'--------------------------------------WOLD'S DECOMPOSITION --------------------------------'
'-----FIRST: generate the data for the example using the nonlinear process
'		y(t)= u(t) + 0.2 u(t-1) + 0.8u(t-1)*u(t-2)

create u 1000
series u=nrnd
series y=u+0.2*u(-1)+0.8*u(-1)*u(-2)

'------ we now do the best possible regression for the data, namely the one
'         of   y   on   u(-1)  and u(-1)*u(-2)    (which corresponds to knowing the dgp)
'	    
equation best.ls y u(-1) u(-1)*u(-2)

'------SECOND: we compute the wold's decomposition for the process y (as if we
'	   didn't know the dgp) in two steps:
'        STEP 1: Estimate an AR(10) for Y 
'
equation ary.ls y c y(-1 to -40)
'
'	    STEP 2: Regress Y on 10 lags of the residuals V of this last regression
'                        
series v=resid
equation wold.ls y c v(-1 to -30)
'
' Finally, we create a table showing the VARIANCES OF THE RESIDUALS for each method
'
table(2,3) variances
variances(1,1)="Knowing the DGP"
variances(1,2)="Estimating with an AR"
variances(1,3)="Wold's Decomposition"
variances(2,1)=best.@ssr/best.@regobs
variances(2,2)=ary.@ssr/ary.@regobs
variances(2,3)=wold.@ssr/wold.@regobs
variances.title Variances of the Residuals
variances.setformat(2) f.3
variances.setlines(a1:c2) +a
variances.setwidth(@all)  20
variances.table