determine optimal p for AR model

hi i wanna determine AR model p using PACF

in this plot how can i determine optimal p? it seems not converged

[Umar]

Hi 민재,

Please try to attach data in .txt or .doc format because it helps us answer your questions by troubleshooting code in matlab editor. Also, what function did you use to compute PACF values in order to access convergence criteria since you mentioned above, “it seems not converged” However, please see my response to your comments below.

You mentioned, “determine AR model p using PACF, in this plot how can i determine optimal p?it seems not converged”

First, load your time series data into MATLAB. Replace data.mat with your actual data file. Use the parcorr function, for more information regarding this function, please refer to

https://www.mathworks.com/help/econ/parcorr.html

Here is illustration of this function in the following code snippet, this function will calculate the PACF up to lag 'p' and returns the PACF values, standard errors, and confidence bounds.

% Load your data or time series

load data.mat

% Calculate the PACF

[acf,~,bounds] = parcorr(data, p);

Visualize the PACF using a stem plot. You will see the PACF values are plotted against the lag and the confidence bounds are shown as dashed red lines.

% Plot the PACF stem(1:p, acf(2:end), 'filled') hold on plot([0, p+1], [bounds(1), bounds(1)], 'r--') plot([0, p+1], [bounds(2), bounds(2)], 'r--') hold off xlabel('Lag') ylabel('Partial Autocorrelation') title('Partial Autocorrelation Function (PACF)')

Now, compare the PACF values with the upper confidence bound. If all PACF values are within the bounds, the PACF has converged; otherwise, consider adjusting the model order, I have illustrated in the following code snippet below.

% Check for convergence if all(abs(acf(2:end)) < bounds(2)) disp('The PACF has converged.') else disp('The PACF has not converged. Consider a different model order.') end

Hope this answers your questions.

[Vinayak]

Hi 민재,

Based on Umar's answer, please verify that you are generating the PACF correctly and have a sufficient number of sample points in your data to obtain reliable results.

Incase that results in the same plot, the image shows a significant correlation at the first lag, well outside the confidence bounds.

Given the graph, you can start with a p value of 1 for your AR model. However, it may also be beneficial to explore nearby values, such as up to p = 5. By fitting AR models with these values and comparing their performance, you can make a more informed decision on the optimal p value.

[민재]

thank u guys for answering my question

[Umar]

No problem, 민재,glad to help you out. Please let us know if you have any further questions.