What to do with missing data in a DCC-GARCH models for 2 assets? Suppose I try to model DCC-GARCH on two assets, let say Apple and Samsung.
I had the daily log return for Apple and Samsung and I merged the data.
2008-08-29 -2.452995e-02 -0.0096434343    
2008-09-01  *****NA***** -0.0195701459   
2008-09-02 -1.989801e-02  0.0215063812

Suppose there was no trade for Apple but there was trade for Samsung on 2008-09-01, when I merge the data into dataframe (I want to fit DCC-GARCH), there was NA in Apple.
Should I replace the NA to the return from yesterday?
Should I replace the NA to zero?
I appreciate your feedback and suggestion, thank you.
 A: NA on a day $t$ is a meaningful value telling you there were no trades on day $t$. It is not the same as there being trades on day $t$ at the same price as on the previous day $t-1$. Nor is it the same as if day $t$ did not happen at all, so there were only days $t-1$ and then immediately $t+1$. No, an NA value on day $t$ signifies that there was a day when no trades took place. 
Replacing the NA value with something else or deleting it altogether will require taking on additional assumptions. For example, if you replace the NA value with the preceding value, you are effectively assuming that the price on day $t$ was the same as the day before. If you just delete the NA value, the time flow gets disrupted as the day $t-1$ is succeeded by day $t+1$, so that if you take lag 1 of day $t+1$ you suddenly get day $t-1$.
When technically possible, I would keep NA as it is. Some methods can treat this as just another parameter to be estimated alongside the parameters you are interested in. Other methods are less well suited for occasional NA values, and for them you must have some number instead, i.e. you have to do data imputation. There are tons of literature on that (see the questions tagged simultaneously with time-series and mising-data here for some inspiration), but the takeaway is to avoid disturbing the time structure in time series models (such as here) and to impute a value that is the most innocuous. Sometimes it can be an average of the adjecent values or perhaps a value given by e.g. a k-nearest neighbours method. 
In financial time series you might have bid and ask prices and derive a likely transaction price from there. Or if you have very similar time series, look at what happened to them on the same day and assume the same could have happened for your series (this is in the spirit of the k-nearest neighbours method).
In summary, keep the NA if you technically can. If not, use your best judgement as to what could have happened if anything were to happen, and set the value accordingly.
