How is the matrix $\mathbf R_x$ not Toeplitz in case of a signal missing one term?
For $\boldsymbol{R}_x$ to be toeplitz it should be:

$$\boldsymbol{R}_x = \begin{bmatrix}r_{x}(0) &amp; r_{x}(2) &amp; r_{x}(3) \\ r_{x}(2) &amp; r_{x}(0) &amp; r_{x}(2) \\
r_{x}(3) &amp; r_{x}(2) &amp; r_{x}(0) \end{bmatrix} $$

Since it is not, it is not a toeplitz matrix.