I asked this question on stats SE but did not find a suitable answer so far. Maybe someone can help.
Given n random variables x1,...,xn (one-dimensional). The following is known (corr() = Pearson correlation):
corr(x1,x2) = a corr(x2,x3) = a
The actual values of the random variables and their covariances are unkown though. Only some of their correlations are known.
From this, is it possible to calculate
corr(x3,x1) = ?
or give an estimate of the lowest possible correlation coefficient
corr(x3,x1) > a
Given set of correlations
corr(x_i, x_i+1) with i=[1..c], c<n
is it possible to either directly calculate
or give a lower bound a of the coefficient with
corr(x_1, x_c+1) > a