In order to give an idea of the estimated ARMA parameters 
and their variations within the regions, table 3 lists all 
estimated process parameters. The parameters of a region 
show a similar behaviour although the most profiles have 
different directions in the terrain. Hence the mean values 
of the parameters within a region are also given. 
The standard deviations of the prediction errors and the 
process parameters may be considered to be typical for a 
region. However, the dependence on the sampling interval - 
Ackermann /1/ assumes a linear dependence - must be 
regarded. The relationship between the properties of ARIMA 
processes and the sampling intervals remains a subject of 
further investigations. 
As a selection the first profiles of the regions Bohuslaen, 
Uppland, Disko Island and Drivdalen are  ploted in the 
figures 1-4. The prediction errors are ploted too below the 
profiles refered. The different scales of the plots should 
be noticed. 
7 Remarks 
7.1 Breaklines 
Different types of terrain require different processes. A 
particular ARIMA process is only capable of modelling a 
homogeneous terrain without breaklines. 
On the other hand ARIMA processes are suitable for detec- 
ting breaklines: suddenly arising great prediction errors 
may indicate them. An example is given by a profile from 
Drivdalen in figure 4. 
For our investigations the measured terrain profiles were 
separated according to the breaklines. Hence the profiles 
examined in chapter 6 are from homogeneous terrain. 
7.2 Observation Errors 
The observation of the time series x(t) represented by an 
ARMA process is usually contaminated with an observation 
error n(t). It can be reasonably assumed that these errors 
are additive white Gaussian noise with 
n(t) = N (0, v 25., 
Therefore only the observed process y(t) is available 
y(C) * x(t) 4 n(t). 
In order to cope with the problem of observational noise, 
two methods became known to the author. 
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