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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?

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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.

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    $\begingroup$ The stambuagh reference at the end of this paper used to be the seminal paper on how to deal with your problem. But this paper is more recent so could be an improvement to Stambaugh ? I didn't read it. arxiv.org/pdf/0710.5837.pdf $\endgroup$
    – mark leeds
    Commented Aug 19, 2020 at 2:13
  • $\begingroup$ Nice paper by Bobby; great work as usual from him. Not sure that applies here though since this isn't monotone missingness. The Stambaugh method could work if we have an MAR situation. Would help if we knew more about the missingness mechanism. $\endgroup$
    – kurtosis
    Commented Aug 19, 2020 at 2:24
  • $\begingroup$ No idea if it applies to his case. I just remember Stambaugh being seminal so I googled for it and that one came up instead. Since Stambaugh is a reference in it, he can still google and find that one. Maybe one of them applies ? $\endgroup$
    – mark leeds
    Commented Aug 19, 2020 at 12:54

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