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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

The dataset can be found here.

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    $\begingroup$ Would it be helpful if the fitted curve more closely matched the data? $\endgroup$
    – James Phillips
    Commented Mar 28, 2019 at 23:49
  • $\begingroup$ yes it will help $\endgroup$
    – Rudresha Parameshappa
    Commented Mar 29, 2019 at 15:03
  • $\begingroup$ The data is not accessible anymore $\endgroup$
    – Firebug
    Commented Jul 13, 2023 at 12:43
  • $\begingroup$ Other than that, it looks like quasi-periodic behavior, with varying amplitude and frequency (a la chirplets). Youc an probably model it with spline terms and a sinusoidal function $\endgroup$
    – Firebug
    Commented Jul 13, 2023 at 12:44

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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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