ejercicios método box jenkins

7/26/2019 Ejercicios Método Box Jenkins

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0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Producto Interno Bruto per Cápita (precio 2012) Null !pot"e#i#$ PIB "a# a unit root

%&o'enou#$ Con#tant

a' en't"$ 2 (uto*atic + a#ed on -IC, *a&la'.9)

t+-tati#tic Pro/

u'*ented ice!+3uller te#t #tati#tic +1/298580 0/6209

e#t critical alue#$ 1 leel +/60559

5 leel +2/96942

10 leel +2/606857

acinnon (1996) one+#ided p+alue#/

u'*ented ice!+3uller e#t %:uation

ependent ;ariale$ (PIB)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 14$45

-a*ple (ad=u#ted)$ 197 2012

Included o#eration#$ 40 a>ter ad=u#t*ent#

;ariale Coe>>icient -td/ %rror t+-tati#tic Pro/

PIB(+1) +0/091255 0/07027 +1/298580 0/202

(PIB(+1)) +0/055275 0/164607 +0/5801 0/790

(PIB(+2)) 0/72164 0/26789 /046445 0/004

C 476/4568 291/970 1/61868 0/1114

?+#:uared 0/22669 ean dependent ar 286/8905

d=u# ted ?+#:uared 0/162251 -// dependent ar 981/60

-/%/ o> re're# #ion 898/2284 aie in>o criterion 16/57-u* #:uared re#id 2904511 -c"@arA criterion 16/70225

o' lieli"ood +26/667 annan+uinn criter/ 16/5944

3+#tati#tic /517767 urin+at#on #tat 1/867174

Pro(3+#tati#tic) 0/024652

+,000

+2,000

+1,000

0

1,000

2,000

,000

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Pri*era i>erencia del PIB per Cápita (precio# 2012) Null !pot"e#i#$ (PIB) "a# a unit root

%&o'enou#$ Con#tant


t+-tati#tic Pro/

u'*ented ice!+3uller te#t #tati#tic +2/64466 0/090


5 leel +2/96942

10 leel +2/606857



ependent ;ariale$ (PIB,2)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 14$49

-a*ple (ad=u#ted)$ 197 2012



(PIB(+1)) +0/611546 0/214 +2/64466 0/0120

(PIB(+1),2) +0/521965 0/181916 +2/869261 0/0068

C 156/1477 157/660 0/99089 0/284



-/%/ o> re're# #ion 906/5207 aie in>o criterion 16/52914-u* #:uared re#id 0405849 -c"@arA criterion 16/65581


3+#tati#tic 29/80897 urin+at#on #tat 1/822751




PRODUCTO INTERNO BRUDO PER CÁPITA (PRECIOS 2012).

+6,000

+4,000

+2,000

0

2,000

4,000

6,000

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

-e'unda i>erencia del PIB per Cápita (precio# 2012) Null !pot"e#i#$ (PIB,2) "a# a unit root

%&o'enou#$ Con#tant


t+-tati#tic Pro/

u'*ented ice!+3uller te#t #tati# tic +14/40288 0/0000


5 leel +2/96942

10 leel +2/606857



ependent ;ariale$ (PIB,)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 14$5

-a*ple (ad=u#ted)$ 197 2012



(PIB(+1),2) +1/880258 0/10547 +14/40288 0/0000

C +15/87689 154/507 +0/102758 0/9187



-/%/ o> re're##ion 975/2 aie in>o criterion 16/65214

-u* #:uared re#id 614875 -c"@arA criterion 16/7658




ate$ 04<01<16 i*e$ 14$54

-a*ple$ 1970 2015

Included o#eration#$ 41

utocorrelation Partial Correlation C PC +-tat Pro

1 +0/61/// +0/61/// 16/881 0/000

2 0/292 +0 /14/// 20/724 0/000

+0/20/// +0/15/// 22/689 0/000

4 0/027 +0 /24/// 22/724 0/000

5 0/022 +0 /1/// 22/746 0/000

6 +0/05/// +0/16/// 22/892 0/001

7 0/022 +0 /20/// 22/917 0/002

8 +0/04/// +0/26/// 2/04 0/00

9 0/192 0/05 25/082 0/00

1/// +0 /07/// 0 /178 25/418 0/005

1/// +0/07/// +0/09/// 25/726 0/007

1/// 0/017 +0/12/// 25/744 0/012

1/// 0/079 0/198 26/141 0/016

1/// +0/1/// +0/01/// 27/72 0/017

1/// 0/146 0/005 28/81 0/017

1/// +0 /10/// 0 /18 29/651 0/020

1/// 0/017 +0/01/// 29/671 0/029

1/// 0/080 +0/0/// 0/164 0/06

1/// +0 /07/// 0 /019 0/640 0/044

2/// 0/080 0/187 1/184 0/05

ependent ;ariale$ (PIB,2)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 14$56

-a*ple (ad=u#ted)$ 197 2012


Coner'ence ac"ieed a>ter iteration#


C +8/4499 82/1940 +0/102801 0/9187

?(1) +0/880258 0/10547 +6/742826 0/0000




-u* #:uared re#id 614875 -c"@arA criterion 16/7658




Inerted ? ?oot# +/88



ate$ 04<01<16 i*e$ 14$58

-a*ple$ 1970 2015


+#tati#tic proailitie# ad=u#ted >or 1 ? ter*


1 0/016 0/016 0/0115

2 +0/06/// +0/06/// 0/1810 0/671

+0/11/// +0/11/// 0/7984 0/6714 +0/07/// +0/07/// 1/0412 0/791

5 +0/14/// +0/15/// 2/0151 0/7

6 +0/16/// +0/20/// /877 0/640

7 +0/1/// +0/20/// 4/51 0/61

8 0/061 +0 /04/// 4/505 0/717

9 0/244 0/152 7/7552 0/458

1/// +0/02/// +0/11/// 7/7884 0/556

1/// +0/17/// +0/25/// 9/4656 0/489

1/// 0/102 0/042 10/090 0/522

1/// 0 /022 +0/04/// 10/120 0/605

1/// +0/04/// +0/07/// 10/25 0/675

1/// 0/051 0/097 10/41 0/71

1/// +0/11/// +0/15/// 11/02 0/71

1/// 0 /055 +0/05/// 11/520 0/776

1/// 0/100 0/041 12/28 0/78

1/// 0/056 0/109 12/58 0/818

2/// +0/08/// +0/00/// 1/19 0/81

etero#eda#ticit! e#t$ ?C

3+#tati#tic 0/072010 Pro/ 3(1,7) 0/7899

D#?+#:uared 0/075755 Pro/ C"i+-:uare(1) 0/781

e#t %:uation$

ependen t ;ariale$ ?%-IE2

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 15$00-a*ple (ad=u#ted)$ 1974 2012



C 966576/4 55986/7 2/71520 0/0100

?%-IE2(+1) +0/044008 0/16998 +0/26846 0/7899


d=u#ted ?+#:uared +0/02502 -// dependent ar 198951/

-/%/ o> re're# #ion 2014278/ aie in>o criterion 1/9194

-u* #:uared re#id 1/50%F14 -c"@arA criterion 2/00465




2009 1154/84

2010 1581/5

2011 10754/59

2012 12771/59

∆2 PIB

t =(1− L )2 PIB

t

∆2 PIBt =(1−2 L+ L

2 ) PIB t

∆2 PIBt = PIBt −2 PIBt −1+ PIBt −2

∆2 PIBt =−8.4440−0.8803∆

2 PIBt −1+et

^∆

2 PIB

t =−8.4440−0.8803∆

2 PIB

t −1

^∆

2 PIB

2013=−8.4440−0.8803∆

2 PIB

2012

^ PIB2013−2 PIB

2012+ PIB

2011=−8.4440−0.8803 ( PIB2012

−2 PIB2011+ PIB

2010)

^

PIB2013−2∗12771.59+10754.59=−8.4440−0.8803 (12771.59−2∗10754.59+13581.35 )

^ PIB2013=10516.18



0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Producto Interno Bruto per Cápita (precio 2012)PredicciGn con ?I



PRECIO DEL PETRÓLEO CRUDO (PRECIOS 2013).

0

20

40

60

80

100

120

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Precio del PetrGleo Crudo (precio 201) Null !pot"e#i#$ PPC "a# a unit root

%&o'enou#$ Con#tant


t+-tati#tic Pro/



5 leel +2/91404

10 leel +2/60944



ependent ;ariale$ (PPC)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 15$28

-a*ple (ad=u#ted)$ 1971 201



PPC(+1) +0/11610 0/079519 +1/46040 0/1518

C 8/219151 4/672276 1/75912 0/0860




-u* #:uared re#id 9289/906 -c"@arA criterion 8/8800




40

20

0

20

40

60

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Prii*era i>erencia Precico del Petroleo Crudo (precio# 201) Null !pot"e#i#$ (PPC) "a# a unit root

%&o'enou#$ Con#tant


t+-tati#tic Pro/



5 leel +2/9158

10 leel +2/604867



ependent ;ariale$ (PPC,2)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 15$1

-a*ple (ad=u#ted)$ 1972 201



(PPC(+1)) +1/070714 0/158118 +6/7716 0/0000

C 2/452 2/46668 1/00685 0/201

?+#:uared 0/54098 ean dependent ar +0/16028









ate$ 04<01<16 i*e$ 15$5

-a*ple$ 1970 2015



1 +0/07/// +0/07/// 0/2280 0/6

2 +0/11/// +0/11/// 0/8159 0/665

0/085 0/070 1/169 0/760

4 +0/06/// +0/06/// 1/764 0/848

5 0/249 0/264 4/522 0/477

6 0/057 0/072 4/6955 0/58

7 +0/17/// +0/09/// 6/2475 0/5118 0/040 +0 /01/// 6/5 0/610

9 +0/1/// +0/17/// 7/4119 0/594

1/// +0/00/// +0/06/// 7/415 0/686

1/// 0/122 0/047 8/175 0/685

1/// +0/12/// +0/0/// 9/286 0/678

1/// +0/06/// +0/04/// 9/5518 0/70

1/// +0/12/// +0/1/// 10/66 0/714

1/// 0/09 0/068 10/79 0/771

1/// 0 /060 +0/0/// 10/997 0/810

1/// +0/06/// +0/00/// 11/287 0/841

1/// +0/04/// +0/02/// 11/472 0/87

1/// +0/17/// +0/18/// 1/98 0/785

2/// +0/06/// +0/10/// 14/289 0/816

ependent ;ariale$ (PPC)

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 15$7

-a*ple (ad=u#ted)$ 1976 201


Coner'ence ac"ieed a>ter 19 iteration#

Bacca#t$ 1971 1975


C 1/124774 2/250742 0/49975 0/6204

?(5) 0/54614 0/16995 /198609 0/0029

(5) +0/802624 0/0894 +8/974615 0/0000


d=u#ted ?+#:uared 0/16658 -// dependent ar 15/12065

-/%/ o> re're# #ion 1/80428 aie in>o criterion 8/16490





Inerted ? ?oot# /89 /27+/84i /27F/84i +/72F/52i

+/72+/52i

Inerted ?oot# /96 /0+/91i /0F/91i +/77F/56i

+/77+/56i

ate$ 04<01<16 i*e$ 15$8

-a*ple$ 1970 2015

Included o#eration#$ 8+#tati#tic proailitie# ad=u#ted >or 2 ? ter*#


1 +0/04/// +0/04/// 0/0742

2 +0/02/// +0/02/// 0/0958

0/214 0/21 2/099 0/148

4 +0/05/// +0/0/// 2/2149 0/0

5 0/111 0/122 2/7852 0/426

6 0/086 0/049 /196 0/55

7 +0/11/// +0/09/// /7879 0/580

8 0/097 0/048 4/2629 0/641

9 +0/16/// +0/20/// 5/684 0/577

1/// +0/0/// +0/00/// 5/7478 0/675

1/// 0/144 0/089 6/9118 0/646

1/// +0 /05/// 0 /045 7/0890 0/717

1/// +0/06/// +0/06/// 7/61 0/771

1/// +0/15/// +0/20/// 8/751 0/7241/// +0 /00/// 0 /06 8/7589 0/791

1/// 0 /007 +0/04/// 8 /762 0/846

etero#eda#ticit! e#t$ ?C

3+#tati#tic 1/16999 Pro/ 3(1,5) 0/2869D#?+#:uared 1/19625 Pro/ C"i+-:uare(1) 0/2741

e#t %:uation$

ependen t ;ariale$ ?%-IE2

et"od$ ea#t -:uare#

ate$ 04<01<16 i*e$ 15$9

-a*ple (ad=u#ted)$ 1977 201



C 145/725 59/55604 2/446859 0/0196

?%-IE2(+1) 0/18001 0/16671 1/08187 0/2869


d=u#ted ?+#:uared 0/00468 -// dependent ar 1/5887

-/%/ o> re're# #ion 12/855 aie in>o criterion 14/8189-u* #:uared re#id 425705/ -c"@arA criterion 14/46896




2004 47/19000 9/2268

2005 65/0000 18/4079

2006 75/28000 /02427

2007 81/000 /679717

2008 105/200 19/50816

2009 66/97000 +7/17419

2010 84/9000 22/51992

2011 115/2200 26/610

2012 11/100 +2/758765201 108/6600 +2/49798



∆ PPC t =(1− L ) PPC

t

∆ PPC t = PPC

t − PPC

t −1

∆ PPC t =1.1248+0.5436∆ PPC

t −5+e

t −0.8026 e

t −5

∆̂ PPC t =

1.1248+

0.5436∆ PPC

t −5−

0.8026et −5

^

∆ PPC 2014=1.1248+0.5436∆ PPC

2009−0.8026 e

2009

^ PPC 2014− PPC

2013=1.1248+0.5436 ( PPC 2009− PPC 2008 )−0.8026 e

2009

^ PPC 2014−108.66=1.1248+0.5436 (66.97−105.23 )−0.8026 (−37.1742 )

^ PPC 2014=118.8227

0

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120

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Precio del PetrGleo Crudo (precio 201)

PredicciGn con ?I

ejercicios método box jenkins

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