I would like to do an analysis on the AEX stock exchange index for the last 20 years, but I ran into some issues. It would be really appreciated if you can answer my questions:

1. In order to apply tecniques like the fractal dimension, R/S analysis, the Hurst exponent, V-analysis, which would be the series taken into consideration? (the original price series or the log-return series)? I read a lot of articles on this subject and there is not a consistent approach (most of them I saw that ar applied on the log-return series, but,in my case, when I tried, for instance, to calculate the fractal dimension in R on both the original and the log-returns series, in the first case the results were as expected, whereas for the log-returns the values were above 2- which is absurd for a financial series)
2. For the analysis shall I take into consideration the entire series at once or split it into periods (before crisis, during crisis and after crisis)? Moreover, shall I use moving windows for the analysis? Are the functions in R consistent enough?
3. Which are the best methods to determine the H exponent?
4. For predicting the time series on short term using the chaos theory, what method shall I apply and on which series? I heard that the MSM – Markov-switcing multifractal method is a good alternative of the ARCH family models. Is it true? (it is calculated based on the return series).
5. Are there any other methods from the chaos theory that can help me predict the evolution of the AEX index? What analysis based on local memory, short memory and long memory can I make? Thank you in advance!

I would like to do an analysis on the AEX stock exchange index for the last 20 years, but I ran into some issues. It would be really appreciated if you can answer my questions:

1. In order to apply tecniques like the fractal dimension, R/S analysis, the Hurst exponent, V-analysis, which would be the series taken into consideration? (the original price series or the log-return series)? I read a lot of articles on this subject and there is not a consistent approach (most of them I saw that ar applied on the log-return series, but,in my case, when I tried, for instance, to calculate the fractal dimension in R on both the original and the log-returns series, in the first case the results were as expected, whereas for the log-returns the values were above 2- which is absurd for a financial series)
2. For the analysis shall I take into consideration the entire series at once or split it into periods (before crisis, during crisis and after crisis)? Moreover, shall I use moving windows for the analysis? Are the functions in R consistent enough?
3. Which are the best methods to determine the H exponent?
4. For predicting the time series on short term using the chaos theory, what method shall I apply and on which series? I heard that the MSM – Markov-switcing multifractal method is a good alternative of the ARCH family models. Is it true? (it is calculated based on the return series).
5. Are there any other methods from the chaos theory that can help me predict the evolution of the AEX index? What analysis based on local memory, short memory and long memory can I make? Thank you in advance!