8-4 Non-linear models: a Definition Campbell, Lo and macKinlay(1997)define a non-linear data generating process as one that can be written y=f(up1,u12,…) where u, is an iid error term and f is a non-linear function. They also give a slightly more specific definition as y1=g(u1,u12,…)+uJ2(u1,u12,…) where g is a function of past error terms only and ol is variance term Models with nonlinear g( are"non-linear in mean", while those with nonlinear o() are"non-linear in variance Models can be linear in mean and variance(Clrm,arma) or linear in mean but non-linear in variance(GarCh)8-4 Non-linear Models: A Definition • Campbell, Lo and MacKinlay (1997) define a non-linear data generating process as one that can be written yt = f(ut , ut-1 , ut-2 , …) where ut is an iid error term and f is a non-linear function. • They also give a slightly more specific definition as yt = g(ut-1 , ut-2 , …)+ ut 2 (ut-1 , ut-2 , …) where g is a function of past error terms only and  2 is a variance term. • Models with nonlinear g(•) are “non-linear in mean”, while those with nonlinear  2 (•) are “non-linear in variance”. • Models can be linear in mean and variance(CLRM,ARMA), or linear in mean but non-linear in variance(GARCH)