You may check out this recent article which reviews methods for interpolations within time series, which will solve your problem.

Lepot M, Jean-Baptiste Aubin and François H.L.R. Clemens. (2017). Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment, Water, 9, 796; doi:10.3390/w9100796.

How to get data that wasn't taken is VERY difficult. I would start with the references that Safa provides. Best, David Booth

HI Belete!

Imputation is also a good method for handling missing values. You can also check the link below for a comparison of various methods for dealing with missing values:

https://www.omicsonline.org/open-access/a-comparison-of-six-methods-for-missing-data-imputation-2155-6180-1000224.php?aid=54590

Best of luck

• If you use Extreme stream flow data you can you Median for missing points. Replace median with missing point .
• If the data is not extreme than you can replace mean .

Represent the data by a suitable mathematical curve and apply the curve in filling the missing data.

I can suggest the following two methods:

(1) Apply the fundamental theorem of calculus of finite difference in finding out the missing data.

(2) Apply Lagrange's interpolation formula or Newton's divided difference interpolation formula in finding out the missing data.