Hi,
The lognormal distribution is not directly supported in some regression functions, you can transform the data to a normal distribution by taking the natural logarithm of your series. This transformation makes the data suitable for many statistical models, including ARMA. I have done the same thing to the data points that you have created and have fit a ARMA model, you can refer the below code for reference.
% Generate lognormal data
mu = 0;
sigma = 0.25;
R = lognrnd(mu, sigma, 12000, 1);
% Transform to normal distribution
log_R = log(R);
% Perform ADF test
[h, pValue] = adftest(log_R);
fprintf('ADF Test p-value: %f\n', pValue);
% Plot ACF and PACF
figure;
subplot(2,1,1);
autocorr(log_R);
title('ACF of log-transformed data');
subplot(2,1,2);
parcorr(log_R);
title('PACF of log-transformed data');
% Fit ARMA model (example: ARMA(1,1))
model = arima('ARLags',1,'MALags',1,'Constant',0);
fit = estimate(model, log_R);
% Display the results
disp(fit);
I hope this clarify your query :)
