I want to implement an iterative algorithm, which calculates weighted average. The specific weight law does not matter, but it should be close to 1 for the newest values and close to 0 to the oldest.
The algorithm should be iterative. i.e. it should not remember all previous values. It should know only one newest value and any aggregative information about past, like previous values of the average, sums, counts etc.
Is it possible?
For example, the following algorithm can be:
void iterate(double value) {
sum *= 0.99;
sum += value;
count++;
avg = sum / count;
}
It will give exponential decreasing weight, which may be not good. Is it possible to have step decreasing weight or something?
EDIT 1
The the requirements for weighing law is follows:
1) The weight decreases into past 2) I has some mean or characteristic duration so that values older this duration matters much lesser than newer ones 3) I should be able to set this duration
EDIT 2
I need the following. Suppose v_i
are values, where v_1
is the first. Also suppose w_i
are weights. But w_0
is THE LAST.
So, after first value came I have first average
a_1 = v_1 * w_0
After the second value v_2 came, I should have average
a_2 = v_1 * w_1 + v_2 * w_0
With next value I should have
a_3 = v_1 * w_2 + v_2 * w_1 + v_3 * w_0
Note, that weight profile is moving with me, while I am moving along value sequence.
I.e. each value does not have it's own weight all the time. My goal is to have this weight lower while going to past.