Time series analysis under stationary assumption 
is well established. However it is not sufficient 
for stationary time series models to describe the 
real world. 
A class of locally stationary processes was introduced 
by Dahlhaus. 
By using nonstationary models with time varying spectra, 
we attempt to analyze some data 
from mining explosions, natural earthquakes and financial 
time series. Although many researchers used the ordinary 
autoregressive or autoregressive moving average models, 
we fit a time varying autoregressive (TVAR) model of 
order $p$ to the data whose coefficients are polynomials 
with respect to time. Moreover we select a favorable 
model by use of AIC, and compare the results with the 
others. Finally, some numerical problems of discriminant 
and cluster analysis will be discussed.