Year on Year growth percentages vs share price returns Say I have 2 time series A and B.
A is a time series of year-on-year growth numbers at quarterly intervals (I don't have the index levels). For example a data point as at 30-Sep-20 of +17.7% represents the year on year growth from 30-Sep-19.
B is a time series of total returns of a stock at quarterly intervals. A data point as at 30-Sep-20 of +10% represents the total return 3 months to 30-Sep-20.
If I wanted to test whether A is a leading indicator of B using a granger causality test or test if there is a relationship between the 2 time series, what would be the best way to make both series comparable?
Does it make sense to turn the time series of year-on-year growth numbers into an index starting from 100? Can think of it as a seasonally adjusted index.
Or should the share price returns also be converted into year-on-year numbers. Ie do time series analysis by converting B into a time series of year-on-year stock returns.
Please see the example below which to visualize it:




Date
A
B
Indexed A
Indexed B




31/03/2020


100
100


30/06/2020
15
5
115
105


30/09/2020
17.7
10
132
115.5



 A: First, note that converting to index doesn't change the inherent information of the series so wouldn't make any difference. In fact, you are just making the series non-stationary, which then again will have to be differenced (or log differenced) for analysis.
Second, whether the series are comparable, is not the right question, I think. You can just think of them as two series that can be compared the way you like.
The problem here is that if for the series A, call it $x_t$, you had QoQ rates, it would have contained more information and would have been better (an interesting thing is that suppose the QoQ rate was available as another series C, it would be a leading indicator of A). Unfortunately, the QoQ information is lost.
Third, converting B to YoY (say the new series is now D) is again losing some information. Yes it might appear now that A is a leading indicator of D, but information gain from A now may be less than the information lost in the process of converting B to D.
Finally, it would be better to just use the current data as it is (though you should appropriately seasonally adjust the series B). This is perhaps the most efficient way of using the available information.
