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I'm trying to replicate part of the empirical analysis of the following paper: https://www.tandfonline.com/doi/full/10.1080/23322039.2020.1719574#aHR0cHM6Ly93d3cudGFuZGZvbmxpbmUuY29tL2RvaS9wZGYvMTAuMTA4MC8yMzMyMjAzOS4yMDIwLjE3MTk1NzQ/bmVlZEFjY2Vzcz10cnVlQEBAMA==

I'm facing some difficulties in understanding exactly how the authors apply the portmanteau test with automatic, data-driven lag selection based on the Pierce-Box test and its refinements (which include the Ljung-Box test). I'm implementing the test by using the R package vrtest (function Auto.Q). Once filled up with the returns' time series vector, the function gives me one single value for the relevant statistics and the associated p value, but the authors of the paper are instead able to report how such statistics evolve during the time frame covered by the time series. What I don't understand is how they can get one value per each date (figures 4, 7, 10, and 13), and how come I'm not getting the same.

Are they maybe implicitly using some kind of rolling/recursive window technique!?

Thanks in advance for your help

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