If I have the similer situation, I will use SATA software and generate missing values by giving "ipolate" command. Simply this command will make average values. You can watch following vedio for further understanding.

https://m.youtube.com/watch?v=RTB2Pe65KpQ

Sure there is... Another thing is if it is a good way or not. To start you can linearly interpolate between known values but probably this is not going to be good. Another option is to observe the volatility pattern between days (pretty much to look at the change between days or return) and then fit a distribution to that. From there, you can create values using T_t = T_{t-1}+\sigma N(0,1). Here I'm implicitly assuming that within a week there is no noticeable trend and also that the volatility can be characterised. The result will be a set of values that behave like the underlying process. Still have some doubts regarding how to glue the last simulated value to the next measured value... But I'm quite sure that there is probably something out there written in R

You can use Kriging to interpolate the gaps. Kriging is indeed a Gaussian Process, therefore any form of GP can be used.

There are a few time series methods that can simultaneously build an ARIMA model for the time series and replace "optimally" the missing data. I have references to some papers in a poster I put on ResearchGate: "Modelling high-frequency time series: a survey".

You can search for TRAMO-SEATS software to deal with missing data.

Gómez and Maravall's TRAMO-SEATS in indeed in my list of references but, unfortunately, TRAMO-SEATS does not work on daily time series, only on monthly and quarterly time series.

you can fill your gap by(missing data) interpolate in tersset software

Parisa, can you be more explicit. What is tersset? Are you sure it is takes care of the fact that time series data do not come from independent observations? Thank you.

TheTerrset software has one part (ETM)Earth Trend Modeler .Which is in this module is associated with a series of times, such as filling the gaps, pre-whitening , Deseason and series trend analysis (R-R2-OLS-Mann-kendal)