The document summarizes a thesis that aimed to analyze monthly money supply data (M1, M2, M3) in Qatar from 1982 to 2006 using ARIMA models to forecast supply from 2007 to 2010. The thesis found the time series was non-stationary and trended due to inflation after 2003, requiring first differencing to make it stationary. It forecasted future M1 supply using an ARIMA(1,1,1) model, M2 using ARIMA(3,1,3), and M3 using ARIMA(1,1,0).

1. ARIMA1
Using ARIMA Models in Forecasting Money Supply in Qatar
State
! " #$ % &' ( ) * + ,- & . / 0 + 1 23M14 -M2
4 -5 -M36 * 7 8 9 :; & - <* =>?@A&' B --5 6 * 7ACCDE +F - G H- I
J . K & $ - & # - ) L ; < L ;M # M N I #$ # M 3 # , < #$ !' O'
P& QE2 < O+$ , H/8 9 & +# 4 5 ) $* = 6 * 7ACCR-5 6 * 7 &' B -
AC>CSH * TARIMA& U $ 1 ' -Box-Jenkins& $ V 6 . / W ,- I
X+ G H- I K Q U, . K ,- 9 # Y #$ % &' ( ) * +#$ % K Q Z E T
* = 6 * 7ACC[L ,- I9 # & $ . / ' . -5 ]- " E X :, I
& +# & $ V 9 O+$ ^"75 SH $ . K
#$ % & +# &' ( # O+$ ,-M1SH $ TARIMA(1,1,1)O+$ - I
' ( ##$ % & +# &M2SH $ TARIMA(3,1,3)&' ( # O+$ I
#$ % & +#M3SH $ T O+$ <ARIMA(1,1,0)
Abstract
The thesis aimed to study and analyzed the monthly data of the money
supply in the narrow (M1), wide (M2) and widest (M3) accuracy for Qatar State
from the period January 1982 till December 2006. That was done because of
the most important role in stationary of money, then the economic stationary of
the developed and growing states. The student used ARIMA models in
forecasting for the coming four years (the period from January 2007 till
December 2010), and that what named as Box-Jenkins methodology. The
thesis attained that the monthly time series for money supply is non-stationary
and has a trend, which was because of the inflation of money which, happened
in the State after January 2003. And that what required the first differences to
change the sires to time series stationary, then the student gain of most
competent models for the forecasting to the future period.
The thesis forecasted for the future monthly data for money supply (M1)
using the model ARIMA (1,1,1), forecasting for the future monthly data for
money supply (M2) using the model ARIMA (3,1,3). Then the forecasting for the
future monthly data for money supply (M3) was using the model ARIMA (1,1,0).
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6 ' <Wilton Friedman- 9 J #$ & 7 ) B, 8 &# N- &; K m $2 6 g ' Er, $ 8 9 J
& ' : ) " < 5 g ) B,-i>?RCj>R>Friedmanl
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#$ 8 PVU7 #* F( s " JM 6 +Y ' &+ $ G s " JM <5 &+Y
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Kent ,1961:472l
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$ # M P h # : ' ", G ' E - I V7 :; 1 L 2 7 . K 4#'L ;M < #
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&' #$ ! . K ' , m $2 6 7
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& FJ & O 2- V7 :; G$ 8K 9 L ) * + (,+ E2 < !, * 9 - &0. /
&$ * = 6 * 7 Z &W - I&N = ! 2 " :; & - #$ %- UJ < ' V, 9 " c-
ACC[B 6 $a < H/ I :# #$ L ;M < #$ . K X : UJ 9 ' . / / G H 4c '- I
! K X : < B 4 U'/ N^ ' #$ % K <. / #$ % K < 9 ' V 9 ": G , X+ ' - I
< 9 NO 8 G H Y- 1 L - 9 o " B 7 #$ . K X : Y g y +
&N = ! 2 " #$ % K 9 ' 9 - a . / g I #$ % Ki3 "M14 -M24 -5 -
M3l
-9 ' J < L ; T , 8 ! / -O' - ! K X : - #$ % K 8 9 U" - 8' + & F( ,
, E & o ; & F( ' E I! K X : &+ $ #$ % K % "T* & J < t F* . / - I #$ % K
:; & - $ - - X Y * ,-
- #$ FZ ` $ -FZ 8 2 Y- ) - & ] 5 :,- u 4 - 9 '
8' n :T,- & ; c- G H 7 . ; I& $ - &+ $ & c T & * ' 9 ' 4 I #$ -
&W I #$ % K < B O+$ & z 5 - ) 4 , 4` :; < 8' +F $ - 4
m $+ < & +$c5 &' #$ 9 W 5 9 ' . / g , W 9 '- I :; & - < :"$ ` :# - = M
. / 4 E2 X :, H/ :# #$ L ;M < #$ % K < 9 +7 9 ' . / ) - &' :#

3. T - n ($,9 ,- ` ", 6- & - !a K 9 ' . K 9 : #$ % K . K ; - : :
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SH * T O+$ . KARIMA-& U $ . 'Box-JenkinsQE &'O+$ 9 # g 6 -
3 ! " #$ % &' ( ) * + , < SH $M14 ! " #$ % K-M2% K-
4 -5 ! " #$M3# Z &N = ! 2 " #$ % K 6 2- I :# #$ L ;M <
E,{ 9 G , < E
) : 4 & F , E *M SH * T O+$ - & $ V , T -
&7ARIMA& $ V L ;M - o LJh O+$ & F & a ' & U $ , -Time
Serieso LJh r * + T , H/SPSS V10ro $ . K L #$ % K ) *
SH * T -ARIMA:; & - < #$ % & # ) $ ) O+$ . K L ,
1!" %2
'3 :$0 +86 2 " & a <#$ % KMoney Supply8 9 :; & - <i>?@Ab
ACCDlK ) Z I#i` ",lG , < T )M ` , . K 9 - vF *
n"$ 9 '- I& c 8 B - n"$ 8 :; & - ) W 9 ' . / | 5 &c ' E2- I& -
2 - ) $ 9 <g & c 8
- n"$ 8 + ) W 9 ' 6/F( #$ %- 9 ' . / g K n"$ ` ", 4 B
. / g & &' = M 4' ( . K &W F ] "*h 4 ,- 2 4 :; & - < +7
g 5 1 L - 4' ( - <5 g #$ %- UJ 9 '
34 % 56 7(
0J + K) * + . KData' E - I *- F M ! ; . K V7 :; G$ 2 ($'
:# L ; - #$ U 8K ) * + ($ & T & & FJ & O
8!" %90 (
0J + K0 + & o # M &#' : . Ki#, &#' : QE2-&K U +, - & # +: & . K
3o # 8b9 2 ( & o LJ/ ) *bQE 3' 8K - * Eo $K- I 2 ", 9 2 e 8K
SH * T ) * +ARIMA) c $ M . / Wl
O+$ ro $ &; ) + X J &+ $ SH $ ,-o , ) W ,- ) c $ S- T G H- &'
K L , ro $ &; - & & 2 -
0 + 8 , #< G E -,^' 7 2 6 7 L< &j
& F( }' . K- I0 + & "' , & # . K g J 0 J 0 + }' -5 L" 8 ,
I! 2 - 0 +L - 0 + & a < . K g J 7 I0 + 8 1 . K-0 + < & T ) * +I
. K-0 + < & + 0 + & U $
L ;M O+$ 8 , #< * = L"Economic Forecasting] G E7- I& 2 - "
" . K- I& F - & K $ K $ O+$E2 g J G E7- I , * F - 2 - K F( & $ V
&N = ! * :; & - < #$ % & $ V . K L"i4 -5 - 4 - 3l
&7 ) : 4 & F , E *M SH $ ~ Z 8 , #< 0 = L"ARIMA,^(*
-, E *M . K &$ U $ - 2Autoregressive (AR)&7 ) : -
Moving Average (MA)&7 ) : 4 , E * n T F( -Autoregressive
Integrated Moving Average (ARIMA)
K 4 L" g J -: F X* U .0 + # +o LJh 8 , H/ IiFl) * +
8 9 :; & - &' ( #$ % Ki>?@AbACCDlG , 8 8 = 5 - ^"75 SH $ 4
ro $ &; ) + 3<- SH $ ; 4 &* # . K &'O+$, 9 ; 3# , - SH $- J ;- I&'O+$

4. +O+$ 0J& +# & 5 ) $ 9 T SH $ T - I&' ( ) * + X J-8 9 IACCR
&' B -AC>CN IM0 + ` a &W T ) W - ) c $
)% (: ; < =6 7 >
)?@ % &' A0B(
)=6 7 > A0B(
. K KM 8 _ (* - &$ & < g ' # - 8 T !* . K L ;M O+$ }' , 8F '
!,P "7- !, + - O+$ & o # & FJ- & ) - 5 - &' L ;M ) * +iI &*->??@jDxl' H/
. K 1 I U 8 T, & K O+$_- Z ) < , H/ ' # - 8 T & K 8 & ; &U $
&$iLapid & Lorry,1999:159)
,• 7 2 O+$ & & 5 W $ -iI +ACCxjxjl
>O+$ 9 2 e ' ,
Aa < 9 2 e m &
[#, P ch O+$ 3o g J/ TSH $ ) '
x' # ro $ €#<- 9 2 e & +# 9 W
))=6 7 > % &'
. K : - # M 8 & a )M 3 # ,- $ - 4 . / ) F - ) O 7 1 ,
M & 2 < 8 +# g 3 # &" T ,V c^ & - g# M - 4 U & K cM - &' L ;
& - #$ -
) F #,--dU O+$ . / 1 , n:T - ) & - < & -O 9V c5 -
. K &# ; ) O+$ ,- I + c T - # M UJ- T - & :+)
9 2 e & K a - &; )M JM =7 4; ,- ' #, . K , * H/ I )M U &< 7 < & +#
H T, +; &+J L ) B - 2 * )M - 2 : & o ) 2 U,M 6 +,- +# < 0 +
*^( ;iI , + - V'VK>?@kj@Rl. K +# n :T & K 3 # & - O+$ + ' G E
Y 1 2• €#<- & - &J 1- e ! c !$ 9 " M - O+$ G H- 75 !c
&J ) * F h P a <-iI ->?@>j@@l
))% (: ; <Time Series
))% (: ; < 4 %
'5 - Z5 - L" - 8 $ 7 8 V X J & U # - ; 5 8 & 2 & $ V &
& K c - &' L ; K N^, w , 6 F, I8 V +K T' , U 8K 9 +K G E < I& $ 9 J- &' -
& f -iI - +ACCxjAx>l
T' : ,- & 3' 8K +# < 9 2 e & ; ' # & $ V T ,-
& $ ) < - ) ;- < B ‚T, # 8 & 2 & $ V & - I a < "* 9 2 e
I I * F G H . K & = 5 8 - I&+;I) L IS -Vƒ„iBrase &Brase: 32
l,^' 7 = , 8F '-j
zn yyyyyy ,...,,,, 4321= …(2-5)
6 0 Jj
321 ,, yyyj&+; ) " & $ V & ;
nj& $ V & ; ` U

5. + & $ QE2 $ < - $ $ -9 :; & - #$ % &' Z ) *i1982-2007l
& U $ TBox-Jenkins
)))% (: *<*< 4 A+(
I& $ V & ) * F ‚ T(, 8 ,^, & $ V & … L SH $ ' , < 9 : 2 6/
y 5 T * 6 8F ' ) * F G , ' , -Q ' , , 4 3< ' E
$ $ n FZ . K 4 B ; &7 K Q U, c- * J … ' * & $ V & = , $K-
) * F = , ) B QE2- IG H Y- J _ +2 N J ` ", - e $ B, FZ . K - n+ ' - L'
7 2- I& $ V &,^'i
Anderson ,1992 :172-175jl
>Q U,M 6 FTrend Component
A&' - 6 FCyclical Component
[& 6 FSeasonal Component
x& o ( 6 Fie $ YlIrregular Component
,• F( = , 8F '-j
C 5 ;+,DE(: *<*< 4 A+(%
)
-6 % (: ; <
&N = ! 2 " #$ % &' ( ) * + 4 U, , I0 + 1 2 4 U *M1, M2 & M39
&$ * = 6 * 7 Z 8>?@A-5 6 * 7 Z &' B -ACCD$' 6 F' G E - IA??E2- I9 2 (
( 8SH * 3 +: c o 6 F' ) 2ARIMAO+$
3 #$ % X7 ( $ †M1:; & - <i1l
4.17856 * 7 Z 8 9
&$ * =>?@A&$ -5 6 * 7 Z . /ACCA.$ #$ % K < 9 +F 9 'V - $ E2- I
3M14c& T 4' ( 8 ' < & * oM ) *- n"$ ` ", . / | 5
&' $ &' L ;M ) K :# 4 c g . K
M- B - n"$ 8 ) L ) o K ' #, a < :; & - &" T &' #$ ) * '-
' < +7 N ! F' 5. / g B - n"$ < +F ` ", M 6 < G H . / &< ah #$ % K 9
& & $+ ' : !$ +7 PVc ‚L E - = M ] "*h 9 ' N 8 - & F ) 'h 9 '
M < &' #$ & 9 ' . / g I& T & o 4' ( E "$,-:# #$ L ;
i1lQ U,M n & #<- I&' ( ) * + 4; - 8 - 0J + +; 8 &' ( $ )M w+ JXbaY ˆˆˆ +=

6. 3 #$ % ( $M1&$ * = 6 * 7 Z 8 9 :; & - <ACC[
&$ -5 6 * 7 Z &' B -ACCD9 QE X7 ( $ 6 7 #< I426.82929 " ##
#$ % ( $ < 9 +7M19 G
4 " #$ % KM23 " #$ % K 8K 9 +K 2 E -M1! / €<
&' M 4o4 " #$ % K . * H/M23 " #$ % K 6^Z G H < !*^ZM1
&$ * = 6 * 7 Z 8 9 +7 F(ACC[&$ -5 6 * 7 Z &' B -ACCD€ * €## I
# +7 ' Z@x @Dxk5 ] < 9 o " ` ", . / o K G H-
#$ % X7 ( $ -M2Q # * 3#J #< :; & - <>>>D >x?C9
&$ * = 6 * 7 Z 8ACC[' B -&$ -5 6 * 7 Z &ACCD
4 -5 " #$ % K = '-M3& & #$ % KM2&K ) M / €<
&' U m $+ SI&" T M 3' $W - M m $+7 M ) O giHosk & Zohn : 4
l
5 #$ % K c--4 -M39 ' . / g & K $L ) ' L ; e$ < : . / o K
^ 2 E - &LLT & < L - & ) T 9 o 4 ,- FZ ,- &: & ) O K
#' FZ5 QE2 )E ^< I& 9 ' c FZ 3' ,- S *h € o € $2 ' V " <5 ) - N . /
L; <- & , & 4< o - . / ' , & * F / 4 8' ) +Y 4 #< ,- X $ o & =
&$F 9 ;^ - 8F w;-)
I % K>?@?j>>kl
4‡ -5 .$ ‡ ‡#$ % K Z-M3Q ‡# ‡+7 ' ‡Z € ‡ * ‡:; &‡ - ‡<>AR C?@@‡Z 8‡ 9 ‡
&$ * = 6 * 7ACC[&$ ‡ -5 6 * ‡7 Z . -ACCD9 ‡'- &‡' U m ‡$+ - 4‡ ‡o K G‡ H- I
#$ % K < 9 +7 9 ' . / g E 5 I) . K +;h 9 ' 4 ) M &+ *M3&‡ - ‡<
Q ‡‡# X‡‡7 ‡‡ * ‡‡ ‡‡:;>xkC [>@C* ‡‡= 6 * ‡‡7 ‡‡Z 8‡‡ 9 ‡‡ACC[‡‡Z .‡‡ --5 6 * ‡‡7
ACCD; F( - IiAl:; & - < #$ % K ) $ $ = ' Q *j
; FZiAl* = 6 * 7 8 9 :; & - < #$ % K>?@A-5 6 * 7 &' B -ACCD
0.00
20,000.00
40,000.00
60,000.00
80,000.00
100,000.00
120,000.00
140,000.00
Jan-82Jan-83Jan-84Jan-85Jan-86Jan-87Jan-88
Jan-89
Jan-90Jan-91Jan-92Jan-93Jan-94Jan-95
Jan-96
Jan-97Jan-98Jan-99Jan-00Jan-01Jan-02
Jan-03Jan-04
Jan-05Jan-06
=F$5GA%*(
M1
M2
M3

7. -
ARIMA
-% $5 %B*ARIMA
a ) * . K 2 K 8 G H- I F O+$ ] 2 g J/ & $ V , & K ,
I K ", n *- I 7 & + - I& 9 2 e +# 8K J a- =7 L, ' # I a -
< NO, ) NO -)I UACCDj>l
-) 8 &cE $ & & 5 ) "L - ‚o LT S $ & $ V , 8 1
+ M ! ' & G X $ SH $ . K L ' J- I& $ V & ) 2 ( ' ,
& +# # O+$ & K , & ˆ J ) a "& $ V &
& U $ L#'Box-Jenkins8 7 #+ & U $ G ,George Box-Gwilyn Jenkins
K & $ V . K>?RCI& $ V 7 ( 8 =F &' ; 9 e* & U $ QE2 #,- I
SH * , H/ I& $ V &# ; ) O+$, : ,-ARIMAU'h G H- SH $ ,- P $+ & e$ &#'
i= 5 SH $l& $ V ) * . K & $+ SH $ 8 8! K L ' = 5 SH $ -
&K SH $ < P : 5 - I o LJ/ & 2 ! < ) 7 w* 7 H/ = cH * '- IP : • .* 5
F(#iKang ,1980 : 7-8 )
-)H I J H5> 6Autocorrelation Function ACF
_ +, M " 6/Correlation& < & ) B 8 &; K c- Q $ ) B 8
$ < &:+, ) 2 ( - ) B 6 # < I& $ ViI +U>??>j[C[l
, E _ +, M v #'-kP&; 9 ;i_ +, Ml9 2 ( # 8tX-ktX −) 2 ( 8
& o ( ) B 8 -iI B>?RAj@@lU,M v"$ B , ) B w* 7 H‰< I9 ' Qi-
6 L#*l9 ' . / O, - ) B J <i6 L#* -lXc _ +, M 6 Eo $K # < • <
! &c . K -i+1l) B J 9 'V< v7 Q U, B , ) B w* 7 H/ Ii!* L#* -l. / O,
6 L#*i9 ' -l#'- Ig 5 # <! &c . K - X _ +, M 6 Eo $Ki-1l8 _ +, M + '-
, _ +, =7 - 8' BPerfectg 5 ) B < B 4 X $ 2 J < B 6 7 H/i
) I * (jA@kl
&; 9 ; &c - FZ 8K & o + 9 F< ) * + ( *M FZ : '-FZ 8 8 +, H‰< I) B 8
~- '- I_ +, M y J 3' 8K , ; , ; &c | ; 6‰< ) B 8 &; K c- ( *M
Xc _ +, M 8 _ +, Mi+1lX _ +, M -i-1l11− riI ZACC[j>k@l
C 5 K (DEJ H5> ;( ( LA*
b[oVU , E _ +, M &PACFPartial Autocorrelation Function
oVU , E _ +, M & = ,PACF8 $ 8 , < B & ; 8 &;
_ +, M & V '- Ig 5 ) " ) +N % < 4 I8 " TV oVU , EkkP_ +, M <
Pk
Zero
+1
! "
- 1
# "

8. 8 oVUtY-ktY −; + 4 I $ _ +, M . / ('tY8 , " 8 4#, g 5
t-t-kiI ~ACC[jRA?l
Y W 8F '-oVU , E _ +, M & a ' & &kkP, E _ +, M & 8ACF
,^' 7iIACCAj>>l
1
11
1
1
21
1
P
P
PP
P
Pkk ÷=
…(3-9)
1
1
1
1
1
12
11
21
312
21
11
PP
PP
PP
PPP
PP
PP
×=
-1M %ARIMA
-1H I 5 " > AARAutoregressive Model
, E *M &#' <AR& 9 " < B & ; ,tY) " < B v"* & ; . K
&#( )nttt YYY −−− ,...,, 21*M & , &#' : QE2 . K 3 :, G E I65 Š *M , H - , E
&# ) " < ! ; . K , B & ;
-1N > H * H I 5 " > AAR(1)
The First–Order Autoregressive Model
; B, SH $ E2 }L'tY9 J - 9 J1−tY. -5 &+, 8 , E *M SH * &Y W 8F '- I
&& ,•iIACCkjRAkl
ttt eYY ++= −1φφ …(3-10)
6 0 Jj
φ2 ' #, XU' , E *M &
φ, E *M w N6 9 K % "* n + - I0=φw N J c ' M
1−tY& $ V & &# ) 2 (tY
teJ n +: 4' 4+ ,- & # 6 F, 6 % "' & o ( ) B‹I "W
Q # w N 8' +,-
2
σ
,• $ . K ^ & M , E *M SH * & 7 8F '-iNamit & Others: 2)
( ) tt eYB =−φ1 …(3-11)
, E *M & 6 7φ6 XU'I9 J 9 o ; 4#, $K &' # M _ Z < ,
J - 2 :; }L* 9 o( )11 <<− φ6 F, $ < I1>φL; $ , E _ +, M FZ 6 F' 2 $K
F(i$2l6 7 H/ I!, Z/ B' 6 6-1<φF( L; $ , E _ +, M FZ 6 F' 2 $K
i$2l^, 7 $K !, Z/ B
, E _ +, M & -kP. -5 &+, 8 , E *M SH $AR(1)2j
1−= kk PP φ …(3-12)
$K0>k
oVU , E _ +, M &kkP, E *M & &'- 6 F,AR(1)) -
"W - , g 5 oVU , E _ +, MiI $BACC[j>>l

9. -1)% O H * H I 5 " > AAR(2)
The Second – Order Autoregressive Model
. -5 &+, 8 , E *M SH * . / 9 ' c , H * & &< a/ $KAR(1)…+L,
& * = &+, 8 , H * & &AR(2)& ,• &B Lj
tttt eYYY +++= −− 2211 φφφ …(3-13)
7 ]- " &#' : Q K & X F,-,•iMahmood : 33l
( ) tt eXBB =−− 2
21 φφ …(3-14)
,• 7 X F, SH $ E2 < , E _ +, M & -j
221 −− += kkk PPP φφ …(3-15)
, E _ +, M & < &' # M _ Z 6 F'-ACF* = &+, 8 , E *M SH $AR(2)
SH $ , E _ +, M & < &' # M _ ( (AR(1),• 7 Ij
11 <<− φ
oVU , E _ +, M &PACFSH $AR(2)* = ^ , o <i
Kang
,1980 : 9l
011 ≠φ
022 ≠φ
6 0 J022 ≠φ* = ^ $K2>k
-1)P " 4 A AMAMoving Average Model
E P B ‰ V '- I& $ V & & # n + n 2 m n) E
2 U, - & 9 2 ( # 8 9 +F ) U" P B / I& $ V & 8 9 +FiI JACC[j
>[l
^:T & ; m n SH * E ^'-te^:T & a # - #+ -
qttt eee −− ...,,, 1v - ! J <, E _ +, &+ $ G E7- I! "* B & ;ACF8
Œ &+; #tY, E *M &#' & J <AR, E _ +, M 6‰< &7 ) : &#' I
) #+ &+; # 8 6 Fi^:TlteiI>??CjA??l
[bkP " 4 A Q( *( + H I 5 " >ARIMA
Autoregressive Integrated Moving Average
I # Q $ a- - G H * 7H 7- I9 # Y 6 F, FZ X Y < &' L ;M & $ V 6/
Y & $ V & ' !*‰</ $K H/ I ]- " E XU' &$7 & $ & . / &$7
]- "dSH * . /ARMA(p, q)SH * . / SH $ 'ARIMA (p, d, q)
(,-p- I , E *M &+, . /d- I]- " &+, . /qX F,- I&7 ) : &+, . /
SH $ & a ' &B LARIMA (p, d, q), E *M SH * rAR(p)n SH * 4
mMA(q)& ,• &B L …+LiBeasley : 33l
qtqtttptpttt eee-eYYYY −−−−−− −−−++++= ...... 2212211 θθθφφφ …(3-31)
^ & M -j
22
21
2
21 ...1...1 qq
p
pt BBBBBBY θθθθφφ −−−−+−−−−= …(3-32)
1+ ;%*"4 %!"
E2 < #$3 ! " #$ % & $ V L"M1! " #$ % K-
4M24 -5 ! " #$ % K-M3&$ 8 & $ V 9 :; & - <>?@A&$ &' B -ACCD
SH * TARIMA, E _ +, M & 8 G H-ACF$ V & &' # &<<- I&

10. & $ & . / ' -5 ] " E ^$ < K Q U, . K = o JM & $ V & # K & J
_ +, M & 9 2 ( 8 - 9 # w +W & $ V & . K g 9 ‚ T(, U* N 9 #
, EACF&7 ) : &+, 'MAoVU , E _ +, M & T - IPACF‚ T(
, E *M &+,AR
) * + O+$ & o SH $ …Z * &J # SH $ ' # #* SH $ X, ‚ T( P c/ -
SH $ 8 8 = 5 SH $ T* 9 :T QE2 - I 7E &"*ˆ & $ VO+$ & Z - 9 T
3 #$ % O+$ G H- O+$ &; v ' # X JM14 -M24 -5 -M38 & +# 9
* = 6 * 7 ZACCR-5 6 * 7 Z &' B -AC>C
1R%S T 4 % ;%*"HM1ARIMA
1A M %
8; * + F(iAl* = 6 * 7 Z 8 9 3 #$ % K &>?@A&' B -
-5 6 * 7 ZACCD6 * 7 Z 8 9 W L ' V K Q U, . K , ) * + 6 •J *
* =ACC[-5 6 * 7 Z &' B -ACCDSH * 6 - IARIMA* + . K n#< 3+:$,, M )
. -5 &c ]- < E 8 G H- Q U,M & / 6• $ K !* I ' V K Q U, . K
, E _ +, M #* & $ V & # 8 7^ -ACF, E _ +, M & -
oVUPACFK - &' # 8K }(F ) * +, E _ +, M & - I& $ V & &' #ACF
,• & =j
VAR00001
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+,D-EH I J H5> 4 ( (ACFM1
&#= - J S 4#' , E _ +, M FZ 6/ I * + F( 8 … '?kŽg . K>D9 U<
I& $ + * +7 2- Pn+ ‚; $ ' _ +, M 6 < G E7->D& 6 < - & $ 9 U<
9 # Y 3 " #$ % K3 #$ % K & . -5 ]- " . K L * 6 B+$' G E
M1
, E _ +, M & 8ACF$ % K ) * + & $ V & 6 U*#M1M !* 9 # Y
]- " E ^* 9 # & $ V & c- Q U,M & h- I& $ V & X $ SH $ ' , $$F '
i-5 ] "lQ U,M & h ]- " QE2 "F, 0 J I) * + +: ' Y E 4 ) * +
-* + F(,M3 #$ % . -5 ]- " & , E _ +, M &M1j

11. VAR00001
Transforms: natural log, difference (1)
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD1EF > V B IW H I J H5> 4 ( (
) 6 … ' I. -5 3 #$ % K & ]- " , E _ +, M & FZ &$'
+, Me , E _ +, M ) ; 6 - I& $ V ) U" X Y5 &#= - J + Y 4#, , E _
8 & F & W5 & 6 - I9 # & $ V & 6 $ ' E2- I "L 8 &+' ; & $ V ) U"
. -5 &cid=1l
E _ +, M & FZ 9 2 ( 8 -m n &+, r $ * Q K ,MA (q)FZ I
, E *M &+, 8 + < Q * oVU , E _ +, M &AR (P)j
VAR00001
Transforms: natural log, difference (1)
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
PartialACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD3EF > V B IW X:9 H I J H5> 4 ( (
1)A C ( $ H
' ,8 7 &+,AR-MAoVU , E _ +, M - , E _ +, M & 9 2 ( 8
w +W & $ V & 6 + K 8F '- I& o ( P : 5 & # & o # & a < +; 4 : * Q K
, P c‰ 6• #* ISH $ ' #, . / # *M 4 : *- 9 #ARIMA3<- & $ V &
& $ V & ) * + o SH $ + M Q K ) :T * G E -AARIMA (1,1,1)
,• 7 !, 6/-j
p = 1, E *M &cd = 1]- " &cq = 1&7 ) : &c

12. L * SH $ ' # -& ,• ro $ . Kj
FINAL PARAMETERS:
Number of residuals 298
Standard error 462.07842
Log likelihood -2249.9688
AIC 4505.9377
SBC 4517.029
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 295 63062626.6 213516.46
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .98489 .035294 27.905585 .00000000
MA1 .94930 .058161 16.321731 .00000000
CONSTANT 116.09705 78.439934 1.480076 .13992015
< ~ # SH $ T 8F '- I& o LJh & J $ 8 &' 2 c 6 Q K ro $ 8 •J *
O+$
+ U*~ # SH $ ; +ARIMA (1,1,1), E _ +, M & 8
ACF_ +, M & -oVU , EPACF& ,•j
Error for VAR00001 from ARIMA, MOD_7 LN CON
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD8EA H I J H5> 6AARIMA (1,1,1)

13. Error for VAR00001 from ARIMA, MOD_7 LN CON
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
PartialACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
;+UC 5DYEJ H5> 6A A X:9 H IARIMA (1,1,1)
6 = ) " &eJ 8 -. -5iP : h ) <l, E _ +, MACF, E _ +, M -
oVUPACF& o LJ/ * U* Ii&' $ Yl8F '- I o (K m ; + 6 $ 'T
#$ % 9 # ) * + = Q * * + F( 6 F'- I O+$ < ~ # SH $M1j
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
Jan-82Jan-83Jan-84Jan-85Jan-86Jan-87Jan-88Jan-89Jan-90Jan-91Jan-92Jan-93Jan-94Jan-95Jan-96Jan-97Jan-98Jan-99Jan-00Jan-01Jan-02Jan-03Jan-04Jan-05Jan-06Jan-07Jan-08Jan-09Jan-10
=F$5GA%*(
% % " C%
0 Z C%
C 5 ;+UD[ETM1O GA P .( * @ Z][)F ^ GA P $ _)` `
1)Q A T 4 % ;%*"HM2ARIMA
1)A M %

14. ; * + F( 8iAlZ 8 €P ' V K Q U, . K , ) * + 6 •J ** = 6 * 7
ACC[SH * 6/- IARIMA6• $ K !* I ' V K Q U, . K , M ) * + . K n#< 3+:$,
. -5 &c ]- < E 8 G H- Q U,M & /
, E _ +, M + U*-ACF(F ) * +&' # K - &' # 8K }&
, E _ +, M & - I& $ VACF,• 7 2j
VAR00001
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD]EH I J H5> 4 ( (ACFM2
&#= - J S 4#, , E _ +, M ) 6/ I * + F( 8 … '?kŽg . K>D9 U<
6 < G E7- I& $ + * +7 2- Pn+ ‚; $ ' _ +, M>D& 6 < - & $ 9 U<
#$ % K & . -5 ]- " . K L * 6 B+$' G E I ' 9 # Y 3 " #$ % K
4M2
, E _ +, M & FZ 8ACF#$ % K ) * + & $ V & 6 U*M2Y]- " E ^*- 9 #
i-5 ] "l9 # & $ & . / & $ V & ' I) * + +: ' Y E 4 ) * +
, E _ +, M & * + F( -ACF,^' 7 ]- " Ej
VAR00001
Transforms: natural log, difference (1)
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD`E> 4 ( (F ^ V B IW H I J H5
m n &+, r $ * Q K , E _ +, M & FZ 8MA (q)_ +, M & I
, E *M &+, 8 + < Q * oVU , EAR (P)j

15. VAR00001
Transforms: natural log, difference (1)
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
PartialACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
;+UDEX:9 H I J H5> 4 ( (F ^ V B IW
1))A C ( $ H
8 7 &+, ' ,AR-MA, E _ +, M FZ- , E _ +, M & FZ 9 2 ( 8
& $ V & 6 + K 8F '- I& o ( P : 5 & # & o # & a < +; 4 : * Q K oVU
*- 9 # w +W, P c‰ #* H/ ISH $ ' #, . / # *M 4 :ARIMA3<- & $ V &
& $ V & ) * + o SH $ + M Q K ) :T * G E -AARIMA (1,1,1)
E -,^' 7 !,j
p = 1, E *M &cd = 1" &c]-q = 1&7 ) : &c
& ,• ro $ . K L * SH $ ' # -j
FINAL PARAMETERS:
Number of residuals 298
Standard error 720.93926
Log likelihood -2383.0529
AIC 4772.1057
SBC 4783.197
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 295 154058889.5 519753.42
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .99306 .01514 65.572039 .00000000
MA1 .90413 .03833 23.585864 .00000000
CONSTANT 552.41670 418.80617 1.319027 .18818299
~ # SH $ T 8F '- I& o LJh & J $ 8 &' 2 c 6 Q K ro $ 8 •J *
ARIMA (1,1,1)O+$ < I
+ U*~ # SH $ ; +ARIMA (1,1,1)& 8, E _ +, M
ACFoVU , E _ +, M & -PACF& ,•i
j

16. Error for VAR00002 from ARIMA, MOD_11 LN CON
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD)E5> 6A A H I J HARIMA (1,1,1)
Error for VAR00002 from ARIMA, MOD_13 LN CON
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
PartialACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD-EJ H5> 6A A X:9 H IARIMA (1,1,1)
. -5 6 = ) " &eJ 8 -iP : h ) <l, E _ +, MACF, E _ +, M -
oVUPACF& o LJ/ * U* Ii&' $ YlT 8F '- I o (K m ; + 6 $ '
O+$ < ~ # SH $Q * * + F( 6 F'-#$ % 9 # ) * + =M2

17. 0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
Jan-82
Jan-83
Jan-84
Jan-85
Jan-86
Jan-87
Jan-88
Jan-89
Jan-90
Jan-91
Jan-92
Jan-93
Jan-94
Jan-95
Jan-96
Jan-97
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
=F$5GA%*(
% % " C%
0 Z C%
C 5 ;+UD1ETM2O GA P .( * @ Z][)F ^ GA P $ _)` `
1-Q ^ T 4 % ;%*"HM3ARIMA
1-A M %
; * + F( 8 … 'iAl&' ( ) * +4 -5 #$ %M38 9 :; & -
>?@AbACCD8 G H- Q U,M & / 6• $ K !* I ' V K Q U, . K , ) * + 6
. -5 &c ]- < E
, E _ +, M & + U* Q U,M & / +;-ACF- &' # 8K }(F ) * +K
, E _ +, M & - I& $ V & &' #ACF,•j
VAR00001
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+,D3EH I J H5> 4 ( (ACFM3

18. &#= - J S 4#' , E _ +, M FZ 6/ I * + F( 8 … '?kŽg . K>DU<I& $ 9
+ * +7 2- Pn+ ‚; $ ' _ +, M 6 < G E7->D#$ % K & 6 < - & $ 9 U<
9 # Y 4 -5 "& $ V & . -5 ]- " . K L * 6 B+$' G E
, E _ +, M & 8ACF% K ) * + & $ V & 6 U*#$M3$$F ' M !* 9 # Y
]- " E ^* 9 # & $ V & c- Q U,M & h- I& $ V & X $ SH $ ' ,i] "
-5lQ U,M & h ]- " QE2 "F, 0 J I) * + +: ' Y E 4 ) * +
* + -, E _ +, M &ACF,^' 7 -5 ] " Ej
VAR00001
Transforms: natural log, difference (1)
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD8EF ^ V B IW H I J H5> 4 ( (
K , E _ +, M & FZ 8m n &+, r $ * QMA (q)_ +, M & I
oVU , E, E *M &+, 8 + < Q *AR (P)j
VAR00001
Transforms: natural log, difference (1)
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
PartialACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UDYEF ^ V B IW X:9 H I J H5> 4 ( (

19. 1-)A C ( $ H
8 7 &+, ' ,AR-MA, M & FZ- , E _ +, M & FZ 9 2 ( 8, E _ +
& $ V & 6 + K 8F '- I& o ( P : 5 & # & o # & a < +; 4 : * Q K oVU
, P c‰ #* H/ ISH $ ' #, . / # *M 4 : *- 9 # w +WARIMA3<- & $ V &
SH $ + M Q K ) :& $ V & ) * + oT * G E -AARIMA (1,1,0)
!, E2 !, -j
p = 1, E *M &+,d = 1]- " &+,q = 0&7 ) : &+,' # -
& ,• ro $ . K L * SH $j
FINAL PARAMETERS:
Number of residuals 299
Standard error 1952.9117
Log likelihood -2688.9157
AIC 5381.8314
SBC 5389.2323
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 297 1133534923.4 3813864.1
Variables in the Model:
S B SEB T-RATIO APPROX. PROB.
AR1 -.44044 .052098 -8.4540806 .00000000
CONSTANT 385.13831 78.486545 4.9070616 .00000153
~ # SH $ T 8F '- I& o LJh & J $ 8 &' 2 c 6 Q K ro $ 8 •J *-
ARIMA(1,1,0)5 &+, 8 , H * SH * 2-. -AR (1)O+$ <
+ U*~ # SH $ ; +ARIMA (1,1,0), E _ +, M & 8
ACFoVU , E _ +, M & -PACF& ,•j
Error for VAR00001 from ARIMA, MOD_3 LN CON
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
ACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD[EH5> 6A A H I JARIMA (1,1,0)

20. Error for VAR00001 from ARIMA, MOD_3 LN CON
Lag Number
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
PartialACF
1.0
.5
0.0
-.5
-1.0
Confidence Limits
Coefficient
C 5 ;+UD]EJ H5> 6A A X:9 H IARIMA (1,1,0)
. -5 6 = ) " &eJ 8 -iP : h ) <l, E _ +, MACFoVU , E _ +, M -
PACF& o LJ/ * U* Ii&' $ Yl6 $ 'SH $ T 8F '- I o (K m ; +
O+$ < ~ ##$ % 9 # ) * + = Q * * + F( 6 F'-M3
0
20000
40000
60000
80000
100000
120000
140000
160000
Jan-82
Jan-83
Jan-84
Jan-85
Jan-86
Jan-87
Jan-88
Jan-89
Jan-90
Jan-91
Jan-92
Jan-93
Jan-94
Jan-95
Jan-96
Jan-97
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
=F$5GA%*(
% % " C%
0 Z C%
C 5 ;+UD)`ETM3O GA P .( * @ Z][)F ^ GA P $ _
)` `

21. 114 % A 4 a >
114 a >
>c- •J ' I :; & - < #$ % K v ' # &' ( ) * + & $ V * + F( 9 2 ( 8
* = 6 * 7 Z E$ #$ % K < +7 ' V,- 9 "ACC[-5 6 * 7 Z &' B -ACCDQE2- I
. / #$, 9 'Vj
#$ % K M15 6 * 7 Z-ACC[Q # X7 *xAD @A?A6 7 6
& a ) $ - 9 QE2 +; X7 $i& ` alx >R@k
#$ % K M2* = 6 * 7 ZACC[Q # X7 *>>>D >x?C6
9 QE2 +; X7 $ 6 7@x @Dxk
#$ % KM3* = 6 * 7 ZACC[Q # X7 *>xkC [>@C6
9 QE2 +; X7 $ 6 7>AR C?@@
A&N = ! 2 " :; & - < #$ % &' ( ) * + ,- & 8i3M1I
4 -M24 -5 - IM3lSH * T IARIMAAutoregressive Integrated -Moving
Average& U $ 1 ' -Box-Jenkins8 7 #+ 8 7 #+ IGeorge Box-
Gwilyn JenkinsK & $ V . K>?RC, E *M SH * 8 r . K & o # - IAR
Autoregressive) : SH *-&7MAMoving AverageT - & w W ,
, E _ +, M & )ACFX :, I9 # Y &N = ! 2 " #$ % & $ V 6 . /
]- " &#' Ti-5 ] " El9 # & $ . / ' & $ V ) * +
[#,SH * 'ARIMA8 - I :; & - < #$ % &' ( ) * + & $ V
% & +# &' ( ) * + 8 O+$ SH $ …Z * O+$ &; v ' # T & a "
* = 6 * 7 Z 8 9 :; & - < #$ACCR6 * 7 Z &' B - I-5AC>C,^' 7 - Ij
SH $ } u ,ARIMA (1,1,1)3 " #$ % O+$M1
SH $ } u ,ARIMA (3,1,3)4 " #$ % O+$M2
SH $ } u ,ARIMA (1,1,0)4 -5 " #$ % O+$M3
x#$ % K < +F ` ", M gV '* = 6 * 7 Z :; & -ACC[. / 2 9 -
& & - &' #$ & } a G E7- I& .$+ 4' ( < 4 . /- I B - n"$ ` ",
:; & - < #$ % - - Wh & K 9 h
11)4 % A
>o * 8 9 " M#$ % K v ' # & # & $ V 9 O+$ 3 ' < W L & QE2 r
iM1, M2, M3l-O Q + K :; & - < V7 G$+ X* c 8 &' #* & $+, - 4a- $K
:; & - < #$ # M 8K -5
A} u , 8 & +# & 0J + • ',Intervention Analysis4
SH *ARIMA9 #$ % K v ' # & $ V m . K z J E B … a G H- I
* = 6 * 7 Z 8ACC[-5 6 * 7 Z &' B -ACCD
[SH * T 0J + W 'ARIMA# o LJ/ , P c/ $KQE2 6‰< I& $ V
&U . K , ; 4 IO+$ < T 8F ' ^"75 SH $ . K L 8 8F ' SH $
& $ V * , 7 ( X Y

22. x&' #* & H T, 0J + W ' I :; & - < #$ % K ! * ' E +F #$ T X+
,n"$ ) - ! c & n:T 4a- 4 I :# L ;M < +$c5 - #$ 3< , 8 8
#$ T & F( ; ",- I :; & - < #$ % K 9 ' < 2 K 8 ' B -
k…+W 6 F' 5 M- :# ' _ +, G" 0J + W '&a K F' 5 M-
M- 8 # =75 &' #$ ) 8 & 8K 0 + X : ' I!< W < 9 ) + #
:# ' 1 W # 6 F' 5

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-I B K / I Bj!$ " h 7cd k6 (I B IP 2V & +: I>?RA
1b• +K 8 JI $Bj"H$6A < % +* C0 ^ 5 ' U % (: *<*< ;%*
%90 (Box-JenkinsI * = IV'V +K G & c & U IACC[
3I# +Kj% 6 7 > !$ "I&' $F h I&K +: & U IACCk
8I * (V 2 $J I 8 Jjh 7cdyI B I& F w & +: I)
YI ~~ " +K cjf* 5 %*%*"H 4 6' mVA< 5 =6 7 > ;W
5 ^I ($ - } ^ V7 I L < G & c IACC[
[IZ 2 6 * Kjf%4 % H V e X 7c>< & F & +: I9 L+ & c I
I9 L+>??C
b% n$:%*+ > _* 56 7
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