algorithms for parameter estimation differentiate between 
these models. Published literature offers a great variety 
of algorithms, some of them published a long time ago, 
without referring to modern computational methods. For a 
suitable selection of algorithms the following demands may 
be set up: 
- high precision of the estimated parameters 
- no influence of the locations of the poles 
- no necessity for using the autocorrelation function 
- numerical advantages (stability, fast convergence, 
independence of approximative values) 
- lesser computational efforts. 
The autor has investigated the precision of estimated 
parameters and the influence of the location of poles by 
using generated processes of varying length and different 
poles. The findings are briefly reviewed. 
4.1 AR Model 
The algorithm published by Ulrych and Clayton /16/ esti- 
mates the parameters of the AR model more precisely than 
the other considered algorithms (Yule /17/,  Levinson /11/, 
Burg /5/), independent of the location of the poles. The 
method of Ulrych/Clayton estimates the parameters by mini- 
mizing the sum of the squared forward and backward predic- 
tion errors with respect to all parameters a, (j = 1,..,P) 
N 
S(a) = X (e, 2 (k) * e, 2(k) 
k=p+1 
The forward and backward prediction errors (e, and e,) are: 
ge (t) = xy + z a; x(t-j) 
j25! 
x a,rx(t-ptj) 
j=1 J 
e,(t) = x(t-p) + 
Statistical tests showed that the estimated parameters are 
significant if they are estimated from processes with a 
length of 20 or more sample values. 
4.2 ARMA Model 
The algorithms for estimating the ARMA parameters can be 
subdivided in three groups. 
1) Joint estimation of the parameters a and b; by 
iterative solution of the non-linear condition 
T e?(t) = minimum 
(Fuller /8/, Box and Jenkins /4/). 
2) Solving the extended Yule-Walker equations which imply 
the autocorrelation function (Akaike /2/, Kay and 
Marple /10/ ). 
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