation will be higly appreciated.

[Mathieu NOE]

and what is the problem ?

Answer 1

[Voss]

Here's how you can perform the calculations you've listed:

% given:
a = 0.3;
x = [0.15 0.11 0.11 0.1 0.09 0.12 0.11 0.09];

N = numel(x);
EWMA = zeros(1,N+1);
EWMA(1) = 0.3; % given

for ii = 2:N+1
    EWMA(ii) = a * x(ii-1) + (1-a) * EWMA(ii-1);
end

format long g
disp(EWMA.')

                       0.3
                     0.255
                    0.2115
                   0.18105
                  0.156735
                 0.1367145
                0.13170015
               0.125190105
              0.1146330735

[A-Rod]

awesome, this really helps me.

thanks a lot