pr.probability - Computing correlation between time series with missing data.

You are right. An idependent filtering of the two signals will introduce errors because it is not contrained to fix the correlation to p. One possible approach is to perform a unified maximum likelihood estimation of both the missing samples and the correlation p. This can be done as follows: Assuming that the processes m_n and e_n have the same variance, hence we may write:

m_n = p * e_n + q * f_n, p^2 + q^2 = 1,

where f_n is a normal white noise uncorrelated to e_n and has the same variance as e_n.

The log likelihood function is proportional to:

sum_n((x_n - sum_i=1 to n(e_n))^2) + sum_n((y_n - sum_i=1 to n(p * e_n + q * f_n))^2) + lambda (p^2 + q^2 -1)

where lambda is a Lagrange multiplier, and the outer sums are of course over the known samples only.