I believe there are two ways to measure Confidence Intervals of Autocorrelation one assumption is assuming the Autocorrelation is following Gaussian Distribution and assuming Lags other than Lag 0 are Equal to 0 and Bartlett’s formula which assumes Moving Average Process.
I want to measure the extent of the Autocorrelation of 10 Year Rolling Returns of Sensex. I have 404 10 Year Rolling Returns which I calculated from April 1979-Nov 2022 and I want to know what is the number of Independent Samples I am having of 10 Year Returns. The simple answer is 4 but that is assuming a very strong Autocorrelation and considering the Start Date Sensitivity of Financial Returns Data I wanted to check how the strong the Autocorrelation is.
I used the ACF function in R to see at what Lag the Autocorrelation is not significant from 0 but I am seeing different results depending on what formula I am using for calculating the ACF Confidence Intervals. If I use the first assumption, then at Lag 46 there is no Autocorrelation (meaning 10 Year Return which was calculated 46 Months Ago does not influence 10 Year Return which was calculated Today) but Bartlett's Formula is showing there is no Autocorrelation at Lag 26.
I believe the later is correct because the former assumes there is no Autocorrelation for all Lags other than Lag 0 which is incorrect in this case due to the 10 Year Rolling Returns being constructed using overlapping Monthly Periods (i.e. First 10 Year Return is calculated From Jan 1979-Jan 1989,Second From Feb 1979-Feb 1989, Third From March 1979-March 1989,etc) so the Autocorrelation of First 10 Lags will definitely not be Equal to 0 but I am not sure on this hence the question.
Thanks and Regards,