CONTENTS (Continued) 
Page 
5.3' ‘Generalt ARMA (nim))Process: ics Sissies lets los seas Sta ies ati cts ronan 181 
53.1 General ARMA(n,m) Process, Its Stationality and Invertibility ......... 181 
Sese2 (GreenisshunctionjomARMA (nim) aero ora ee eee 182 
53.3 Autocovariance and Spectrum Function of ARMA(n,m) ............+.- 183 
5.3.4 Estimation of a, ...@n,b,...bn of ARMA(n,m) .. 0... cece eee 184 
5.3.5 Adoption of ARMA(n,n—1), ARMA(2n, 2n-I) 0... ce 185 
5.4 General Autoregressive Process AR(D) ......... 0. cece eee cece tence 186 
Saul Adoption OAR (in) MOdel nee a eee ee Laer OCS KT oer: 186 
4 Zu GheenisvHUNCTLONIOPAR() Hen eee ere 186 
5.4.3 Autocorrelation and Spectrum Function for AR(n) ..............500- 187 
5.4.4 Estimation of Parameter a, ...Gn GN Wo... cece ce cee ee eee 189 
5:4 Su Esiimationof Ga foWAR (ek eee ee eee Eee 193 
5.5 Determination of the Order of the Fitted Model .....................-4. 193 
DJ eResiduah Enron Method va wari aoe oe a OS ccs eek 193 
55.2 Partial Autocorrelation Method ............cc cc cc ec nc ceccecesees 194 
55.3 Visual Inspection of the Autocorrelation .......0 cc cece nce cence 195 
Sv Akaike: Hee AlG\ and BIG Criteria anne 196 
55.5 Examples of Order Determination through MAIC ..........0.000000 198 
Chapter 6 Model Fitting to the Response of the Linear Dynamic 
System to Irregular Input, 2 o...06.< cs sc eesyers.cictet senystueie > © BS andere 201 
OL AntroductiOne ass s cae ia tree are suelo heirs Ne ar eke Pane oe 201 
62 Response’ Systemiwithtkeedback <n.) cio ace 201 
62-1 Onelinput One Output System ia eo Ore 201 
6.2.2 General Two-Dimensional, P—Dimensional Case ..........0.000000 206 
6:3) Autoregressive Continuous/Process fee nore one eee ee ene 209 
6.3.1 The First Order Continuous Autoregressive Process A(1) ............: 209 
6.3.2 Correspondence of A(2) to ARMA(2.1) 01.0.0 ce cece cece cc cc cc ecucs 213 
Chapter 7 Examples of Model Fitting Technique Applied to the 
Analysis of Seakeeping Data .................0 ccc ccc ec ec eeee 227 
7.1 Examples of AR(n) Model Fitting for the Prediction of 
Seakeepin gData eyii hide ee owas wie ee aero ee ee eee 227 
| 7.2 Examples of Model Fitting Technique Applied to the Seakeeping Data ..... 228 
| 7.3 Examples of Parametric Analysis of Response Characters of 
MarineVehiclesrand/Structures) see eo oe ee nee 232 
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