eoftheautocovaria
ces
withoutk
owi
gthedisturba
cevaria
ce
10Whichofthefollowi
gstateme
tsaretrueiA
MAqca
beexpressedasa
ARi
fi
ityifitisi
vertibleiiA
ARpca
bewritte
asa
MAi
fi
ityifitisstatio
aryiiiTheu
co
ditio
almea
ofa
ARMAprocesswilldepe
do
lyo
thei
tercepta
do
theARcoefficie
tsa
d
oto
theMAcoefficie
tsivAra
domwalkserieswillhavezeropacfexceptatlag1
aiia
divo
lybia
diiio
ly
fciiia
diiio
lydiiiiiia
div
11Co
siderthefollowi
gpicturea
dsuggestthemodelfromthefollowi
glistthatbestcharacterisestheprocess
acfa
dpacf
09
08acf
07
pacf
06
05
04
03
02
01
0
1
2
3
4
5
6
7
8
9
10
01
Lags
aA
AR1bA
AR2cA
ARMA11dA
MA3
Theacfisclearlydecli
i
gveryslowlyi
thiscasewhichisco
siste
twiththeirbei
ga
autoregressiveparttotheappropriatemodelThepacfisclearlysig
ifica
tforlagso
ea
dtwobutthequestio
isdoesitthembecomei
sig
ifica
tforlags2a
d4i
dicati
ga
AR2processordoesitremai
sig
ifica
twhichwouldbemoreco
siste
twithamixedARMAprocessWellgive
thehugesize
fofthesamplethatgaverisetothisacfa
dpacfeve
apacfvalueofwouldstillbestatisticallysig
ifica
tThusa
ARMAprocessisthemostlikelyca
didatealthough
otethatitwould
otbepossibletotellfromtheacfa
dpacfwhichmodelfromtheARMAfamilywasmoreappropriateTheDGPforthedatathatge
eratedthisplotwasy_ty_t1u_t1u_t
12Whichofthefollowi
gmodelsca
beestimatedusi
gordi
aryleastsquaresiA
AR1iiA
ARMA20iiiA
MA1ivA
ARMA11
aio
lybia
diio
lyciiia
diiio
lydiiiiiia
div
13Ifaseriesyisdescribedas“mea
reverti
g”whichmodelfromthefollowi
glistislikelytoproducethebestlo
gtermforecastsforthatseriesyaAra
domwalkbThelo
gtermmea
oftheseriescAmodelfromtheARMAfamilydAra
domwalkwithdrift
f14Co
siderthefollowi
gAR2modelWhatistheoptimal2stepaheadforecastforyifalli
formatio
availableisuptoa
di
cludi
gtimetifthevaluesofyattimett1a
dt2area
drespectivelya
dthevalueofuattimet1is
ytut
abcd
15WhatistheoptimalthreestepaheadforecastfromtheAR2modelgive
i
questio
14abcd
16Supposeyouhadtoguessatthemostlikelyvalueofao
ehu
dredstepaheadforecastfortheAR2modelgive
i
questio
14whatwouldyourforecastbeabcd
ffr