Exemplo Séries Temporais: consumo Morettin e Toloi - formatos ts e tsibble

Licença

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

License: CC BY-SA 4.0

Citação

Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Exemplo Séries Temporais: consumo Morettin e Toloi - formatos ts e tsibble. Campo Grande-MS, Brasil: RStudio/Rpubs, 2021. Disponível em https://rpubs.com/amrofi/exemplo_consumo_morettin_toloi.

1 Introdução

Os dados vem do livro de Morettin e Toloi, Análise de Séries Temporais (https://www.ime.usp.br/~pam/ST.html), consumo no varejo de São Paulo, mensais de Jan/1984 a Out/1996, em https://www.ime.usp.br/~pam/CONSUMO.XLS.

Inicialmente, trabalharemos com o formato ts, conforme o livro de Hyndman (2018), segunda edição. Depois faremos a parte da decomposição e lags com formato tsibble, conforme o livro de Hyndman (2021), terceira edição.

2 Dados em formato ts

#vou puxar os libraries que tenho costume de usar: destaque para o readxl e tseries
library(readxl) # puxar Excel
library(fpp2) # livro Hyndman formato ts - já carrega ggplot2 e forecast
library(fpp3) # livro Hyndman formato tsibble - já carrega fable, feasts e tidyr e dplyr
#library(forecast) # pacote para forecast em formato ts
#library(fable) # pacote para forecast em formato fable
#library(feasts) # pacote para forecast em formato fable
#library(foreign);library(dynlm);library(car);library(lmtest); library(sandwich);library(tseries);
library(lattice) # pacoe gráfico
#dados <- read_excel("CONSUMO morettin R.xlsx", 
#                    sheet = "dados")
dados <-structure(list(obs = structure(c(441763200, 444441600, 446947200, 
449625600, 452217600, 454896000, 457488000, 460166400, 462844800, 
465436800, 468115200, 470707200, 473385600, 476064000, 478483200, 
481161600, 483753600, 486432000, 489024000, 491702400, 494380800, 
496972800, 499651200, 502243200, 504921600, 507600000, 510019200, 
512697600, 515289600, 517968000, 520560000, 523238400, 525916800, 
528508800, 531187200, 533779200, 536457600, 539136000, 541555200, 
544233600, 546825600, 549504000, 552096000, 554774400, 557452800, 
560044800, 562723200, 565315200, 567993600, 570672000, 573177600, 
575856000, 578448000, 581126400, 583718400, 586396800, 589075200, 
591667200, 594345600, 596937600, 599616000, 602294400, 604713600, 
607392000, 609984000, 612662400, 615254400, 617932800, 620611200, 
623203200, 625881600, 628473600, 631152000, 633830400, 636249600, 
638928000, 641520000, 644198400, 646790400, 649468800, 652147200, 
654739200, 657417600, 660009600, 662688000, 665366400, 667785600, 
670464000, 673056000, 675734400, 678326400, 681004800, 683683200, 
686275200, 688953600, 691545600, 694224000, 696902400, 699408000, 
702086400, 704678400, 707356800, 709948800, 712627200, 715305600, 
717897600, 720576000, 723168000, 725846400, 728524800, 730944000, 
733622400, 736214400, 738892800, 741484800, 744163200, 746841600, 
749433600, 752112000, 754704000, 757382400, 760060800, 762480000, 
765158400, 767750400, 770428800, 773020800, 775699200, 778377600, 
780969600, 783648000, 786240000, 788918400, 791596800, 794016000, 
796694400, 799286400, 801964800, 804556800, 807235200, 809913600, 
812505600, 815184000, 817776000, 820454400, 823132800, 825638400, 
828316800, 830908800, 833587200, 836179200, 838857600, 841536000, 
844128000), class = c("POSIXct", "POSIXt"), tzone = "UTC"), t = c(1, 
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 
52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 
68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 
84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 
100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 
113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 
126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 
139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 
152, 153, 154), consumo = c(114.13, 110.79, 116.46, 111.57, 120.66, 
121.15, 121.27, 127.02, 129.04, 133.3, 130.6, 179.39, 120.64, 
114.05, 130.6, 118.26, 145.54, 135.13, 153.35, 159.95, 150.01, 
164.93, 170.37, 220.96, 134.26, 133.11, 147.84, 164.46, 181.86, 
170.44, 186.64, 174.21, 181.62, 194.16, 181.9, 232.01, 140.16, 
130.78, 119.04, 120.73, 129.81, 111.04, 122.75, 133.95, 125.41, 
132.05, 129.54, 176.37, 110.09, 113.25, 124.03, 110.63, 116.72, 
124.63, 124.38, 130.27, 119.87, 115.75, 122.44, 162.43, 105.89, 
115.59, 147, 131.7, 131.32, 136.66, 126.43, 134.88, 128.26, 125.32, 
124.61, 166.11, 116.25, 96.93, 89.27, 101.87, 125.57, 113.31, 
109.39, 127.33, 120.56, 117.73, 113.81, 147.25, 100.15, 95.11, 
112.26, 109.39, 114.2, 113.8, 126.47, 128.36, 115.71, 116.09, 
99.53, 127.27, 87.08, 85.67, 82.02, 98.2, 96.44, 90.23, 97.15, 
95.08, 94, 93, 96.09, 129.21, 75.39, 77.7, 97.34, 84.97, 87.55, 
86.64, 90.52, 95.4, 95.2, 95.8, 101.23, 128.49, 85.63, 82.77, 
96.55, 81.33, 96.91, 83.76, 90.19, 114.84, 108.4, 106.05, 109.71, 
143.86, 99.12, 99.28, 114.75, 106.13, 110.02, 108.07, 112.52, 
113.87, 107.84, 112.12, 112.03, 139.37, 92.24, 93.56, 107.37, 
102.89, 114.78, 102.88, 118.41, 119.23, 117.36, 122.06)), row.names = c(NA, 
-154L), class = c("tbl_df", "tbl", "data.frame"))
attach(dados)
dados2<- matrix(consumo)
dados.ts<- ts(dados2,start=c(1984,1), frequency = 12)
plot(dados.ts,main="Consumo do varejo de Sao Paulo, Morettin e Toloi (2006)",
              xlab="Ano",ylab="Indice")

plot(consumo, main="Consumo do varejo de Sao Paulo, Morettin e Toloi (2006)")

# no pacote lattice
xyplot.ts(dados.ts)

#no ggplot
library(ggplot2)
datas <- seq(as.Date(paste(c(start(dados.ts),1), collapse="/")), 
             by = "month", length.out = length(consumo))
dados.df <- data.frame(date = datas, value = consumo)
ggplot(data=dados.df) + geom_line(aes(date, consumo))

2.1 Seasonal plots do Hyndman:

# semelhante grafico sazonal do consumo do Morettin e Toloi:
seasonplot(dados.ts,ylab="indice", xlab="Ano", 
           main="Seasonal plot: Consumo do varejo de Sao Paulo, Morettin e Toloi (2006)",
           year.labels=TRUE, year.labels.left=TRUE, col=1:20, pch=19)

#Seasonal subseries plots: consumo do Morettin e Toloi:
monthplot(consumo,ylab="indice",xlab="Mes",xaxt="n",
          main="Seasonal deviation plot: Consumo do varejo de Sao Paulo, Morettin e Toloi (2006)")
axis(1,at=1:12,labels=month.abb,cex=0.8)

2.2 Operador Defasagem (Lag)

consumo.ts<- ts(consumo,start=c(1984,1), frequency = 12)
# fazendo lag de 6 meses
# observar que a função lag do stats faz com objeto ts 
# enquanto a do dplyr requer um vetor
cons.l6<-stats::lag(consumo.ts, -6)
plot(consumo.ts, type="o",col = "black",lwd=2,lty=1)
lines(cons.l6,type="o",col = "red",lwd=2,lty=2)
legend("topright",c("Consumo varejo", "Consumo varejo t-6"),lwd=2,lty=1:2,col=c(1,2))

knitr::kable(cbind(consumo.ts,cons.l6))

consumo.ts	cons.l6
114.13	NA
110.79	NA
116.46	NA
111.57	NA
120.66	NA
121.15	NA
121.27	114.13
127.02	110.79
129.04	116.46
133.30	111.57
130.60	120.66
179.39	121.15
120.64	121.27
114.05	127.02
130.60	129.04
118.26	133.30
145.54	130.60
135.13	179.39
153.35	120.64
159.95	114.05
150.01	130.60
164.93	118.26
170.37	145.54
220.96	135.13
134.26	153.35
133.11	159.95
147.84	150.01
164.46	164.93
181.86	170.37
170.44	220.96
186.64	134.26
174.21	133.11
181.62	147.84
194.16	164.46
181.90	181.86
232.01	170.44
140.16	186.64
130.78	174.21
119.04	181.62
120.73	194.16
129.81	181.90
111.04	232.01
122.75	140.16
133.95	130.78
125.41	119.04
132.05	120.73
129.54	129.81
176.37	111.04
110.09	122.75
113.25	133.95
124.03	125.41
110.63	132.05
116.72	129.54
124.63	176.37
124.38	110.09
130.27	113.25
119.87	124.03
115.75	110.63
122.44	116.72
162.43	124.63
105.89	124.38
115.59	130.27
147.00	119.87
131.70	115.75
131.32	122.44
136.66	162.43
126.43	105.89
134.88	115.59
128.26	147.00
125.32	131.70
124.61	131.32
166.11	136.66
116.25	126.43
96.93	134.88
89.27	128.26
101.87	125.32
125.57	124.61
113.31	166.11
109.39	116.25
127.33	96.93
120.56	89.27
117.73	101.87
113.81	125.57
147.25	113.31
100.15	109.39
95.11	127.33
112.26	120.56
109.39	117.73
114.20	113.81
113.80	147.25
126.47	100.15
128.36	95.11
115.71	112.26
116.09	109.39
99.53	114.20
127.27	113.80
87.08	126.47
85.67	128.36
82.02	115.71
98.20	116.09
96.44	99.53
90.23	127.27
97.15	87.08
95.08	85.67
94.00	82.02
93.00	98.20
96.09	96.44
129.21	90.23
75.39	97.15
77.70	95.08
97.34	94.00
84.97	93.00
87.55	96.09
86.64	129.21
90.52	75.39
95.40	77.70
95.20	97.34
95.80	84.97
101.23	87.55
128.49	86.64
85.63	90.52
82.77	95.40
96.55	95.20
81.33	95.80
96.91	101.23
83.76	128.49
90.19	85.63
114.84	82.77
108.40	96.55
106.05	81.33
109.71	96.91
143.86	83.76
99.12	90.19
99.28	114.84
114.75	108.40
106.13	106.05
110.02	109.71
108.07	143.86
112.52	99.12
113.87	99.28
107.84	114.75
112.12	106.13
112.03	110.02
139.37	108.07
92.24	112.52
93.56	113.87
107.37	107.84
102.89	112.12
114.78	112.03
102.88	139.37
118.41	92.24
119.23	93.56
117.36	107.37
122.06	102.89
NA	114.78
NA	102.88
NA	118.41
NA	119.23
NA	117.36
NA	122.06

2.3 Operador Diferença

dcons<-diff(consumo.ts,1)
print(dcons)

##         Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct
## 1984         -3.34   5.67  -4.89   9.09   0.49   0.12   5.75   2.02   4.26
## 1985 -58.75  -6.59  16.55 -12.34  27.28 -10.41  18.22   6.60  -9.94  14.92
## 1986 -86.70  -1.15  14.73  16.62  17.40 -11.42  16.20 -12.43   7.41  12.54
## 1987 -91.85  -9.38 -11.74   1.69   9.08 -18.77  11.71  11.20  -8.54   6.64
## 1988 -66.28   3.16  10.78 -13.40   6.09   7.91  -0.25   5.89 -10.40  -4.12
## 1989 -56.54   9.70  31.41 -15.30  -0.38   5.34 -10.23   8.45  -6.62  -2.94
## 1990 -49.86 -19.32  -7.66  12.60  23.70 -12.26  -3.92  17.94  -6.77  -2.83
## 1991 -47.10  -5.04  17.15  -2.87   4.81  -0.40  12.67   1.89 -12.65   0.38
## 1992 -40.19  -1.41  -3.65  16.18  -1.76  -6.21   6.92  -2.07  -1.08  -1.00
## 1993 -53.82   2.31  19.64 -12.37   2.58  -0.91   3.88   4.88  -0.20   0.60
## 1994 -42.86  -2.86  13.78 -15.22  15.58 -13.15   6.43  24.65  -6.44  -2.35
## 1995 -44.74   0.16  15.47  -8.62   3.89  -1.95   4.45   1.35  -6.03   4.28
## 1996 -47.13   1.32  13.81  -4.48  11.89 -11.90  15.53   0.82  -1.87   4.70
##         Nov    Dec
## 1984  -2.70  48.79
## 1985   5.44  50.59
## 1986 -12.26  50.11
## 1987  -2.51  46.83
## 1988   6.69  39.99
## 1989  -0.71  41.50
## 1990  -3.92  33.44
## 1991 -16.56  27.74
## 1992   3.09  33.12
## 1993   5.43  27.26
## 1994   3.66  34.15
## 1995  -0.09  27.34
## 1996

split.screen(c(1,2))

## [1] 1 2

plot(consumo.ts,type="o",col = "black",lwd=2,lty=1)
legend("topright",c("consumo do varejo SP"),lwd=2,lty=1,col=c(1))
screen(2)
plot(dcons,type="o",col = "red",lwd=2,lty=1)
legend("bottomright",c("dcons"),lwd=2,lty=1,col=c(2))

close.screen(all = TRUE)    # exit split-screen mode

2.4 Decomposição clássica

2.4.1 Modelo aditivo

cons.components.ad<- decompose(consumo.ts, type=c("additive"))
cons.components.ad

## $x
##         Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct
## 1984 114.13 110.79 116.46 111.57 120.66 121.15 121.27 127.02 129.04 133.30
## 1985 120.64 114.05 130.60 118.26 145.54 135.13 153.35 159.95 150.01 164.93
## 1986 134.26 133.11 147.84 164.46 181.86 170.44 186.64 174.21 181.62 194.16
## 1987 140.16 130.78 119.04 120.73 129.81 111.04 122.75 133.95 125.41 132.05
## 1988 110.09 113.25 124.03 110.63 116.72 124.63 124.38 130.27 119.87 115.75
## 1989 105.89 115.59 147.00 131.70 131.32 136.66 126.43 134.88 128.26 125.32
## 1990 116.25  96.93  89.27 101.87 125.57 113.31 109.39 127.33 120.56 117.73
## 1991 100.15  95.11 112.26 109.39 114.20 113.80 126.47 128.36 115.71 116.09
## 1992  87.08  85.67  82.02  98.20  96.44  90.23  97.15  95.08  94.00  93.00
## 1993  75.39  77.70  97.34  84.97  87.55  86.64  90.52  95.40  95.20  95.80
## 1994  85.63  82.77  96.55  81.33  96.91  83.76  90.19 114.84 108.40 106.05
## 1995  99.12  99.28 114.75 106.13 110.02 108.07 112.52 113.87 107.84 112.12
## 1996  92.24  93.56 107.37 102.89 114.78 102.88 118.41 119.23 117.36 122.06
##         Nov    Dec
## 1984 130.60 179.39
## 1985 170.37 220.96
## 1986 181.90 232.01
## 1987 129.54 176.37
## 1988 122.44 162.43
## 1989 124.61 166.11
## 1990 113.81 147.25
## 1991  99.53 127.27
## 1992  96.09 129.21
## 1993 101.23 128.49
## 1994 109.71 143.86
## 1995 112.03 139.37
## 1996              
## 
## $seasonal
##               Jan          Feb          Mar          Apr          May
## 1984 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1985 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1986 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1987 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1988 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1989 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1990 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1991 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1992 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1993 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1994 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1995 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1996 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
##               Jun          Jul          Aug          Sep          Oct
## 1984  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1985  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1986  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1987  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1988  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1989  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1990  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1991  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1992  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1993  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1994  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1995  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1996  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
##               Nov          Dec
## 1984   2.99663431  41.48548848
## 1985   2.99663431  41.48548848
## 1986   2.99663431  41.48548848
## 1987   2.99663431  41.48548848
## 1988   2.99663431  41.48548848
## 1989   2.99663431  41.48548848
## 1990   2.99663431  41.48548848
## 1991   2.99663431  41.48548848
## 1992   2.99663431  41.48548848
## 1993   2.99663431  41.48548848
## 1994   2.99663431  41.48548848
## 1995   2.99663431  41.48548848
## 1996                          
## 
## $trend
##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1984        NA        NA        NA        NA        NA        NA 126.55292
## 1985 133.40667 136.11542 138.36125 140.55292 143.52792 146.91708 149.21667
## 1986 164.01542 165.99667 167.90792 170.44292 172.14125 173.08208 173.78833
## 1987 155.84625 151.50667 147.48708 142.55708 137.78750 133.28750 129.71625
## 1988 126.68625 126.60083 126.21667 125.30667 124.33167 123.45500 122.69917
## 1989 128.69375 128.97125 129.51292 130.26125 130.75042 130.99417 131.57917
## 1990 120.02417 118.99958 118.36417 117.72708 116.96083 115.72500 114.26833
## 1991 115.79333 116.54792 116.38875 116.11833 115.45500 114.02750 112.65042
## 1992 103.20083 100.59250  98.30125  96.43458  95.32917  95.26667  94.86042
## 1993  92.56708  92.30417  92.36750  92.53417  92.86500  93.04917  93.44583
## 1994  94.45208  95.24833  96.60833  97.58542  98.36583  99.35958 100.56208
## 1995 110.13208 111.02208 110.95833 111.18792 111.53750 111.44708 110.97333
## 1996 109.53458 110.00333 110.62333 111.43417        NA        NA        NA
##            Aug       Sep       Oct       Nov       Dec
## 1984 126.96000 127.68500 128.55292 129.86833 131.48750
## 1985 150.57833 152.09083 154.73417 158.17250 161.15708
## 1986 173.93708 172.64000 169.61792 165.62708 160.98333
## 1987 127.73292 127.21042 126.99750 126.03125 126.05208
## 1988 122.62167 123.67625 125.51125 126.99750 128.10708
## 1989 131.23333 128.05042 124.40208 122.91958 121.70708
## 1990 113.52167 114.40375 115.67500 115.51458 115.06125
## 1991 111.71250 110.05917 108.33292 107.12667 105.40458
## 1992  94.04125  94.34750  94.43458  93.51292  92.99292
## 1993  94.08375  94.26208  94.07750  94.31583  94.58583
## 1994 101.81208 103.25833 105.05000 106.62958 108.18875
## 1995 110.44833 109.90250 109.46000 109.52333 109.50542
## 1996        NA        NA        NA                    
## 
## $random
##               Jan          Feb          Mar          Apr          May
## 1984           NA           NA           NA           NA           NA
## 1985   2.82614347  -4.08458570  -0.70385653 -12.18927320   2.26676847
## 1986 -14.16260653 -14.90583570 -13.01052320   4.12072680   9.97343513
## 1987  -0.09343987  -2.74583570 -21.38968987 -11.72343987  -7.72281487
## 1988  -1.00343987   4.62999763   4.87072680  -4.57302320  -7.35698153
## 1989  -7.21093987   4.59958097  24.54447680  11.54239347   0.82426847
## 1990  11.81864347  -4.08875237 -22.03677320  -5.75343987   8.86385180
## 1991  -0.05052320  -3.45708570   2.92864347   3.37531013  -1.00031487
## 1992  -0.52802320   3.05833097  -9.22385653  11.86906013   1.36551847
## 1993  -1.58427320   3.37666430  12.02989347   2.53947680  -5.06031487
## 1994   6.77072680   5.50249763   6.99906013  -6.15177320  -1.20114820
## 1995   4.58072680   6.23874763  10.84906013   5.04572680  -1.26281487
## 1996  -1.70177320   1.53749763   3.80406013   1.55947680           NA
##               Jun          Jul          Aug          Sep          Oct
## 1984           NA  -5.37340515  -6.34132181  -0.20104403   0.59767124
## 1985  -6.09705729   4.04284485   2.97034485  -3.63687737   6.04642124
## 1986   3.04794271  12.76117819  -6.12840515   7.42395597  20.39267124
## 1987 -16.55747396  -7.05673848  -0.18423848  -3.35646070   0.90308791
## 1988   6.86502604   1.59034485   1.24701152  -5.36229403 -13.91066209
## 1989  11.35585938  -5.23965515  -2.75465515  -1.34646070  -3.23149542
## 1990   3.27502604  -4.96882181   7.40701152   4.60020597  -2.09441209
## 1991   5.46252604  13.72909485  10.24617819   4.09478930   3.60767124
## 1992   0.65335938   2.19909485  -5.36257181  -1.90354403  -5.58399542
## 1993  -0.71914062  -3.01632181  -5.08507181  -0.61812737  -2.42691209
## 1994  -9.90955729 -10.46257181   6.62659485   3.58562263  -3.14941209
## 1995   2.31294271   1.45617819  -2.97965515  -3.61854403  -1.48941209
## 1996           NA           NA           NA           NA           NA
##               Nov          Dec
## 1984  -2.26496765   6.41701152
## 1985   9.20086569  18.31742819
## 1986  13.27628235  29.54117819
## 1987   0.51211569   8.83242819
## 1988  -7.55413431  -7.16257181
## 1989  -1.30621765   2.91742819
## 1990  -4.70121765  -9.29673848
## 1991 -10.59330098 -19.62007181
## 1992  -0.41955098  -5.26840515
## 1993   3.91753235  -7.58132181
## 1994   0.08378235  -5.81423848
## 1995  -0.48996765 -11.62090515
## 1996                          
## 
## $figure
##  [1] -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
##  [6]  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## [11]   2.99663431  41.48548848
## 
## $type
## [1] "additive"
## 
## attr(,"class")
## [1] "decomposed.ts"

# pega os valores estimados do componente sazonal
cons.saz.ad<-cons.components.ad$seasonal 
print(cons.saz.ad)  # Indice Estacional (IE) aditivo

##               Jan          Feb          Mar          Apr          May
## 1984 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1985 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1986 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1987 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1988 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1989 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1990 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1991 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1992 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1993 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1994 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1995 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
## 1996 -15.59281013 -17.98083097  -7.05739347 -10.10364347  -0.25468513
##               Jun          Jul          Aug          Sep          Oct
## 1984  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1985  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1986  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1987  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1988  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1989  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1990  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1991  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1992  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1993  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1994  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1995  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
## 1996  -5.69002604   0.09048848   6.40132181   1.55604403   4.14941209
##               Nov          Dec
## 1984   2.99663431  41.48548848
## 1985   2.99663431  41.48548848
## 1986   2.99663431  41.48548848
## 1987   2.99663431  41.48548848
## 1988   2.99663431  41.48548848
## 1989   2.99663431  41.48548848
## 1990   2.99663431  41.48548848
## 1991   2.99663431  41.48548848
## 1992   2.99663431  41.48548848
## 1993   2.99663431  41.48548848
## 1994   2.99663431  41.48548848
## 1995   2.99663431  41.48548848
## 1996

plot(cons.components.ad)

plot(cons.saz.ad)

2.4.2 Modelo multiplicativo

cons.components.mu<- decompose(consumo.ts, type=c("multiplicative"))
cons.components.mu

## $x
##         Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct
## 1984 114.13 110.79 116.46 111.57 120.66 121.15 121.27 127.02 129.04 133.30
## 1985 120.64 114.05 130.60 118.26 145.54 135.13 153.35 159.95 150.01 164.93
## 1986 134.26 133.11 147.84 164.46 181.86 170.44 186.64 174.21 181.62 194.16
## 1987 140.16 130.78 119.04 120.73 129.81 111.04 122.75 133.95 125.41 132.05
## 1988 110.09 113.25 124.03 110.63 116.72 124.63 124.38 130.27 119.87 115.75
## 1989 105.89 115.59 147.00 131.70 131.32 136.66 126.43 134.88 128.26 125.32
## 1990 116.25  96.93  89.27 101.87 125.57 113.31 109.39 127.33 120.56 117.73
## 1991 100.15  95.11 112.26 109.39 114.20 113.80 126.47 128.36 115.71 116.09
## 1992  87.08  85.67  82.02  98.20  96.44  90.23  97.15  95.08  94.00  93.00
## 1993  75.39  77.70  97.34  84.97  87.55  86.64  90.52  95.40  95.20  95.80
## 1994  85.63  82.77  96.55  81.33  96.91  83.76  90.19 114.84 108.40 106.05
## 1995  99.12  99.28 114.75 106.13 110.02 108.07 112.52 113.87 107.84 112.12
## 1996  92.24  93.56 107.37 102.89 114.78 102.88 118.41 119.23 117.36 122.06
##         Nov    Dec
## 1984 130.60 179.39
## 1985 170.37 220.96
## 1986 181.90 232.01
## 1987 129.54 176.37
## 1988 122.44 162.43
## 1989 124.61 166.11
## 1990 113.81 147.25
## 1991  99.53 127.27
## 1992  96.09 129.21
## 1993 101.23 128.49
## 1994 109.71 143.86
## 1995 112.03 139.37
## 1996              
## 
## $seasonal
##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1984 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1985 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1986 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1987 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1988 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1989 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1990 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1991 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1992 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1993 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1994 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1995 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1996 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
##            Aug       Sep       Oct       Nov       Dec
## 1984 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1985 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1986 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1987 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1988 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1989 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1990 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1991 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1992 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1993 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1994 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1995 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1996 1.0562029 1.0136767 1.0299569                    
## 
## $trend
##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1984        NA        NA        NA        NA        NA        NA 126.55292
## 1985 133.40667 136.11542 138.36125 140.55292 143.52792 146.91708 149.21667
## 1986 164.01542 165.99667 167.90792 170.44292 172.14125 173.08208 173.78833
## 1987 155.84625 151.50667 147.48708 142.55708 137.78750 133.28750 129.71625
## 1988 126.68625 126.60083 126.21667 125.30667 124.33167 123.45500 122.69917
## 1989 128.69375 128.97125 129.51292 130.26125 130.75042 130.99417 131.57917
## 1990 120.02417 118.99958 118.36417 117.72708 116.96083 115.72500 114.26833
## 1991 115.79333 116.54792 116.38875 116.11833 115.45500 114.02750 112.65042
## 1992 103.20083 100.59250  98.30125  96.43458  95.32917  95.26667  94.86042
## 1993  92.56708  92.30417  92.36750  92.53417  92.86500  93.04917  93.44583
## 1994  94.45208  95.24833  96.60833  97.58542  98.36583  99.35958 100.56208
## 1995 110.13208 111.02208 110.95833 111.18792 111.53750 111.44708 110.97333
## 1996 109.53458 110.00333 110.62333 111.43417        NA        NA        NA
##            Aug       Sep       Oct       Nov       Dec
## 1984 126.96000 127.68500 128.55292 129.86833 131.48750
## 1985 150.57833 152.09083 154.73417 158.17250 161.15708
## 1986 173.93708 172.64000 169.61792 165.62708 160.98333
## 1987 127.73292 127.21042 126.99750 126.03125 126.05208
## 1988 122.62167 123.67625 125.51125 126.99750 128.10708
## 1989 131.23333 128.05042 124.40208 122.91958 121.70708
## 1990 113.52167 114.40375 115.67500 115.51458 115.06125
## 1991 111.71250 110.05917 108.33292 107.12667 105.40458
## 1992  94.04125  94.34750  94.43458  93.51292  92.99292
## 1993  94.08375  94.26208  94.07750  94.31583  94.58583
## 1994 101.81208 103.25833 105.05000 106.62958 108.18875
## 1995 110.44833 109.90250 109.46000 109.52333 109.50542
## 1996        NA        NA        NA                    
## 
## $random
##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1984        NA        NA        NA        NA        NA        NA 0.9598431
## 1985 1.0366261 0.9814219 0.9957447 0.9164827 1.0178221 0.9661237 1.0294031
## 1986 0.9383618 0.9392454 0.9288382 1.0510118 1.0604205 1.0343623 1.0757297
## 1987 1.0309464 1.0110610 0.8514482 0.9224709 0.9456365 0.8750710 0.9478643
## 1988 0.9961546 1.0477783 1.0366433 0.9616677 0.9423005 1.0603938 1.0153785
## 1989 0.9432045 1.0497723 1.1973567 1.1012776 1.0081234 1.0958289 0.9624586
## 1990 1.1102803 0.9540707 0.7956180 0.9425322 1.0776341 1.0284764 0.9588944
## 1991 0.9914613 0.9558493 1.0174974 1.0261317 0.9928399 1.0483008 1.1245370
## 1992 0.9672608 0.9975414 0.8801973 1.1091875 1.0154471 0.9948630 1.0258334
## 1993 0.9336101 0.9859786 1.1117098 1.0002067 0.9463025 0.9780459 0.9702947
## 1994 1.0392565 1.0178490 1.0542825 0.9078041 0.9888950 0.8854829 0.8983450
## 1995 1.0317056 1.0474183 1.0909681 1.0396971 0.9900944 1.0185673 1.0156174
## 1996 0.9653313 0.9962129 1.0238952 1.0057292        NA        NA        NA
##            Aug       Sep       Oct       Nov       Dec
## 1984 0.9472352 0.9969767 1.0067674 0.9835182 1.0189520
## 1985 1.0057138 0.9730109 1.0348905 1.0534275 1.0240100
## 1986 0.9482733 1.0378218 1.1113964 1.0740979 1.0763803
## 1987 0.9928703 0.9725457 1.0095415 1.0052363 1.0449960
## 1988 1.0058422 0.9561471 0.8954045 0.9429109 0.9469631
## 1989 0.9730968 0.9881225 0.9780784 0.9914580 1.0193419
## 1990 1.0619513 1.0395934 0.9881630 0.9635763 0.9557981
## 1991 1.0878790 1.0371587 1.0404359 0.9086548 0.9017923
## 1992 0.9572457 0.9828743 0.9561650 1.0049608 1.0377344
## 1993 0.9600335 0.9963237 0.9886912 1.0497047 1.0145727
## 1994 1.0679391 1.0356302 0.9801568 1.0062619 0.9931113
## 1995 0.9761191 0.9679944 0.9945087 1.0003920 0.9505471
## 1996        NA        NA        NA                    
## 
## $figure
##  [1] 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
##  [8] 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 
## $type
## [1] "multiplicative"
## 
## attr(,"class")
## [1] "decomposed.ts"

# pega os valores estimados do componente sazonal
cons.saz.mu<-cons.components.mu$seasonal 
print(cons.saz.mu)  # Indice Estacional (IE) multiplicativo

##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1984 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1985 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1986 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1987 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1988 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1989 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1990 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1991 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1992 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1993 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1994 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1995 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
## 1996 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457
##            Aug       Sep       Oct       Nov       Dec
## 1984 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1985 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1986 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1987 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1988 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1989 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1990 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1991 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1992 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1993 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1994 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1995 1.0562029 1.0136767 1.0299569 1.0224863 1.3389367
## 1996 1.0562029 1.0136767 1.0299569

plot(cons.components.mu)

plot(cons.saz.mu)

3 Dados em formato tsibble

Usaremos o pacote tsibble para converter de ts em tsibble. Outra opção é carregar novamente a série a partir dos dados básicos. Ver também https://rpubs.com/amrofi/decomposicao_time_series.

Primeiro, converterei para tsibble.

library(readxl) # puxar Excel
library(fpp2) # livro Hyndman formato ts - já carrega ggplot2 e forecast
library(fpp3) # livro Hyndman formato tsibble - já carrega fable, feasts e tidyr e dplyr
dados_tsbl <- as_tsibble(dados, key = t, index = obs)

Farei as médias móveis de 12 meses em fim de período e de 3 meses centrada.

dados_MA <- dados_tsbl %>%
  mutate(
    `3-MA` = slider::slide_dbl(consumo, mean,
                .before = 1, .after = 1, .complete = TRUE)
  )
dados_MA <- dados_MA %>%
  mutate(
    `12-MA` = slider::slide_dbl(consumo, mean,
                .before = 11, .complete = TRUE)
  )
attach(dados_MA)

## The following objects are masked from dados:
## 
##     consumo, obs, t

dados_MA[3:5] %>%
  plot.ts(main="Consumo de Morettin e Toloi, Médias Móveis de 3 e 12 meses",
          plot.type = c("single"),
          col=c("blue","red","black"),
          lty = 1:3)

dados_MA[3:5] %>%
  plot.ts(main="Consumo de Morettin e Toloi, Médias Móveis de 3 e 12 meses",
          plot.type = c("multiple"),
          col=c("blue"),
          lty = 1)

3.1 Obtendo a Sazonalidade

Farei essa parte com o formato ts apenas para ilustrar, pois em geral a operação será automatizada.

# calculo manual do IE
# multiplicativo
# farei com a série em formato ts
consumo.ts<-ts(dados_MA$consumo,start = c(1984,1),frequency = 12)
cons12.ma<-forecast::ma(consumo.ts,12)
S<-100*consumo.ts/cons12.ma
print(S)

##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1984        NA        NA        NA        NA        NA        NA  95.82553
## 1985  90.43026  83.78919  94.39059  84.13913 101.40188  91.97705 102.77002
## 1986  81.85816  80.18836  88.04826  96.48978 105.64580  98.47351 107.39501
## 1987  89.93479  86.31963  80.71215  84.68888  94.21029  83.30864  94.62962
## 1988  86.89972  89.45439  98.26753  88.28740  93.87793 100.95176 101.36988
## 1989  82.28061  89.62463 113.50219 101.10451 100.43563 104.32526  96.08664
## 1990  96.85549  81.45407  75.41978  86.53064 107.36073  97.91316  95.73081
## 1991  86.49030  81.60592  96.45262  94.20562  98.91300  99.80049 112.26767
## 1992  84.37916  85.16540  83.43739 101.83069 101.16526  94.71309 102.41363
## 1993  81.44364  84.17822 105.38339  91.82554  94.27664  93.11206  96.86895
## 1994  90.65973  86.89916  99.93962  83.34237  98.51998  84.29987  89.68589
## 1995  90.00102  89.42365 103.41720  95.45102  98.63947  96.96979 101.39373
## 1996  84.21085  85.05197  97.05909  92.33254        NA        NA        NA
##            Aug       Sep       Oct       Nov       Dec
## 1984 100.04726 101.06121 103.69271 100.56339 136.43122
## 1985 106.22378  98.63185 106.58926 107.71152 137.10846
## 1986 100.15691 105.20158 114.46904 109.82503 144.12051
## 1987 104.86725  98.58469 103.97842 102.78403 139.91835
## 1988 106.23734  96.92241  92.22281  96.41135 126.79236
## 1989 102.77877 100.16367 100.73786 101.37522 136.48343
## 1990 112.16361 105.38116 101.77653  98.52436 127.97532
## 1991 114.90209 105.13436 107.16041  92.90871 120.74428
## 1992 101.10457  99.63168  98.48087 102.75586 138.94607
## 1993 101.39902 100.99501 101.83094 107.33087 135.84487
## 1994 112.79604 104.97942 100.95193 102.88889 132.97131
## 1995 103.09798  98.12334 102.43011 102.28871 127.27224
## 1996        NA        NA        NA

# tapply(S, cycle(S), mean) #fazendo assim eu nao consigo todos os meses
# farei uma janela para 1984,7 a 1996,4
Sw<-window(S, start=c(1984,7),end=c(1996,4))
IEM<-tapply(Sw, cycle(Sw), mean) # IE medio mensal
# agora somo todos os IEM e faço o IE
IEM.total<-sum(IEM)
IE<-12*IEM/IEM.total
IE

##         1         2         3         4         5         6         7         8 
## 0.8723518 0.8537530 0.9479397 0.9180656 0.9962633 0.9520214 0.9983457 1.0562029 
##         9        10        11        12 
## 1.0136767 1.0299569 1.0224863 1.3389367

plot(IE, type = "o")

# pega os valores estimados do componente sazonal
cons.saz.mu<-cons.components.mu$seasonal 
knitr::kable(cbind(IE=IE,CONS.SAZ=unique(cons.saz.mu)))

IE	CONS.SAZ
0.8723518	0.8723518
0.8537530	0.8537530
0.9479397	0.9479397
0.9180656	0.9180656
0.9962633	0.9962633
0.9520214	0.9520214
0.9983457	0.9983457
1.0562029	1.0562029
1.0136767	1.0136767
1.0299569	1.0299569
1.0224863	1.0224863
1.3389367	1.3389367

# CONFERE

3.2 Seasonal plots

as_tsibble(consumo.ts) %>%
  gg_season( labels = "both") +
  labs(y = "Índice",
       title = "Seasonal plot: varejo de SP")

## Plot variable not specified, automatically selected `y = value`

3.3 Decomposição com tsibble

3.3.1 Modelo Aditivo

decomp.ad<-as_tsibble(consumo.ts) %>%
  model(classical_decomposition(value,type="additive")) %>%
  components()
decomp.ad

decomp.ad %>% 
  autoplot()+
  labs(title = "Decomposição clássica aditiva do consumo do varejo de SP")

## Warning: Removed 6 rows containing missing values (`geom_line()`).

3.3.2 Modelo Multiplicativo

decomp.mu<-as_tsibble(consumo.ts) %>%
  model(classical_decomposition(value,type="mult")) %>%
  components()
decomp.mu

decomp.mu %>% 
  autoplot()+
  labs(title = "Decomposição clássica multiplicativa do consumo do varejo de SP")

## Warning: Removed 6 rows containing missing values (`geom_line()`).

4 Referências

HYNDMAN, Rob. (2018). fpp2: Data for “Forecasting: Principles and Practice” (2nd Edition). R package version 2.3. Disponível em: https://CRAN.R-project.org/package=fpp2.

HYNDMAN, R.J., & ATHANASOPOULOS, G. (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. Disponível em: https://otexts.com/fpp2/. Accessed on 27 Mar 2023.

HYNDMAN, R.J., & ATHANASOPOULOS, G. (2021) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. Disponível em: https://otexts.com/fpp3/.

MORETTIN, Pedro A.; TOLOI, Clélia M.C. Análise de Séries Temporais. São paulo: Editora Edgard Blücher, 2004. https://www.ime.usp.br/~pam/st/