How to add variables to the equation by using loop?

How to write a loop to add variables to an equation in a loop if some indicator gets bigger every time?

For example:

sss(i,1) = ((y(i,1)-b(1,1)- b(2,1)*y(i-1,1)- b(3,1)*(y(i-1,1)-y(i-2,1)) - b(4,1)*(y(i-2,1)-y(i-3,1)))^2);

In this equation the lag (input variable) is 2 and therefore we have 4 'b' values. How to create a loop function for automatically adding extra b's when the lag(input variable) is increasing or removing b's when the lag is decreasing?

Answer 1

[Kautuk Raj]

Hello Rufat Ismayilov,

I see that you want to dynamically adjust the number of terms in an equation based on a specified lag variable.

To create a loop in MATLAB that automatically adjusts the number of terms in your equation based on the value of a lag variable, you can use a for loop to construct the summation of the b terms. Here is a general approach to do this:

% Define the lag input variable 
lag = 2; % You can change this to increase or decrease the number of 'b' terms 

% Define a column vector 'y' with random values for the sake of example 
% The length of 'y' should be greater than the lag 
n = 10; % Total number of observations in 'y' 
y = rand(n, 1); % 'y' is a column vector with random values 

% Define the 'b' vector with random coefficients 
% The length of 'b' should be lag + 2 
b = rand(lag + 2, 1); 

% Preallocate the sss array for performance 
sss = zeros(n, 1); 

% Loop through the elements of y starting from the point where there is enough data to apply the lag 
for i = (lag + 1):n 
    % Initialize the sum of b terms for the current i 
    b_sum = b(1,1); 
    
    % Loop through the lag terms and add them to the b_sum 
    for j = 1:lag 
        b_sum = b_sum + b(j+1,1) * (y(i-j+1,1) - y(i-j,1)); 
    end 
    
    % Calculate the sss(i,1) according to the equation 
    sss(i,1) = ((y(i,1) - b_sum)^2); 
end 

% Display the result 
disp(sss); 

I hope this helps you with your question.