Interpolation in time series for gaps in time series

I have a time series that contains daily data with gaps. I need to fill the gaps with some values. I am attaching the figure of the time series as well as the data associated with it. The interpolation should be such that the values retain the overall shape of the curve.

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2016.5832 -0.263604

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2016.5996 -0.243126

2016.6023 -0.25129

2016.6051 -0.249604

2016.6078 -0.23739

2016.6105 -0.247194

2016.6133 -0.238546

2016.616 -0.245879

2016.6188 -0.251745

2016.6215 -0.244146

2016.6242 -0.243846

2016.627 -0.241877

2016.6297 -0.237797

2016.6324 -0.248902

2016.6352 -0.256025

2016.6379 -0.251198

2016.6407 -0.249747

2016.6434 -0.239595

2016.6461 -0.236323

2016.6489 -0.262833

2016.6516 -0.250725

2016.6543 -0.257749

2016.6571 -0.263473

Answer 1

[Benjamin Thompson]

There is the fillgaps function in the Signal Processing Toolbox for more intelligent filling. You may need to preprocess your data for that to work. There is the ismissing and fillmissing functions for general data preprocessing, see the help article "Preprocessing Data" for a description of these and related functions.