Let $\{X_t\}$ be a stationary process with zero 
mean and true spectral density $g(\lambda)$. We 
assume that all the values $\{X_t\}$ are known, 
except for the value $X_0$. It is important to 
interpolate missing value $X_0$ by linear combination 
of $\{X_t : t \neq 0\}$. In this paper, we consider 
the misspecified interpolation problems for $\{X_t\}$ 
under the condition that the true structure $g(\lambda)$ 
is not completely specified. Next we shall discuss 
the interpolation problems for square-transformed process, 
$Y_t=X_t^2$ and Hermite-transformed process, $Y_t=H_q(X_t)$. 
Moreover, we compare the mean square interpolation error 
for the respective results. Also, we numerically plot 
interpolators for missing values, and illuminiate unexpected 
effects from the misspecification of spectra. Finally, 
as an example, we conclude the paper with applications 
to real data.