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I have fit the wave data as below using Least Square optimization and used Root Mean square to calculate upper and lower bounds. I wanted to know is there any other alternative exists which gives a higher value for the upper bound and a lower value for the lower bound.

In the below picture, I want upper bound to be above 0.9 or 1 and lower bound to be below 0.2 or 0.3

enter image description here

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I tried fitting your data to the equation in the link, as well as several other sine functions, with what I consider to be poor results. Upon investigation, it appears that the data has more than one sine wave, see the rather crudely annotated scatterplot below showing different widths between two minimum points - with a single sine wave, these should be equal widths.

scatterplot

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