ejemplo desestacionalizacion de la demanda

Parcialmente traducido y adapatado de Heizer/Render –Principles of Operations Management, 5e, and Operations Management, 7e

Víctor Vergara Cuesta 20072-70

Series temporales: Series temporales: desestacionalizardesestacionalizarPaso 1: CPaso 1: Cáálculo de la MM centradalculo de la MM centrada

GrGrááfico de la serie original: estacionalidad de orden 4fico de la serie original: estacionalidad de orden 4Gráfico 2.1.1. Serie de ventas

20000

30000

40000

50000

60000

70000

80000

90000

100000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Periodo (tr imestre)

Ven

tas




Serie originalSerie original

5670020

9280519

5896018

2670017

4788016

6757515

5016014

2761513

6026012

8613011

5200010

233109

438608

732457

537606

293255

558804

49618,75759003

453602

213351

Coef estactrimmmc(4)mmc2(4)mmc3(4)Ventasperiodo (trim)





5670020

9280519

5896018

2670017

4788016

6757515

5016014

2761513

6026012

8613011

5200010

233109

438608

732457

537606

293255

51616,25558804

49618,75759003

453602

1213351






5670020

9280519

5896018

2670017

4788016

6757515

5016014

2761513

6026012

8613011

5200010

233109

438608

732457

537606

53716,25293255

51616,25558804

49618,75759003

453602

213351






5670020

58791,259280519

56586,255896018

50278,752670017

48078,754788016

48307,56757515

51402,55016014

56041,252761513

56501,256026012

554258613011

513255200010

48103,75233109

48543,75438608

50047,5732457

53052,5537606

53716,25293255

51616,25558804

49618,75759003

49618,75453602

1213351






5670020

58791,259280519

56586,255896018

50278,752670017

48078,754788016

48307,56757515

51402,55016014

56041,252761513

56501,256026012

554258613011

513255200010

48103,75233109

48543,75438608

50047,5732457

53052,5537606

53716,25293255

51616,25558804

51616,2549618,75759003

49618,75453602

213351






5670020

58791,259280519

56586,255896018

50278,752670017

48078,754788016

48307,56757515

51402,55016014

56041,252761513

56501,256026012

554258613011

513255200010

48103,75233109

48543,75438608

50047,5732457

53052,5537606

53716,25293255

53716,2551616,25558804

51616,2549618,75759003

49618,75453602

213351






5670020

58791,259280519

58791,2556586,255896018

56586,2550278,752670017

50278,7548078,754788016

48078,7548307,56757515

48307,551402,55016014

51402,556041,252761513

56041,2556501,256026012

56501,25554258613011

55425513255200010

5132548103,75233109

48103,7548543,75438608

48543,7550047,5732457

50047,553052,5537606

53052,553716,25293255

53716,2551616,25558804

50617,551616,2549618,75759003

49618,75453602

213351






5670020

58791,259280519

58791,2556586,255896018

56586,2550278,752670017

50278,7548078,754788016

48078,7548307,56757515

48307,551402,55016014

51402,556041,252761513

56041,2556501,256026012

56501,25554258613011

55425513255200010

5132548103,75233109

48103,7548543,75438608

48543,7550047,5732457

50047,553052,5537606

53052,553716,25293255

52666,2553716,2551616,25558804

50617,551616,2549618,75759003

49618,75453602

213351






5670020

58791,259280519

58791,2556586,255896018

56586,2550278,752670017

50278,7548078,754788016

48078,7548307,56757515

48307,551402,55016014

51402,556041,252761513

56041,2556501,256026012

56501,25554258613011

55425513255200010

5132548103,75233109

48103,7548543,75438608

48543,7550047,5732457

50047,553052,5537606

53384,37553052,553716,25293255

52666,2553716,2551616,25558804

50617,551616,2549618,75759003

49618,75453602

213351




Series temporales: Series temporales: desestacionalizardesestacionalizarPaso 2: CPaso 2: Cáálculo del coeficiente estacional (periodo)lculo del coeficiente estacional (periodo)


45670020

358791,259280519

257688,7558791,2556586,255896018

153432,556586,2550278,752670017

449178,7550278,7548078,754788016

348193,12548078,7548307,56757515

24985548307,551402,55016014

153721,87551402,556041,252761513

456271,2556041,2556501,256026012

355963,12556501,25554258613011

25337555425513255200010

149714,3755132548103,75233109

448323,7548103,7548543,75438608

349295,62548543,7550047,5732457

25155050047,553052,5537606

153384,37553052,553716,25293255

452666,2553716,2551616,255588041,4994814350617,551616,2549618,75759003

249618,75453602

1213351


dividir





45670020

358791,259280519

257688,7558791,2556586,255896018

153432,556586,2550278,752670017

449178,7550278,7548078,754788016

348193,12548078,7548307,56757515

24985548307,551402,55016014

153721,87551402,556041,252761513

456271,2556041,2556501,256026012

355963,12556501,25554258613011

25337555425513255200010

149714,3755132548103,75233109

448323,7548103,7548543,75438608

349295,62548543,7550047,5732457

25155050047,553052,5537606

153384,37553052,553716,25293255

1,06102105452666,2553716,2551616,255588041,4994814350617,551616,2549618,75759003

249618,75453602

1213351


dividir





45670020

358791,259280519

1,02203636257688,7558791,2556586,255896018

0,49969588153432,556586,2550278,752670017

0,97359124449178,7550278,7548078,754788016

1,40217095348193,12548078,7548307,56757515

1,0061177424985548307,551402,55016014

0,51403641153721,87551402,556041,252761513

1,07088433456271,2556041,2556501,256026012

1,53904915355963,12556501,25554258613011

0,9742388825337555425513255200010

0,46887847149714,3755132548103,75233109

0,90762824448323,7548103,7548543,75438608

1,48583165349295,62548543,7550047,5732457

1,04287125155050047,553052,5537606

0,54931804153384,37553052,553716,25293255

1,06102105452666,2553716,2551616,255588041,4994814350617,551616,2549618,75759003

249618,75453602

1213351




Series temporales: Series temporales: desestacionalizardesestacionalizarPaso 3: CPaso 3: Cáálculo del coeficiente estacional (trimestre)lculo del coeficiente estacional (trimestre)


Trimestre 4

Trimestre 3

Trimestre 2

0,507982199Trimestre 1

Coeficientes estacionales

45670020

39280519

1,02203635925896018

0,49969587812670017

0,97359123644788016

1,40217095336757515

1,00611774125016014

0,51403641412761513

1,07088433346026012

1,53904915138613011

0,97423887625200010

0,4688784681233109

0,9076282374438608

1,4858316533732457

1,0428709992537606

0,5493180351293255

1,0610210524558804

1,4994814053759003

2453602

1213351

Serie desesCoef estactrimVentasperiodo (trim)

media





Trimestre 4

Trimestre 3




4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,54931803512932551,06102105245588041,4994814053759003

24536021213351


media





Trimestre 4





4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,54931803512932551,06102105245588041,4994814053759003

24536021213351


media










4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,54931803512932551,06102105245588041,4994814053759003

24536021213351


media



Series temporales: Series temporales: desestacionalizardesestacionalizarPaso 4: Dividir por los coeficientes trimestralesPaso 4: Dividir por los coeficientes trimestrales

Serie sin estacionalidadSerie sin estacionalidad






4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,54931803512932551,06102105245588041,4994814053759003

2453602

41999,50321213351











4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,54931803512932551,06102105245588041,4994814053759003

44852,452453602

41999,50321213351











4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,5493180351293255

1,0610210524558804

51227,25071,4994814053759003

44852,452453602

41999,50321213351











4567002039280519

1,022036359258960180,499695878126700170,973591236447880161,402170953367575151,006117741250160140,514036414127615131,070884333460260121,539049151386130110,974238876252000100,46887846812331090,90762823744386081,48583165337324571,04287099925376060,5493180351293255

55697,24541,0610210524558804

51227,25071,4994814053759003

44852,452453602

41999,50321213351




Series temporales: eliminar el cicloSeries temporales: eliminar el cicloPaso 1: Detectar posible pauta cPaso 1: Detectar posible pauta cííclicaclica







56514,563645670020

62636,956539280519

58300,27451,0220363592589601852560,89690,4996958781267001747723,40930,9735912364478801645608,45151,40217095336757515

49598,7411,0061177412501601454362,14110,5140364141276151360062,92071,0708843334602601258131,79321,5390491513861301151418,15250,9742388762520001045887,43470,468878468123310943716,55660,907628237443860849435,30931,485831653373245753158,45921,042870999253760657728,40080,549318035129325555697,24541,061021052455880451227,25071,4994814053759003

44852,452453602

41999,50321213351




Series temporales: eliminar el cicloSeries temporales: eliminar el cicloPaso 1: Detectar posible patrPaso 1: Detectar posible patróón cn cííclicoclico

Pauta cPauta cííclica de orden 7clica de orden 7Gráfico 2.1.2 Serie desestacionalizada

20000,0

30000,0

40000,0

50000,0

60000,0

70000,0

80000,0

90000,0

100000,0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Periodo (trimestre)

Ven

tas



Series Series temporales:eliminartemporales:eliminar el cicloel cicloPaso 2: CPaso 2: Cáálculo de la m. mlculo de la m. móóvil centrada (m=7)vil centrada (m=7)

56514,5636

62636,9565

58300,2745

52560,8969

47723,4093

45608,4515

49598,741

Ciclo 754362,1411

Ciclo 660062,9207

Ciclo 558131,7932

Ciclo 451418,1525

Ciclo 345887,4347

Ciclo 243716,5566

Ciclo 149435,3093

Coeficientes cíclicos53158,4592

57728,4008

50585,516955697,2454

51227,2507

44852,45

41999,5032

Serie sin c ni eCoef CíclicoCICLOmmc(7)Serie deses




media

56514,5636

62636,9565

58300,2745

52560,8969

47723,4093

45608,4515

49598,741

Ciclo 754362,1411

Ciclo 660062,9207

Ciclo 558131,7932

Ciclo 451418,1525

Ciclo 345887,4347

Ciclo 243716,5566

Ciclo 149435,3093

Coeficientes cíclicos53158,4592

50830,810357728,4008

50585,516955697,2454

51227,2507

44852,45

41999,5032





56514,5636

62636,9565

58300,2745

52560,8969

47723,4093

45608,4515

49598,741

Ciclo 754362,1411

Ciclo 660062,9207

Ciclo 558131,7932

Ciclo 451418,1525

Ciclo 345887,4347

Ciclo 243716,5566

Ciclo 149435,3093

Coeficientes cíclicos50978,665353158,4592

50830,810357728,4008

50585,516955697,2454

51227,2507

44852,45

41999,5032




Series Series temporales:eliminartemporales:eliminar el cicloel cicloPaso 3: CPaso 3: Cáálculo de los coeficientes clculo de los coeficientes cííclicos (periodo)clicos (periodo)

media

656514,5636

562636,9565

458300,2745

353277,613352560,8969

252970,124447723,4093

152602,40545608,4515

752578,336249598,741

Ciclo 7652415,08754362,1411

Ciclo 6552152,804960062,9207

Ciclo 5451882,534358131,7932

Ciclo 4351859,186951418,1525

Ciclo 3251687,232345887,4347

Ciclo 2151353,729543716,5566

Ciclo 1751005,936949435,3093


550830,810357728,4008

1,10105122450585,516955697,2454

351227,2507

244852,45

141999,5032


dividir




media

656514,5636

562636,9565

458300,2745

353277,613352560,8969

252970,124447723,4093

152602,40545608,4515

752578,336249598,741

Ciclo 7652415,08754362,1411

Ciclo 6552152,804960062,9207

Ciclo 5451882,534358131,7932

Ciclo 4351859,186951418,1525

Ciclo 3251687,232345887,4347

Ciclo 2151353,729543716,5566

Ciclo 1751005,936949435,3093


1,13569704550830,810357728,4008

1,10105122450585,516955697,2454

351227,2507

244852,45

141999,5032


dividir



Series Series temporales:eliminartemporales:eliminar el cicloel cicloPaso 4: CPaso 4: Cáálculo de los coeficientes clculo de los coeficientes cííclicos (totales)clicos (totales)

656514,5636

562636,9565

458300,2745

0,98654751353277,613352560,8969

0,90094954252970,124447723,4093

0,86704118152602,40545608,4515

0,94333036752578,336249598,741

Ciclo 71,03714683652415,08754362,1411

Ciclo 61,15167191552152,804960062,9207

Ciclo 51,12045015451882,534358131,7932

Ciclo 40,99149554351859,186951418,1525

Ciclo 30,88779052251687,232345887,4347

Ciclo 20,85128299151353,729543716,5566

0,85916209Ciclo 10,96920696751005,936949435,3093

Coeficientes cíclicos1,04275895650978,665353158,4592

1,13569704550830,810357728,4008

1,10105122450585,516955697,2454

351227,2507

244852,45

141999,5032


Media




656514,5636

562636,9565

458300,2745

0,98654751353277,613352560,8969

0,90094954252970,124447723,4093

0,86704118152602,40545608,4515

0,94333036752578,336249598,741

Ciclo 71,03714683652415,08754362,1411

Ciclo 61,15167191552152,804960062,9207

Ciclo 51,12045015451882,534358131,7932

Ciclo 40,99149554351859,186951418,1525

Ciclo 30,88779052251687,232345887,4347

0,89437003Ciclo 20,85128299151353,729543716,5566

0,85916209Ciclo 10,96920696751005,936949435,3093

Coeficientes cíclicos1,04275895650978,665353158,4592

1,13569704550830,810357728,4008

1,10105122450585,516955697,2454

351227,2507

244852,45

141999,5032


Media



Series temporales: eliminaciSeries temporales: eliminacióón del ciclon del cicloPaso 4: dividir por los Paso 4: dividir por los coefcoef. C. Cííclicosclicos

Serie sin estacionalidad ni cicloSerie sin estacionalidad ni ciclo

Ciclo 3

Ciclo 2

Ciclo 1

656514,5636

562636,9565

458300,2745

0,98654751353277,613352560,8969

0,90094954252970,124447723,4093

0,86704118152602,40545608,4515

0,94333036752578,336249598,741

0,95626866Ciclo 71,03714683652415,08754362,1411

1,03995289Ciclo 61,15167191552152,804960062,9207

1,14368448Ciclo 51,12045015451882,534358131,7932

1,11075069Ciclo 40,99149554351859,186951418,1525

0,989021530,88779052251687,232345887,4347

0,894370030,85128299151353,729543716,5566

0,859162090,96920696751005,936949435,3093

1,04275895650978,665353158,4592

1,13569704550830,810357728,4008

1,10105122450585,516955697,2454

351227,2507

244852,45

48884,26033141999,5032


dividir



Series temporales: eliminaciSeries temporales: eliminacióón del ciclon del cicloPaso 4: dividir por los Paso 4: dividir por los coefcoef. C. Cííclicosclicos

Serie sin estacionalidad ni cicloSerie sin estacionalidad ni ciclo

Ciclo 3

Ciclo 2

Ciclo 1

656514,5636

562636,9565

458300,2745

0,98654751353277,613352560,8969

0,90094954252970,124447723,4093

0,86704118152602,40545608,4515

0,94333036752578,336249598,741

0,95626866Ciclo 71,03714683652415,08754362,1411

1,03995289Ciclo 61,15167191552152,804960062,9207

1,14368448Ciclo 51,12045015451882,534358131,7932

1,11075069Ciclo 40,99149554351859,186951418,1525

0,989021530,88779052251687,232345887,4347

0,894370030,85128299151353,729543716,5566

0,859162090,96920696751005,936949435,3093

1,04275895650978,665353158,4592

1,13569704550830,810357728,4008

1,10105122450585,516955697,2454

351227,2507

50149,76853244852,45

48884,26033141999,5032


dividir



Series temporales: eliminaciSeries temporales: eliminacióón del ciclon del cicloSerie sin estacionalidad ni cicloSerie sin estacionalidad ni ciclo

51931,05014media

54343,38842656514,5636

54767,68966562636,9565

52487,27295458300,2745

53144,340650,98654751353277,613352560,8969

53359,803770,90094954252970,124447723,4093

53084,804430,86704118152602,40545608,4515

51866,95210,94333036752578,336249598,741

0,95626866Ciclo 752273,657681,03714683652415,08754362,14111,03995289Ciclo 652517,037581,15167191552152,804960062,92071,14368448Ciclo 552335,590591,12045015451882,534358131,79321,11075069Ciclo 451988,911380,99149554351859,186951418,15250,98902153Ciclo 351306,990640,88779052251687,232345887,43470,89437003Ciclo 250882,781230,85128299151353,729543716,55660,85916209Ciclo 151696,046530,96920696751005,936949435,3093

Coeficientes cíclicos51116,218771,04275895650978,665353158,459250475,81041,13569704550830,810357728,4008

50143,786611,10105122450585,516955697,2454

51795,89049351227,2507

50149,76853244852,45

48884,26033141999,5032




Series temporales: estimar la tendenciaSeries temporales: estimar la tendenciaPaso 1: detectar posible patrPaso 1: detectar posible patróón n tendencialtendencial

Pauta Pauta tendencialtendencial ascendenteascendenteGráfico 2.1.3 Ventas sin estacionalidad ni ciclo

20000

30000

40000

50000

60000

70000

80000

90000

100000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Periodo (trimestre)

Ven

tas



Series temporales: estimaciSeries temporales: estimacióón de la tendencian de la tendenciaPaso 2: MPaso 2: Méétodo aproximado: ctodo aproximado: cáálculo de los incrementoslculo de los incrementos

media(t)

media (V)

V(1) = a'+b'(t1) es decir, 48884 = a' + 287,32'*1 entonces despejar

media de incrementos absolutos

a' (aprox)10,5

b' (aprox)51931,05014

54343,38842

54767,68966

52487,27295

53144,34065

53359,80377

53084,80443

51866,9521

52273,65768

52517,03758

52335,59059

51988,91138

51306,99064

50882,78123

51696,04653

51116,21877

50475,8104

50143,78661

51795,89049

1265,5082150149,76853

48884,2603348884,26033a'

Tend (aprox)incr absoluSerie sin c ni e (V)b'

restar



Series temporales: estimaciSeries temporales: estimacióón de la tendencian de la tendenciaPaso 3: MPaso 3: Méétodo aproximado: ctodo aproximado: cáálculo de alculo de a’’ y by b’’

a’ = 48884,26 – 287,32a'

b'

a' (aprox)48596,937810,5media(t)

b' (aprox)287,32253151931,05014media (V)

-424,30124354343,38842

2280,4167254767,68966

-657,06769852487,27295

-215,46312253144,34065

274,99934153359,80377

1217,8523353084,80443

-406,70557951866,9521

-243,37990652273,65768

181,44698852517,03758

346,67921352335,59059

681,92073951988,91138

424,20941551306,99064

-813,26530150882,78123

579,82776351696,04653

640,4083751116,21877

332,02378650475,8104

-1652,1038950143,78661

1646,1219651795,89049

1265,5082150149,76853

48884,2603348884,26033V(1) = a'+b'(t1) es decir, 48884 = a' + 287,32'*1 entonces despejar

Tend (aprox)incr absoluSerie sin c ni e (V)media de incrementos absolutos

media



Series temporales: estimaciSeries temporales: estimacióón de la tendencian de la tendenciaPaso 4: MPaso 4: Méétodo aproximado: estimar la tendencia de todo aproximado: estimar la tendencia de

cada periodocada periodo

T(2) = 48596,93 +287,32*2

a'

b'

a' (aprox)48596,937810,5media(t)

b' (aprox)287,32253151931,05014media (V)

-424,30124354343,38842

2280,4167254767,68966

-657,06769852487,27295

-215,46312253144,34065

274,99934153359,80377

1217,8523353084,80443

-406,70557951866,9521

-243,37990652273,65768

181,44698852517,03758

346,67921352335,59059

681,92073951988,91138

424,20941551306,99064

-813,26530150882,78123

579,82776351696,04653

640,4083751116,21877

332,02378650475,8104

-1652,1038950143,78661

1646,1219651795,89049

49171,582861265,5082150149,76853





Series temporales: estimaciSeries temporales: estimacióón de la tendencian de la tendenciaPaso 4: estimar la tendencia de cada periodoPaso 4: estimar la tendencia de cada periodo

T(3) = 48596,93 + 287,32*3

a'

b'

a' (aprox)48596,937810,5media(t)

b' (aprox)287,32253151931,05014media (V)

-424,30124354343,38842

2280,4167254767,68966

-657,06769852487,27295

-215,46312253144,34065

274,99934153359,80377

1217,8523353084,80443

-406,70557951866,9521

-243,37990652273,65768

181,44698852517,03758

346,67921352335,59059

681,92073951988,91138

424,20941551306,99064

-813,26530150882,78123

579,82776351696,04653

640,4083751116,21877

332,02378650475,8104

-1652,1038950143,78661

49458,905391646,1219651795,89049

49171,582861265,5082150149,76853





Series temporales: estimaciSeries temporales: estimacióón de la tendencian de la tendenciaa'

b'

a' (aprox)48596,937810,5media(t)

b' (aprox)287,32253151931,05014media (V)

54343,38842-424,30124354343,38842

54056,065892280,4167254767,68966

53768,74336-657,06769852487,27295

53481,42083-215,46312253144,34065

53194,0983274,99934153359,80377

52906,775761217,8523353084,80443

52619,45323-406,70557951866,9521

52332,1307-243,37990652273,65768

52044,80817181,44698852517,0375851757,48564346,67921352335,59059

51470,16311681,92073951988,91138

51182,84058424,20941551306,99064

50895,51805-813,26530150882,78123

50608,19551579,82776351696,04653

50320,87298640,4083751116,21877

50033,55045332,02378650475,8104

49746,22792-1652,1038950143,78661

49458,905391646,1219651795,89049

49171,582861265,5082150149,76853





Series temporales: predicciSeries temporales: prediccióónnModelo MultiplicativoModelo Multiplicativo

♦ Una vez estimados los coeficientes estacionales, cíclico y la tendencia se procede a la predicción:♦ VPt+1 = (coef. estac)m*(coef. cíclico)m* Tt+1♦ Tt+1 = a’ + b’*(t+1)♦ No hay estacionalidad: coeficiente estacional = 1♦ No hay componente cíclico: coef. cíclico = 1♦ No hay tendencia: tomar como tendencia la media de la serie sin

ciclo ni estacionalidad.♦ Para evaluar la predicción, como es habitual, se calcula MCE.



Series temporales: predicciSeries temporales: prediccióónnModelo multiplicativoModelo multiplicativo

1073908,85MCE

05670054343,388421,039952961,003281456700201454101,7891599,1385754056,065891,143684551,481633392805192072163,8760399,5012653768,743361,110750741,0113162589601828679,720326869,3508853481,420830,989021530,5079821267001722108,207947731,3117153194,09830,8943721,0032814478801651358,404667348,3760752906,775760,859162111,48163336757515529599,9350887,7361752619,453230,956268771,01131625016014954,1912827645,8899952332,13071,039952960,50798212761513

293605,29359718,1464352044,808171,143684551,00328146026012905165,55685178,5981151757,485641,110750741,48163338613011269214,57551481,1410851470,163110,989021531,011316252000103181,4519723253,5956451182,840580,8943720,5079821233109120,53618843870,978950895,518050,859162111,00328144386082375637,3571703,6897350608,195510,956268771,4816333732457699701,88652923,5181550320,872981,039952961,011316253760666018,348129068,0596450033,550451,143684550,5079821293255196282,25655436,9624749746,227921,110750741,003281455880411727483,672475,4586449458,905390,989021531,4816333759003782800,0144475,2401449171,582860,8943721,0113162453602

02133548884,260330,859162110,5079821213351error 2estimacióntendenciacoef. ciclocoef. est.VentasPeriodo

ejemplo desestacionalizacion de la demanda

Documents

series temporales

and operations management

evctor vergara

estacionalidad de orden