Time series Analysis of Global CO2 Emissions

8/15/2019 Time series Analysis of Global CO2 Emissions

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Contents

EXECUTIVE SUMMARY.................................................................................................2

INTRODUCTION...........................................................................................................2

TIME SERIES ANALYSIS................................................................................................4

Modelling Approach 1 !in"er#$ Addi"i%e Me"hod....................................................&

Modelling Approach 2 ARIMA Modelling.................................................................'

RESULT AND CONCLUSION........................................................................................11

A((ENDI)................................................................................................................. 11

Re*erence$................................................................................................................1+

,ig-re 1 Tie Serie$ (lo" o* Model /-ilding Da"a 0enera"ed in Mini"a3

,ig-re 2 AC, (AC, and 5ariogra *or "he da"a4,ig-re 3 Spec"ral Den$i"6 graph *or "he da"a.4

,ig-re 4 Error inii7ing Di$co-n" *ac"or$ *or 8in"er#$ Addi"i%e e"hod&

,ig-re & Re$-l"$ *or Me"hod 8i"h Di$co-n" *ac"or a$ 9.2+,ig-re + Re$id-al plo"$ 8in"er#$ Me"hod'

,ig-re ' Tie $erie$ Model 8i"h *oreca$" *or ARIMA odel:

,ig-re : ARIMA ;9 1 1< ) ;9 1 1


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EXECUTIVE SUMMARY

We have performed a time series analysis on the Gloal atmospheri! C"# !ontent in this term pro$e!t% The

data otained for the series is in terms of the parts per millions in the atmosphere for many different sites

aro&nd the 'orld% We initially analy(ed the data as a asi! time series to find o&t its asi! !hara!teristi!s%

We &sed )*+ of the availale data for the Modellin, part% The remainin, data 'as &sed to !he!- the

fore!astin, a!!&ra!y of the model% "n reali(in, that the data had an in!reasin, trend 'ith seasonal

!han,es 'e &sed a 'inter.s additive method to model the data% We modeled the data 'ith different val&es

for the smoothin, !onstants% /o'ever0 tryin, to fit an error minimi(in, model &sin, 1M2 res&lted in

smoothin, val&es of 3 for the level and no trend or seasonal terms% This 'as stran,e as there 'as !learly a

trend and seasonal !omponent apparent from the time series plot% The model also 'as not invertile for an

e4&ivalent ARIMA model% Apart from this0 the initial plot indi!ated that the data 'as not stationary% So

'e needed differen!in, model for this data apart from an appropriate AR and MA terms% A ,eneral

ARIMA model 'ith different n&mer of AR and MA terms 'ere fit &sin, 1M2% We sele!ted ARIMA 5*0

30 36 X 5*0 30 363# model from vario&s options as this model offered etter performan!e meas&rement

val&es% We fore!asted the Gloal atmospheri! C" # !ontent for the remainder of the #*+ data points to

!he!- the performan!e of the models% The fore!asted error 'as minimal sho'in, a very ,ood fit of the

model to the data%

INTRODUCTION

With in!reasin, ind&strial development over the past !ent&ry the effe!ts of modern te!hnolo,y has startedsho'in, its impa!t on the environment% The avera,e ,loal temperat&re has steadily in!reased over this

time period% M&!h of this temperat&re !han,e or Gloal 'armin, is attri&ted to the in!reased amo&nts of

Greenho&se ,ases in the atmosphere0 spe!ifi!ally C"#%

O/@ECTI5E 7

To analy(e the Gloal monthly C"# !on!entration in the air as a time series% The data &sed for model

&ildin, spans from 1an&ary0 38)* to April0 #**) 5data split in to )*+ for model &ildin,0 #* + for

testin,6% We 'ant to fore!ast the C"# !on!entrations after April0 #**) &sin, the model that 'e &ild from

the previo&s data% We 'ill e !omparin, these fore!asted val&es to a!t&al meas&red val&es for the same

time period%

DATA7

The data 'as otained from the Earth System resear!h 9aoratory Wesite :3;% The sites that are

!onsidered for this meas&rement have samples predominantly of Marine


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sites are &s&ally lo!ated at =remote marine sea level lo!ations 'ith prevailin, onshore 'inds> :#;% They

!al!&late the C"# !on!entration y ta-in, means of the val&es fo&nd from different M9< sites from all

over the 'orld% The a!t&al data is meas&red !ontin&o&sly at the sites and avera,e val&es are ta-en over

the entire month% The lin- to the data is provided in the referen!e% As mentioned efore0 'e have split the

data in to a model &ildin, data for modellin, and a test data for !omparin, the fore!asts%

INITIAL (LOT

We plotted the time series data for the test data in ?i,&re 3% The plot sho's an in!reasin, trend 'hi!h

loo-s linear and a seasonal !y!le pattern% The season len,th seems to e0 more or less 3# months 'hi!h is

possile sin!e the data is the monthly val&es of C"# !on!entration%

Year

Month

20082004200019961992198819841980

Jan Jan Jan Jan Jan Jan Jan Jan

390

380

370

360

350

340

330

A v e r a g

e G l o b a l C O 2 i n P P M

Global CO2 Conenration in PPM

Figure 1 Time Series Plot of Model Building Data Generated in Minitab

The linear increa$e i$ a""ri-"ed "o ind-$"riali7a"ion increa$ed n-er o* 5ehicle$

igh"$ and o"her *ac"or$ -$-all6 rela"ed "o gloal econoic de%elopen". Bo8e%er

"he $ea$onal pa""ern a6 e d-e "o %er6 dieren" rea$on$ and i$ no" %er6 ea$6 "o

eplain. Apar" *ro "he$e 2 charac"eri$"ic$ "he da"a $ee$ "o e %er6 CleanF 8i"h

%er6 le$$ %aria"ion o%er "ie and no apparen" e"ree %al-e$.


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TIME SERIES ANALYSIS There are *e8 8a6$ "o odel $ea$onal "ie $erie$ da"a. Thi$ can e decided *ro

"he ini"ial anal6$i$ o* "he "ier $erie$ da"a. A$ $een in ,ig-re 1 "here i$ a "rend and

$ea$onal coponen" "o "he odel. The AC, and (AC, graph$ can e -$ed "o G-dge

"he na"-re o* "he da"a. The$e graph$ along 8i"h "he 5ariogra i$ $ho8n in ,ig-re 2.

Figure 2 ACF, PACF and Variogram for the data

The %er6 $lo8 deca6ing o* "he AC, plo" near -ni" %al-e o* (AC, a" lag 1 and non

$"ale 5ariogra plo" indica"e "ha" "he da"a i$ non$"a"ionar6. Thi$ $-gge$"$ "ha"

dierencing 8ill e reH-ired on "he original da"a "o odel i" -$ing ARIMA "echniH-e.

The $pec"ral den$i"6 anal6$i$ $ho8n in ,ig-re 3 conr$ "he pre$ence o* 12 period

$ea$onal pa""ern in "he da"a.


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Figure S!e"tral Densit# gra!h for the data$

Modelling Approach 1 !in"er#$ Addi"i%e Me"hod The "e" $-gge$"$ 8in"er#$ e"hod *or odelling da"a 8i"h $ea$onal or c6clical

pa""ern. !e per*ored 8in"er#$ Addi"i%e e"hod on "he da"a -$ing @M( $o*"8are.

The addi"i%e odel 8a$ -$ed $ince "he apli"-de o* "he $ea$onal pa""ern 8a$

independen" o* "he le%el o* "he da"a. The %al-e$ o* "he di$co-n" *ac"or$ *or le%el

"rend and $ea$onal coponen"$ 8ere "o e Jep" e"8een 9 and 1 8hile inii7ing

"he $H-ared $- o* error$.

The e$"ia"e$ gi%en 6 @M( i$ $ho8n in ,ig-re 4. I" $-gge$"ed "ha" "he le%el o*

$oo"hing *ac"or e $e" a" 1 and "ha" *or "rend and $ea$onali"6 e $e" a" 9.

Bo8e%er "he anal6$i$ o* "he linear " on "he odel $ho8n in "he A((ENDI)

AppTale I $ho8$ "ha" "here i$ $ignican" linear "rend in "he odel. The $ea$onal

c6cle pa""ern can al$o no" e o%erlooJed looJing a" "he Spec"ral den$i"6.

Figure % &rror minimi'ing Dis"ount fa"tors for (inter)s Additi*e method

@M( re$-l"$ al$o $-gge$" "ha" "hi$ odel ha$ a nonin%er"ile MA coponen" in "he

eH-i%alen" ARIMA odel 8hich i$ "ro-ling. Th-$ 8e decided "o all "he di$co-n"

*ac"or$ a" 9.2 a$ $-gge$"ed in "he "e" K3. The o-"p-" o* "hi$ odel and "he

$-ar6 $"a"i$"ic$ i$ $ho8n in ,ig-re &. Thi$ odel ha$ a -ch higher $- o*

$H-ared error$ and higher AIC and S/C %al-e$. Thi$ i$ epec"ed a$ "hi$ odel ha$

ore parae"er$ in i" and AIC and S/C p-ni$he$ odel$ 8i"h ore parae"er$ "o

e$"ia"e.


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Figure + esults for Method (ith Dis"ount fa"tor as -$2

The *oreca$"ed %al-e$ *or "he ne" 12 on"h$ i$ $ho8n in Tale 1. !e ha%e al$o

*oreca$"ed "he %al-e$ *or "he reaining %al-e$ *or "he da"a "ha" 8e ha%e in

AppTale II in "he A((ENDI). The de"eriora"ion in "he predic"i%e capaci"6 o* "he

odel i$ %er6 le$$ a$ $een *ro "he predic"ed and ac"-al %al-e$ *or "he la"e$" da"a.

!ate"##er C$

95%At&al'al&e(

)orea(te*

+rror

$o,er C$95%

299:9&3:+.'&':

+3 3:+.2=3:+.1==+

'9.9

=3:&.+414

'+=

299:9+ 3:&.=+&4144 3:&.3&

3:&.3=13'94

9.9

43:4.:1'3

2+4

299:9' 3:4.44&199+ 3:3.:2

3:3.:&91+

9.93

3:3.2&&21=4

299:9: 3:3.22&+43' 3:2.&9

3:2.+944+'3

9.1

93:1.=:32

=1

299:9= 3:3.4&&=&:2 3:2.2=

3:2.:939:'

9.&

13:2.1&92

1&:

299:19 3:4.:':'+1 3:3.43

3:4.1::'+&'

9.'

+3:3.4=:'

'94

299:11 3:+.33+'2&= 3:4.=2

3:&.+943222

9.+

:3:4.:'1=

1:4

299:12 3:'.3+3'22& 3:+.91

3:+.&:3:4:'

9.&

'3:&.:93=

'4=299=91 3::.9:=&

:=:3:+.'' 3:'.2&'4

&14

9.43:+.42&3

13


7/19

+

=

299=92 3::.+4='994 3:'.21

3:'.'+9':':

9.&

&3:+.:'1:

'&2

299=93 3:=.1&==&:' 3:'.43

3::.21994&=

9.'

:3:'.2+91

332

299=94 3:=.+241&2 3:'.'3

3::.+9=2:3=

9.:

:3:'.&=44

1&:

299=9& 3:=.'11:'&: 3:'.'1

3::.&=3=2':

9.:

:3:'.4'&=

'=:Table 1 A"tual *.s !redi"ted *alues for (inter/s Method

,ro "he *oreca$" error %al-e$ i" $ee$ "ha" "he odel $ligh"l6 o%ere$"ia"e$ "he

%al-e o* CO2 concen"ra"ion. !e $-gge$" -$ing a con$"an" "er "o o$e" "hi$ error "o

ipro%e "he odel. The re$id-al plo"$ *or "he odel i$ $ho8n in ,ig-re + doe$ no"

ipl6 an6 $erio-$ %iola"ion in "he norali"6 a$$-p"ion or "he con$"an" %ariance

a$$-p"ion.

10-1-2

99.9

99

90

50

10

1

0.1

/e(i*&al

P e r e n t

380370360350340

1

0

-1

-2

)itte* 'al&e

/ e

( i * & a l

1.350.900.450.00-0.45-0.90-1.35-1.80

80

60

40

20

0

) r e 0 & e n 1

300250200150100501

1

0

-1

-2

/ e ( i * & a l

oral Probabilit Plot 'er(&( )it(

i(togra 'er(&( Or*er

/e(i*&al Plot( or Average Global CO2 in PPM

Figure 0 esidual !lots, (inter)s Method


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Modelling Approach 2 ARIMA Modelling The $aple AC, and (AC, plo"$ $ho8n in ,ig-re 2 indica"ed "he da"a i$ non

$"a"ionar6. Th-$ dierencing i$ nece$$ar6 *or ARIMA odelling. !e per*ored

general ARIMA odelling -$ing @M( 8i"h "he dierencing order $e" 1 *or o"h "he

non$ea$onal and $ea$onal "er$ ;"he r$" dierence reo%ed $oe $"a"ionari"6

-" "he 5ariogra plo" $-gge$"$ "ha" a $ea$onal dierencing igh" al$o e

reH-ired


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Figure Time series Model (ith fore"ast for AMA model

Figure 3 AMA 4-, 1, 15 6 4-, 1, 1512 Model summar# statisti"s

Error Re*erence $o-rce no" *o-nd $ho8$ "he $-ar6 $"a"i$"ic$ *or "he ARIMA

odel along 8i"h e$"ia"e$ *or "he $ea$onal and non$ea$onal parae"er *or "he

Mo%ing a%erage "er.


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60544842363024181261

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

$ag

A & t o o r r e l a t i o n

AC) o /e(i*&al( or Average Global CO2 in PPM,ith 5% (igniiane liit( or the a&toorrelation(

Figure 7 Sam!le ACF for AMA 4-, 1, 15 4-, 1, 1512

60544842363024181261

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

$ag

P a r t i a l A & t o o r r e l a t i o n

PAC) o /e(i*&al( or Average Global CO2 in PPM,ith 5% (igniiane liit( or the #artial a&toorrelation(7

Figure 1- Sam!le PACF for AMA 4-, 1, 15 4-, 1, 1512

,ig-re = and ,ig-re 19 $ho8 "he $aple AC, and (AC, plo" *or "he ARIMA odel.

Thi$ odel ha$ $-cce$$*-ll6 reo%ed "he non$"a"ionari"6 o* "he da"a. The $aple

(AC, %al-e$ i$ $ligh"l6 high *or $oe lag$ *or "he da"a ho8e%er i" i$ no" %er6

$erio-$. The %al-e$ are %er6 lo8 a" lag$ 12 and i" i$ -l"iple 8hich ean$ "ha" "he

$ea$onali"6 ha$ een cap"-red.


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Figure 11 esidual !lot for AMA model

The re$id-al plo"$ *or "he ARIMA odel in ,ig-re 11 doe$ no" $ho8 an6 apparen"

prole$ 8i"h "he norali"6 and con$"an" %ariance a$$-p"ion o* "he da"a. The

copari$on o* "he *oreca$"ed %al-e$ *or "he ne" 12 on"h$ a*"er "he la$" on"h o*

"he odelling da"a $e" i$ $ho8n in Tale 3.

!ate$o,er C$0.95

At&al'al&e(

Pre*ite*'al&e

)orea(t+rror

"##er C$0.95

299:9&3:+.9=1+:+

4 3:+.2= 3:+.33132== 9.94 3:+.&'9='33

299:9+3:&.92'223

: 3:&.3& 3:&.&23'4&= 9.1' 3:+.9292+:

299:9'3:3.313:'&

1 3:3.:2 3:3.='3=94= 9.1& 3:4.+33=34:

299:9:3:1.:=3+9+

' 3:2.&9 3:2.+:4914+ 9.1: 3:3.4'4422&

299:9=3:1.:=3:+:

: 3:2.2= 3:2.'=+99&1 9.&1 3:3.+=:1413

299:193:3.19&'31

3 3:3.43 3:4.19'29': 9.+: 3:&.19:+:42

299:113:4.3++'='

& 3:4.=2 3:&.4&:+12+ 9.&4 3:+.&&942''

299:123:&.1==':9

2 3:+.91 3:+.3'&9192 9.3' 3:'.&&92491299=91 3:&.'&4+3' 3:+.'' 3:'.99''41' 9.24 3::.2+9:4+2


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3

299=923:+.1+&=22

= 3:'.21 3:'.4=233'+ 9.2: 3::.:1:'&23

299=93 3:+.&&92&: 3:'.43 3:'.=4+13: 9.&2 3:=.34291:1

299=943:+.=922:1

= 3:'.'3 3::.3+4339+ 9.+3 3:=.:2+3'=3Table A"tual and Fore"asted *alues of the AMA model

All "he ac"-al %al-e$ *all 8i"hin "he -pper and lo8er =& predic"ion in"er%al$ *or "hi$

odel 8hich indica"ed "ha" "he odel i$ a %er6 good predic"i%e odel. The

predic"ed %al-e$ *or "he reainder o* "he a%ailale da"a i$ $ho8n in AppTale I5 in

"he A((ENDI). The *oreca$" error$ *or "he la"e$" on"h$ $ho8n in AppTale I5 i$ %er6

lo8 and "he odel ha$ no" de"eriora"ed -ch 8i"h %al-e$ $o *ar ahead in "he *-"-re.

RESULT AND CONCLUSIONCoparing "he "8o od-le$ 8in"er#$ e"hod and ARIMA 5*0 30 36 X 5*0 30 363#0 sho's that

the AIC and S


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A((ENDI)

A!!Table Anal#sis of 8inear 9t

!ate "##er C$ At&al )orea(t +rr $o,er C$ 95%299=9+ 3::.='3+ 3:+.'4 3:'.':&+ 3:+.&='+33=299=9' 3:'.&9&: 3:4.:' 3:+.2444 3:4.=:2=&9=299=9: 3:+.33+: 3:3.&9 3:4.==:' 3:3.++9&&11299=9= 3:+.+1&2 3:3.'1 3:&.1='3 3:3.''=492+299=19 3::.9:3+ 3:&.24 3:+.&:39 3:&.9:249':299=11 3:=.&:4+ 3:+.'' 3:'.==:& 3:+.412&2&'

299=12 3=9.+&22 3:'.'9 3::.=':1 3:'.393='3=291991 3=1.41+4 3::.4& 3:=.+&1' 3:'.::+='14291992 3=2.912: 3:=.14 3=9.1&&9 3::.2='2''1291993 3=2.&&'4 3:=.4' 3=9.+943 3::.+&11'93291994 3=3.9&42 3:=.'+ 3=1.993& 3::.=&2'=1'29199& 3=3.1+'2 3:=.'2 3=9.=::1 3::.:9=9:+:29199+ 3=2.4&=+ 3::.:1 3=9.1'=: 3:'.=991+1129199' 3=1.9211 3:'.21 3::.+3:+ 3:+.2&+1=1&29199: 3:=.::92 3:+.9= 3:'.3=2= 3:4.=9&+'9+29199= 3=9.1:&' 3:+.&3 3:'.&=1+ 3:4.=='4&1:291919 3=1.+:92 3::.9= 3::.=''2 3:+.2'433&&291911 3=3.29+4 3:=.&9 3=9.3=2: 3:'.&'=1=94

291912 3=4.2=:& 3=9.22 3=1.3'23 3::.44+1&4+291191 3=&.9:+& 3=9.'4 3=2.94&= 3:=.99&3''1291192 3=&.'9+9 3=1.1= 3=2.&4=3 3:=.3=2&&&1291193 3=+.2'32 3=1.&9 3=2.==:& 3:=.'23=13&291194 3=+.'=29 3=1.:: 3=3.3='' 3=9.993&4&29119& 3=+.=222 3=1.=9 3=3.3:24 3:=.:42+91&29119+ 3=+.23+9 3=9.=' 3=2.&'41 3::.=121=3229119' 3=4.:1:+ 3:=.94 3=1.932= 3:'.24'21&+29119: 3=3.+=:3 3:'.'4 3:=.':'2 3:&.:'+12'3


14/19

13

29119= 3=4.923= 3::.1& 3:=.=:&: 3:&.=4''&12291119 3=&.&3:2 3:=.'3 3=1.3'1& 3:'.294:+9+291111 3='.9:3: 3=1.19 3=2.':'9 3::.4=92==+291112 3=:.1=&9 3=1.=9 3=3.'+++ 3:=.33:1:42291291 3==.991: 3=2.42 3=4.4492 3:=.:':+432291292 3==.+3=' 3=3.92 3=4.=43& 3=9.24'3&&=291293 499.22&1 3=3.&4 3=&.3=2: 3=9.&+9&39'291294 499.'+1: 3=3.:9 3=&.'=29 3=9.:2224&329129& 499.=9+: 3=3.+= 3=&.''+' 3=9.+4+&21329129+ 499.23:3 3=2.++ 3=4.=+:4 3:=.+=:444229129' 3=:.:3:3 3=9.:: 3=3.42'1 3::.91+94&'29129: 3='.'3&2 3:=.'' 3=2.1:14 3:+.+2'''2129129= 3=:.9'': 3=9.3' 3=2.3:91 3:+.+:243&1291219 3==.+9:' 3=1.=+ 3=3.'+&' 3:'.=22'='=291211 491.1'19 3=3.3' 3=&.1:13 3:=.1=1+=4'291212 492.2=:& 3=4.1= 3=+.1+9: 3=9.9232331291391 493.1214 3=4.=9 3=+.:344 3=9.&4'&33+291392 493.''&3 3=&.&1 3='.33': 3=9.=992+''291393 494.3'+& 3=+.9' 3='.':'9 3=1.1='+3'291394 494.=2:= 3=+.&2 3=:.1:+3 3=1.443'12+29139& 49&.9:'3 3=+.&: 3=:.1'9= 3=1.2&4&:::29139+ 494.4342 3=&.:9 3='.3+2+ 3=9.2=1942=29139' 493.94=& 3=4.2: 3=&.:214 3::.&=3333:29139: 491.=+1+ 3=3.9: 3=4.&'&' 3:'.1:==92329139= 492.31=1 3=3.9' 3=4.''43 3:'.22=&&4:291319 493.:+&9 3=4.34 3=+.1+99 3::.4&&94=1291311 49&.4429 3=&.'' 3='.&'&+ 3:=.'9=21&2291312 49+.&:41 3=+.'2 3=:.&&&1 3=9.&2+1&&'291491 49'.4214 3='.43 3==.22:' 3=1.93&=:'3

291492 49:.9:=' 3='.:& 3==.'329 3=1.3'43''&291493 49:.'9&1 3=:.11 499.1:13 3=1.+&'&24291494 49=.2'1+ 3=:.43 499.&:9& 3=1.::=4=4429149& 49=.4424 3=:.4= 499.&+&2 3=1.+:'=+9329149+ 49:.:933 3='.&2 3==.'&+= 3=9.'19441&29149' 49'.432& 3=&.=9 3=:.21&' 3::.==::'2:29149: 49+.3&:3 3=4.'= 3=+.='99 3:'.&:1+=1329149= 49+.'2=& 3=4.=9 3='.1+:+ 3:'.+9''99'291419 49:.2::= 3=+.1: 3=:.&&43 3::.:1=+&&=291411 49=.:'=3 3='.+= 3==.=+=: 3=9.9+93:4291412 411.934: 3=:.+2 499.=4=3 3=9.:+3=:&2291&91 411.::&4 3==.2+ 491.+22= 3=1.3+9&'3+

291&92 412.&++: 3==.:& 492.12+3 3=1.+:&:142291&93 413.1=&2 499.34 492.&'&& 3=1.=&&=92+291&94 413.''4' 499.=4 492.='4: 3=2.1'4=941291&9& 413.=&'2 499.== 492.=&=4 3=1.=+1'3=+291&9+ 413.339= 3==.'+ 492.1&11 3=9.='13+9:291&9' 411.='2= 3=:.1' 499.+9== 3:=.24'91:3

A!!Table A"tual *.s !redi"ted *alues for (inter/s Method$


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14

A!!Table First di:eren"e model ; t < 41=B5> t

!ate$o,er C$0.95

At&al'al&e(

Pre*ite*'al&e

)orea(t+rror

"##er C$0.95

299:9&

3:+.9=1+:+4 3:+.2= 3:+.33132== 9.94 3:+.&'9='33

299:9+

3:&.92'223: 3:&.3& 3:&.&23'4&= 9.1' 3:+.9292+:

299:9'

3:3.313:'&1 3:3.:2 3:3.='3=94= 9.1& 3:4.+33=34:

299:9:

3:1.:=3+9+' 3:2.&9 3:2.+:4914+ 9.1: 3:3.4'4422&

299:

9=

3:1.:=3:+:

: 3:2.2= 3:2.'=+99&1 9.&1 3:3.+=:1413299:19

3:3.19&'313 3:3.43 3:4.19'29': 9.+: 3:&.19:+:42

299:11

3:4.3++'='& 3:4.=2 3:&.4&:+12+ 9.&4 3:+.&&942''

299:12

3:&.1==':92 3:+.91 3:+.3'&9192 9.3' 3:'.&&92491

299=91

3:&.'&4+3' 3:+.'' 3:'.99''41' 9.24 3::.2+9:4+2


16/19

1&

3299=92

3:+.1+&=22= 3:'.21 3:'.4=233'+ 9.2: 3::.:1:'&23

299=93 3:+.&&92&: 3:'.43 3:'.=4+13: 9.&2 3:=.34291:1299=

94

3:+.=922:1= 3:'.'3 3::.3+4339+ 9.+3 3:=.:2+3'=3

299=9&

3:+.:&9'1:4 3:'.'1 3::.3:2:==2 9.+' 3:=.=1&9:91

299=9+

3:&.='2&1:: 3:+.'4 3:'.&''322 9.:4 3:=.1:212&2

299=9'

3:4.3&&29=4 3:4.:' 3:+.92=4:': 1.1+ 3:'.'93'++2

299=9:

3:3.999+29= 3:3.&9 3:4.'41+943 1.24 3:+.4:2&:''

299=9=

3:3.9&93'+2 3:3.'1 3:4.:&&+91& 1.1& 3:+.++9:2+'

299=19 3:4.391&&2' 3:&.24 3:+.1+::19= 9.=3 3::.93+9+=2299=11

3:&.&=4=2+= 3:+.'' 3:'.&22222& 9.'& 3:=.44=&1:1

299=12

3:+.4&&19:4 3:'.'9 3::.449+2+: 9.'4 3=9.42+14&2

291991

3:'.9332:33 3::.4& 3:=.9'&3+&1 9.+3 3=1.11'44'

291992

3:'.4+4:4'& 3:=.14 3:=.&+1=+': 9.42 3=1.+&=9::

291993

3:'.:+'9243 3:=.4' 3=9.91'''4= 9.&& 3=2.1+:&2&+

291994

3::.234:=:4 3:=.'+ 3=9.43'='43 9.+: 3=2.+419&92

29199&

3::.1==2=&4 3:=.'2 3=9.4&:&4=' 9.'4 3=2.'1':94

29199+

3:'.33+'133 3::.:1 3:=.+&4='=2 9.:4 3=1.='324&1

29199'

3:&.'3333=+ 3:'.21 3::.19=1&1' 9.=9 3=9.4:4=+3=

29199:

3:4.3=12'': 3:+.9= 3:+.:232'4= 9.'3 3:=.2&&2'21

29199=

3:4.4&23+&: 3:+.&3 3:+.=3=2':= 9.41 3:=.42+1=2

291919

3:&.'13:&2: 3::.9= 3::.2&44=&1 9.1+ 3=9.'=&13'&

291911

3:'.91++&4: 3:=.&9 3:=.+9==134 9.11 3=2.2931'2

291912

3:'.::&4=+2 3=9.22 3=9.&39324& 9.31 3=3.1'&1&2=

291191 3::.4'1+&: 3=9.'4 3=1.1+'9+=+ 9.43 3=3.:+24:12


17/19

1+

291192

3::.=19+1+1 3=1.1= 3=1.+&&+'= 9.4' 3=4.499'41=

291193

3:=.31=++9= 3=1.&9 3=2.1134=2= 9.+1 3=4.=9'324=

291194

3:=.+=3=34: 3=1.:: 3=2.&3&+== 9.++ 3=&.3''4+32

29119& 3:=.++&9:1 3=1.=9 3=2.&&:2:11 9.++ 3=&.4&14:1229119+

3::.:9=49&& 3=9.=' 3=1.'&+'1'4 9.'= 3=4.'9492=2

29119'

3:'.21244:: 3:=.94 3=9.212:=+' 1.1' 3=3.213344+

29119:

3:&.:'+3+'& 3:'.'4 3::.=2=92+' 1.1= 3=1.=:1+:&:

29119=

3:&.=4394&1 3::.1& 3:=.94'93'3 9.=9 3=2.1&192=+

291119

3:'.29=''92 3:=.'3 3=9.3+42+93 9.+3 3=3.&1:'&9&

291111

3::.&1'4=31 3=1.19 3=1.'21+:&4 9.+2 3=4.=2&:'''

291112 3:=.3=9=+: 3=1.=9 3=2.+441932 9.'4 3=&.:='23:4291291

3:=.=:1&92& 3=2.42 3=3.2:2:&&1 9.:+ 3=+.&:429''

291292

3=9.424&=&4 3=3.92 3=3.''34'12 9.'& 3='.12234'

291293

3=9.:3'&&': 3=3.&4 3=4.2332=1= 9.+= 3='.+2=92&=

291294

3=1.21&&&9

4 3=3.:9 3=4.+&'&94' 9.:+ 3=:.9==4&=129129&

3=1.1=9+:&4 3=3.+= 3=4.+:29=3+ 9.== 3=:.1'3&91:

29129+

3=9.33=1+43 3=2.++ 3=3.::2&3++ 1.22 3='.42&=9:=

29129'

3::.'4+13'& 3=9.:: 3=2.349'22' 1.4+ 3=&.=3&39'=

29129:

3:'.413':9' 3:=.'' 3=1.9&::&=4 1.2= 3=4.'93=3:1

29129=

3:'.4:3==4' 3=9.3' 3=1.1'::'+: 9.:1 3=4.:'3'&=

2912

19

3::.'&49:3

3 3=1.=+ 3=2.4=:19++ 9.&4 3=+.24212=:291211

3=9.9+&919: 3=3.3' 3=3.:&'&3:4 9.4= 3='.+&99++

291212

3=9.=41&43+ 3=4.1= 3=4.':1=+3 9.&= 3=:.+223:24

291391

3=1.&3&9993 3=4.=9 3=&.422'21+ 9.&2 3==.319442:

291392

3=1.=:9::= 3=&.&1 3=&.=1&3444 9.41 3==.:4='==


18/19

1'

=291393

3=2.3=+&32' 3=+.9' 3=+.3''1'1= 9.31 499.3&':11

291394

3=2.'''9='4 3=+.&2 3=+.:933=1& 9.2: 499.:2=+:&&

29139&

3=2.'&&911& 3=+.&: 3=+.:2==:'1 9.2& 499.=94=+2'

29139+

3=1.=9+49== 3=&.:9 3=+.93243+= 9.23 499.1&:4+3=

29139'

3=9.31+1'&2 3=4.2: 3=4.4=2+2=' 9.21 3=:.++=9:41

29139:

3::.=:+4=2= 3=3.9: 3=3.212''31 9.13 3='.43=9&34

29139=

3:=.9&=2'1= 3=3.9' 3=3.334'='3 9.2+ 3='.+19322:

291319 3=9.331:24 3=4.34 3=4.+&+933: 9.32 3=:.=:9243'

291311 3=1.+4&1292 3=&.'' 3=+.91'4'24 9.2& 499.3:=:24+291312

3=2.&23=33& 3=+.'2 3=+.=43=93' 9.22 491.3+3:'4

291491

3=3.11=&::4 3='.43 3='.&:+++=1 9.1+ 492.9&3'4='

291492

3=3.&+'&==3 3='.:& 3=:.9:12=:' 9.23 492.&=4==:2

291493

3=3.=:&2=13 3=:.11 3=:.&4&132= 9.44 493.194='4&

291494

3=4.3+':3'' 3=:.43 3=:.='33&=2 9.&4 493.&':::9:

29149&

3=4.34':='& 3=:.4= 3==.991=+1+ 9.&1 493.+&+92&'

29149+

3=3.&91&&:4 3='.&2 3=:.29+41:2 9.+= 492.=112''=

29149' 3=1.=13&9& 3=&.=9 3=+.++:+1'' 9.'' 491.423'39&29149:

3=9.&:&=2'' 3=4.'= 3=&.3=9'+'= 9.+9 499.1=&+9:1

29149=

3=9.++9'49+ 3=4.=9 3=&.&14'=:= 9.+1 499.3+::&'1

291419

3=1.=3&2&== 3=+.1: 3=+.:3:9421 9.++ 491.'49:244

291411

3=3.2&94+9' 3='.+= 3=:.2914:'4 9.&1 493.1&2&142

291412

3=4.13111== 3=:.+2 3==.12==2&& 9.&1 494.12:'312

291&91

3=4.'2:&+&4 3==.2+ 3==.''4+='+ 9.&1 494.:29:2=:

291&92 3=&.1':31& 3==.:& 499.2'1334 9.42 49&.3+43&3


19/19

1:

291&93

3=&.&='+=+= 499.34 499.'3'1'4= 9.49 49&.:'++&3

291&94

3=&.=:1::'2 499.=4 491.1+'49: 9.23 49+.3&2=2:=

291&9& 3=&.=+3'2& 499.== 491.1=:91'2 9.21 49+.43239=4

291&9+

3=&.11=2+2+ 3==.'+ 499.4944:9& 9.+4 49&.+:=+=:3

291&9'

3=3.&3392=3 3=:.1' 3=:.:+:+:+: 9.'9 494.2943443

A!!Table V A"tual *.s !redi"ted *alues for AMA Method$

Re*erence$

K1

0loal Mean A"o$pheric CO2 Da"a Ear"h S6$"e Re$earch laora"or6KOnline. A%ailale *"p>>a*"p.cdl.noaa.go%>prod-c"$>"rend$>co2>co2PPgl."".

K2

NOAA>ESRL calc-la"ion o* gloal ean$ Ear"h S6$"e Re$earch laora"or6KOnline. A%ailale

h""p>>888.e$rl.noaa.go%>gd>ccgg>ao-">gloalPean$.h"l.

K3

D. C. Mon"goer6 C. L. @enning$ and M. Q-lahci In"rod-c"ion "o TIe Serie$

Anal6$i$ and ,oreca$"ing Ne8 @er$e6 @ohn !ile6 Son$ Inc. 291&.

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Time series Analysis of Global CO2 Emissions

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