'S SPEAKINGNOTES · 2021. 2. 9. · d) It: Ex, Et , 02) You tell Findthe ACVS 8h 41 = 0,1 Me. ← 7...
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EC 402 (20/21) - LTWK 3 - HELP WK3 RACNIR 'S SPEAKING NOTES ( UNOFFICIAL )
Transcript of 'S SPEAKINGNOTES · 2021. 2. 9. · d) It: Ex, Et , 02) You tell Findthe ACVS 8h 41 = 0,1 Me. ← 7...
EC402 (20/21) - LTWK 3 - HELP WK3
RACNIR'S SPEAKINGNOTES (UNOFFICIAL)
ACVS of a stationary time series XtIft ,teh) : = Cov (Xt ,Xtih) ,
1hI = 0,1 , . - -but due to stationcity , we know
✓ ft,
Eth) = 810,
h) = Th .
ACF of a stationary time series Xt
µ :-. f(t ,tthYf8t¥= 8h / No -
(Note : these are infinite ,two-sided
,symmetric)D
d) It : Ex , Etwww.lo ,02) . , }
You tell
Find the ACVS 8h ,41 = 0,1 , . . .
Me.
← 7 yt= Yt . , + Et , Etww -N 10,5) . Ill .Find the ACVS
.
Method ' :
y, set - jNo tricks
⇒yqy.z.IE?o4JolkEfEtjsx-kI--.fI4iso=o/4-4'I= To .
For h > 0,Efytyt.in/=Efytf4yEEEIo4kstth-kI/--4hf
.
= 8h .
For ha 0,8,= 10hTo = 8- h .
It follows thatfin :-. of" 02/4-4' ) , h= -9 . . ,9 . .
. ,N .
=
D
Method 2 : Recognise .
. to = Off , to
YulefWalker 8*08141 ,h >0
f. = 01%+5 ,or go -
. EY4-0IY ,and
for h > 0 , 8h= 4 pm , = 42th -z= . . .=4%
,
noting also that yn = f- h for all h .
It follows that In = 4M¥42 ,h= -9 .
. .
.9 . . . ,A .
Method 3 : However you learnedit in UG (usually ,
by induction) .
Just make sure you get the right answer .gg
(3) Find the ACVS of y+=Et- 04 - i10K' ,
ETNWNIO,8) .
Method 1 :No tricks E t-OEt.it/Et+n'-0Etth- I]= E§tEt+h+0Et-iEt+n+0EtEt+h - I +EI.it.ch-I ,h= - oo
,. . . ,O ,
- . .
,0
.
Thus, tn÷EHtY*n)={ It )0
, ofwI
op.net#PPEN=DlXl: The handiest trick (byfar ! ) in- - my toolkit .To 8
, if - . - JI,
8 , Jo fi . . - JT2
K K fo- - - Ky
%
i. : :"
J04FI IT-2 AT-3-
THIlov µ ,Xtxlhl)out"" IEEFEIDiagonalsRows / Columns
OPTIONAL APPENDIX 2 : RAGVIR'S EXTREMELYUNOFFICIAL PRACTICE
QUESTIONS
(CAN BE SAFELY IGNOREDFOR EC402)
i ) Find the ACVS for(a) Xt = Et- O Et - i , Etw WN10 ,1)(b) yt-07t-7.ly , 7.tv WN19
') .
Comment on your findings .
Discusswhich model
you prefer .
4)
(9) Xf set . AXE is W.nl/0i/.IhIXt=t+EE,EEWNloil .(3) Explain why Xtin Q241 will not satisfy a CLT .
(4) Find a peer onthe course
. Studyergodicity with him/her. Discuss(a) official definition ; intuition .
(b) the famous Xt = y + Et examplewhere Etw WN10 ,E) and you N 10,1) .
(c) the ergodic theorem for weaklystationary line series with absolutelyterminable Act f.
(d) Talk about something fun for awhile.
[Hope it helps ! Next week : VARS]
