Wie 
18. 
19. 
20. 
differential equation can be expressed by the coefficient of difference equation 
and visa versa. The second order autoregressive continuous process A(2) is then 
the basic process, as the response of a linear vibration system to the white noise 
with one degree of freedom. Conversely, when a dynamic process with one 
degree of freedom is excited by white noise, the digitized response can be ex- 
pressed by an ARMA(2.1) model. When the input is colored and not white, we 
can invert this system to a pure random process (white noise as mentioned in item 
14) although the order increases. Thus the ARMA model is the most general pro- 
cess for expressing the oscillatory response of a linear system. 
An advantage of the parametric analysis is that, by fitting a certain discrete model 
to the response process, theoretically we can estimate the characteristics of the 
differential equation that governs the response of a continuous process by invert- 
ing the difference equation that expresses the discrete model into the equivalent 
differential equation that formulates the continuous process. 
The confidence limit of each parameter of a fitted discrete model can be eva- 
luated. The remaining statistical considerations are taken care of by adopting the 
most adequate order of the model based on Akaike’s information criteria. How- 
ever, if we could express the overall reliability by some simple expression, say, 
for example by a confidence band at some level of probability, it would be easier 
to give us more confidence in the parametric method, directly comparing with the 
result by the nonparametric method: 
The AR model was adopted here first and was applied to the seakeeping data of 
ships and offshore structures, both for models in the tank and for the actual ships 
and structures at sea. From the results, we found this model fitting technique was 
practical to apply and was a promising method of analysis, sometimes giving us 
better results than the conventional nonparametric method. At least this model 
fitting or parametric analysis technique supplements the nonparametric method. 
The ARMA model is the most general and is directly connected with the continu- 
ous AR model or its formulating differential equations that govern the behavior 
of the system. It seems to be the most desirable for estimating the physical char- 
acteristics of the process, although its handling in the estimation of parameters is 
more complicated than for a pure AR model. Accumulation of experience with 
this application is now very much needed, this author believes. 
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