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I have daily return data of 11 sectors of MSCI World Index and the MSCI ACWI index. I want to know the stationarity of correlations between the sectors and MSCI ACWI index.

This is what I have done:

1) aggregate the daily returns into month and calculate correlation between each of the sectors and the MSCI ACWI index (so for each monthly correlation, around 20 daily returns were used). Then I used the Augmented Dickey-Fuller test to see if the monthly correlation time series is stationary or not.

2) aggregate the daily returns into week and calculate correlation between each of the sectors and the MSCI ACWI index (so for each weekly correlation, around 5 daily returns were used). Then I used the Augmented Dickey-Fuller test to see if the weekly correlation time series is stationary or not.

The result is reproduced here: enter image description here

As you can see, the stationary result is different for monthly and weekly correlations.

My question is:

1) which model is a better one?

2) what other kinds of tests or useful stuff can I do with this stationary test?

Thank you in advance!

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