Estimating the decay parameter in Exponentially Weighted Moving Average (EWMA) model

Given the data , ; I would like to like to estimate the decay parameter λ in Exponentially Weighted Moving Average (EWMA) model, such that

where is the error term in the nonlinear regression, .

I am wondering, is there any convenient way to estimate the decay parameter λ uisng nonlinear fitting function? Because K could be very large, which around 200.

Answer 1

[Pranavkumar Mallela]

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

lambda_estimated = 1.1158

% 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!