If I want to calculate the Covariance between two stocks but there are missing days in both, how can I deal with missing data? I want to use Pairwise deletion and only use the days of which both observations are seen. I have been reading up on pairwise deletion and I have seen that the data must be missing at random. If the missing days where every Monday for example, would this be missing a random?
If the days are missing is a systematic way but you have reason to believe that the mechanism for missingness would not affect your inferences... then yes, your data are MAR and you can proceed. However, that belief tha the missingness mechanism is immaterial is often tough to defend: even a relation to liquidity would undermine a claim of MAR.
Regarding your example about Mondays... The Monday Effect is the purported effect that stocks which declined Friday are more likely to rise on Monday. The effect is often attributed to short sellers not risking being short over a weekend since more news comes out on weekends and good news would cause losses. If you (or your critics) believe there is a Monday Effect, then data missing on Mondays would not be MAR.