Autocorrelation plots for stationary time series

Hello,

Please, i have stationnarized times series (removing trends and seasonality using differencing) in order to find most significant lagged values for forecasting model.

Questions about PACF and ACF plots:

The PACF and ACF are for stationary time series or i need to more stationnarize data ?

Thank you.

Answer 1

[Aman]

Hi Hamza,

From the information you shared, I think you are having doubts regarding the usage of PACF and ACF for stationary data.

The ACF and PACF are suitable for stationarized data; if the data is not stationarized, then the output of the ACF and PACF may be misleading. If you've already removed trends and seasonality and the series appears stationary, additional stationarization may not be necessary. You can check stationarization of the data using the Augmented Dickey-Fuller (ADF) test. You can refer to the below code snippet for reference.

% Assuming 'data' is your differenced time series
[h, pValue] = adftest(data);
if h == 0
    disp('The series is not stationary. Consider further differencing.');
else
    disp('The series is stationary.');
end

figure;
autocorr(data);
title('Autocorrelation Function (ACF)');

figure;
parcorr(data);
title('Partial Autocorrelation Function (PACF)');

I hope it helps you to proceed ahead with your workflow.