Filtering of non-stationary time series

Think about an overdetermined and underdetermined problem:

$$\begin{eqnarray} d &=& B m \nonumber \\ Rank(B) &<=& dim(d) =235 \nonumber \\ B'd &=& B'B m \nonumber \\ Rank(B'B) &=& Rank(B)<= 235 \nonumber \end{eqnarray}$$

B'B is underdetermined since

dim(B'B) = 250x250 but Rank(B'B) <= 235

We should probably use BB' instead! Try it out!

d = M b Rank(M) <= dim(b)=16

very few unknowns b many equations

M'd = M'M b Rank(M'M) = Rank(M) <= 16

M'M is overdetermined?