I have 5 non-stationary multivariate time series' and I need to compare the "strength" of long range dependence among them. I have found many papers on long range dependence estimation (parametric, semi parametric, Whittle, etc.), but as my background is not in this field, which makes it a little difficult to understand the math, I still could not find a way to determine which time series has the fastest/slowest decay of some statistic compared to other time series. Although I have to implement a computer program for this analysis, I need some theoretical base. So, please help me find an approach to this problem, if there exists one.
EDIT: More information regarding the time series.
The multivariate time series consists of 8 vehicle signals, like velocity, acceleration, etc., recorded every 10 millisecond. There are approx. 2500 data points in each time series, which represent an instance of car journey. I have to grade 5 different journeys on the basis of long range dependency and carry out further analysis. Hope this helps. As I am using proprietor data, I cannot provide any plots or data samples. One can imagine the signal values to be in a usual range as a result of normal driving on a road.