Hi Vivek,
You asked, how to calculate the Largest Lyapunov exponent value for a time series data value. As I recall, it is a measure of the rate of separation of nearby trajectories in a dynamical system and provide insights into the system's chaotic behavior. However, you need to load your time series data into Matlab. Let's assume you have a vector data containing your time series values.
>> % Example time series data data = randn(1000, 1); % Replace this with your actual data
Next, you need to define the parameters for the calculation. This includes the time delay tau and the embedding dimension m. These parameters are crucial for the calculation of the Largest Lyapunov Exponent.
tau = 1; % Time delay m = 3; % Embedding dimension
Now, you can calculate the Largest Lyapunov Exponent using the Rosenstein algorithm.
>> % Rosenstein algorithm for Largest Lyapunov Exponent N = length(data); D = zeros(N-m+1, m);
for i = 1:N-m+1 D(i, :) = data(i:i+m-1); end
% Calculate distances distances = pdist(D);
% Sort distances [~, order] = sort(distances);
% Calculate the Largest Lyapunov Exponent lambda = mean(log(distances(order(2:end)) ./ distances(order(1:end-1))));
disp(['Largest Lyapunov Exponent: ', num2str(lambda)]);
Hope, my friend, this will help resolve your problem.