The extension of classical discriminant analysis techniques in multivariate 
analysis to time series data is a problem of practical interest. Discrimination
between different classes of multivariate locally stationary processes, which 
constitute a class of non-stationary processes, can be characterized by 
differing covariance or time varying spectral structures. For discrimination 
between the multivariate non-Gaussian locally stationary processes, 
Kullback-Leibler discrimination information measure has been developed. 
In this paper, asymptotic error rates and limiting distributions are given for 
a generalized time varying spectral disparity measure that includes foregoing 
criteria as special case. It is well known that the log-likelihood ratio based 
on observed stretch gives optimal classification. It is shown that the 
discriminant criterion based on such generalized disparity measure is Gaussian 
optimal. A non-Gaussian optimal discriminant criterion is also proposed in 
view of the LAN theorem.