▁additional ▁assumption ▁is ▁im posed ▁— ▁that ▁all ▁observations ▁are ▁independent ▁and ▁ident ically ▁distributed . ▁This ▁means ▁that ▁all ▁observations ▁are ▁taken ▁from ▁a ▁random ▁sample ▁which ▁makes ▁all ▁the ▁assumptions ▁listed ▁earlier ▁simpler ▁and ▁easier ▁to ▁interpret . ▁Also ▁this ▁framework ▁allows ▁one ▁to ▁state ▁asympt otic ▁results ▁( as ▁the ▁sample ▁size ▁), ▁which ▁are ▁understood ▁as ▁a ▁theoretical ▁possibility ▁of ▁fetch ing ▁new ▁independent ▁observations ▁from ▁the ▁data ▁generating ▁process . ▁The ▁list ▁of ▁assumptions ▁in ▁this ▁case ▁is : ▁ ▁i id ▁observations : ▁( xi , ▁y i ) ▁is ▁independent ▁from , ▁and ▁has ▁the ▁same ▁distribution ▁as , ▁( x j , ▁y j ) ▁for ▁all ▁; ▁ ▁no ▁perfect ▁mult icol linear ity : ▁ ▁is ▁a ▁positive - defin ite ▁matrix ; ▁ ▁ex ogene ity : ▁▁ ▁hom os ced astic ity : ▁. ▁▁ ▁Time ▁series ▁model ▁▁ ▁The ▁st ochastic ▁process ▁{ xi , ▁y i } ▁is ▁station ary ▁and ▁er god ic ; ▁if ▁{ xi , ▁y i } ▁is ▁non station ary , ▁O LS ▁results ▁are ▁often ▁sp ur ious ▁unless ▁{ xi , ▁y i } ▁is ▁co - integr ating . ▁ ▁The ▁re gress ors ▁are ▁pred et erm ined : ▁E [ xi ε i ] ▁= ▁ 0 ▁for ▁all ▁i ▁= ▁ 1 , ▁... , ▁n ; ▁ ▁The ▁p × p ▁matrix ▁ ▁is ▁of ▁full ▁rank , ▁and ▁hence ▁positive - defin ite ; ▁