Hi,
As per my understanding, you want to estimate the decay parameter using a non-linear fitting function.
This can be done using the 'fminsearch' function.
Please find the code for the same as follows:
K = 4; % value of K
y = [1 4 8 16 32 64 128 256 512 1024]; % your data
lambda_initial = 0.5; % starting value of lambda
objective = @(lambda) sum((y-EWMA(lambda,y,K)).^2); % function handle of the function to be minimized
lambda_estimated = fminsearch(objective, lambda_initial) % calling fminsearch to find lambda
% function to compute the series using the EWMA model
function result = EWMA(lambda,y,K)
N = numel(y);
% result that is fed into the objective function
result = [];
% iterate for each term
for t=1:N
yt = 1;
% iterate for all k <= K
for k=1:K
if t-k <= 0
continue
end
yt = yt + lambda^k * result(t-k);
end
result = [result yt];
end
end
For more information regarding the 'fminsearch' function, please refer to the following documentation: https://www.mathworks.com/help/matlab/ref/fminsearch.html
Hope this helps! Thanks!
