There are two series , Sa and Sb. Sa ranges always within 0-1 . Sb ranges variably sometimes from 130-145, 2017-2077 and many more etc..
The data points are real time in nature. For each second there is a new data point received such that slopes are in-equal in nature. For example for the 12th(index-11) data point received Sa[11]-Sa[10] != Sb[11]-Sb[10] .
For each data point received, how do I convert the value of Sa into the range of Sb with no information loss?
Note- I have tried using normalisation- converting the values of both the series to [0,1] . The series Sb had higher highs and normalising the series value in each incoming instance distorted the information and trends contained in Sb.
Any help is appreciated.
Not sure how useful it is, but you might try something that transforms the $(-\infty,\infty)$ or the $[0,\infty)$ intervals into something finite, like $\arctan$ function. So for example, if your values are all positive $\frac{2}{\pi}\arctan{\rm S_b}$ is always in $(0,1)$ interval. It is not a linear transformation, but it preserves the trends (it is monotonic function).