Introdução
Pacotes necessários
library(readxl)
library(forecast)
library(tidyverse)
library(xts)
Importação dos dados
dados <- read_excel("dados.xlsx")
head(dados)
## # A tibble: 6 x 4
## Data Ouro Boi Ferro
## <dttm> <dbl> <dbl> <dbl>
## 1 2021-08-01 00:00:00 1790. 124. 161.
## 2 2021-07-01 00:00:00 1813. 122. 212.
## 3 2021-06-01 00:00:00 1772. 122. 215.
## 4 2021-05-01 00:00:00 1905. 116. 206.
## 5 2021-04-01 00:00:00 1770. 116 180.
## 6 2021-03-01 00:00:00 1718. 121. 167.
# Colocando data em ordem crescente:
dados <- arrange(dados,Data)
head(dados)
## # A tibble: 6 x 4
## Data Ouro Boi Ferro
## <dttm> <dbl> <dbl> <dbl>
## 1 2011-01-01 00:00:00 1334. 109. 180.
## 2 2011-02-01 00:00:00 1409. 110. 187.
## 3 2011-03-01 00:00:00 1439. 122. 174
## 4 2011-04-01 00:00:00 1556 117. 179.
## 5 2011-05-01 00:00:00 1536. 104. 169.
## 6 2011-06-01 00:00:00 1502. 113. 164
Análise geral
Gerar algumas visualizações
boi <- xts(dados$Boi,order.by = dados$Data)
ouro <- xts(dados$Ouro,order.by = dados$Data)
ferro <- xts(dados$Ferro,order.by = dados$Data)
dadosxts <- xts(dados[,-1],order.by = dados$Data )
plot(boi,main = "Preço fechamento mensal do Boi",
col="blue")
plot(ouro,main = "Preço fechamento mensal do Ouro",
col="blue")
plot(ferro,main = "Preço fechamento mensal do Min. Ferro",
col="blue")
plot(dadosxts,legend.loc = "top",
main = "Preço de todos")
Algumas estatísticas
summary(dados)
## Data Ouro Boi Ferro
## Min. :2011-01-01 00:00:00 Min. :1121 Min. : 90.0 Min. : 39.58
## 1st Qu.:2013-08-24 06:00:00 1st Qu.:1295 1st Qu.:112.9 1st Qu.: 68.35
## Median :2016-04-16 00:00:00 Median :1387 Median :121.4 Median : 92.59
## Mean :2016-04-16 04:52:30 Mean :1463 Mean :123.8 Mean :103.62
## 3rd Qu.:2018-12-08 18:00:00 3rd Qu.:1622 3rd Qu.:129.2 3rd Qu.:135.57
## Max. :2021-08-01 00:00:00 Max. :2017 Max. :169.5 Max. :214.55
hist(dados$Ouro,main = "Histograma preço ouro",xlab="")
hist(dados$Boi,main = "Histograma preço boi",xlab="")
hist(dados$Ferro,main = "Histograma preço Min. Ferro",xlab="")
boxplot(dados$Ouro,main = "boxplot preço ouro",xlab="")
boxplot(dados$Boi,main = "boxplot preço boi",xlab="")
boxplot(dados$Ferro,main = "boxplot preço Min. Ferro",xlab="")
Gerando séries temporais
boi <- ts(dados$Boi,start = c(2011,1),frequency = 12)
ouro <- ts(dados$Ouro,start = c(2011,1),frequency = 12)
ferro <- ts(dados$Ferro,start = c(2011,1),frequency = 12)
Decomposição de série temporal
plot(decompose(boi))
plot(decompose(ouro))
plot(decompose(ferro))
Autoarima - Previsão
modelo_ouro <- auto.arima(ouro)
modelo_ferro <- auto.arima(ferro)
modelo_boi <- auto.arima(boi)
previsao_ouro <- forecast(modelo_ouro,h=24)
previsao_ouro
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Sep 2021 1790.15 1699.297 1881.003 1651.202 1929.098
## Oct 2021 1790.15 1661.665 1918.635 1593.648 1986.652
## Nov 2021 1790.15 1632.788 1947.512 1549.486 2030.814
## Dec 2021 1790.15 1608.444 1971.856 1512.255 2068.045
## Jan 2022 1790.15 1586.997 1993.303 1479.454 2100.846
## Feb 2022 1790.15 1567.607 2012.693 1449.799 2130.501
## Mar 2022 1790.15 1549.776 2030.524 1422.529 2157.771
## Apr 2022 1790.15 1533.179 2047.121 1397.147 2183.153
## May 2022 1790.15 1517.591 2062.709 1373.307 2206.993
## Jun 2022 1790.15 1502.848 2077.452 1350.759 2229.541
## Jul 2022 1790.15 1488.825 2091.475 1329.313 2250.987
## Aug 2022 1790.15 1475.426 2104.874 1308.821 2271.479
## Sep 2022 1790.15 1462.575 2117.725 1289.167 2291.133
## Oct 2022 1790.15 1450.209 2130.091 1270.256 2310.044
## Nov 2022 1790.15 1438.278 2142.022 1252.008 2328.292
## Dec 2022 1790.15 1426.738 2153.562 1234.360 2345.940
## Jan 2023 1790.15 1415.554 2164.746 1217.254 2363.046
## Feb 2023 1790.15 1404.694 2175.606 1200.645 2379.655
## Mar 2023 1790.15 1394.131 2186.169 1184.491 2395.809
## Apr 2023 1790.15 1383.843 2196.457 1168.757 2411.543
## May 2023 1790.15 1373.809 2206.491 1153.412 2426.888
## Jun 2023 1790.15 1364.012 2216.288 1138.428 2441.872
## Jul 2023 1790.15 1354.435 2225.865 1123.781 2456.519
## Aug 2023 1790.15 1345.063 2235.237 1109.449 2470.851
plot(previsao_ouro)
previsao_ferro <- forecast(modelo_ferro,h=24)
previsao_ferro
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Sep 2021 144.6144 132.59615 156.6326 126.23409 162.9946
## Oct 2021 144.1821 123.45643 164.9077 112.48493 175.8792
## Nov 2021 142.3083 115.57507 169.0416 101.42332 183.1934
## Dec 2021 140.2368 108.61749 171.8562 91.87922 188.5945
## Jan 2022 138.9383 103.09277 174.7837 84.11732 193.7592
## Feb 2022 137.6379 98.01445 177.2613 77.03909 198.2366
## Mar 2022 137.8976 94.82637 180.9688 72.02585 203.7693
## Apr 2022 135.1672 88.90446 181.4300 64.41443 205.9201
## May 2022 134.1070 84.85908 183.3550 58.78879 209.4253
## Jun 2022 135.9461 83.88387 188.0083 56.32379 215.5684
## Jul 2022 137.8769 83.14487 192.6089 54.17151 221.5822
## Aug 2022 148.0292 90.75179 205.3067 60.43094 235.6275
## Sep 2022 150.4230 91.11789 209.7280 59.72368 241.1223
## Oct 2022 149.4524 88.33741 210.5674 55.98509 242.9197
## Nov 2022 150.8859 88.01305 213.7587 54.73019 247.0415
## Dec 2022 159.5888 95.00600 224.1716 60.81792 258.3597
## Jan 2023 163.0755 96.82683 229.3242 61.75689 264.3942
## Feb 2023 162.5575 94.68380 230.4312 58.75363 266.3614
## Mar 2023 162.8737 93.41301 232.3344 56.64273 269.1047
## Apr 2023 166.6594 95.64711 237.6716 58.05550 275.2632
## May 2023 173.8506 101.32004 246.3813 62.92466 284.7766
## Jun 2023 176.0046 101.98681 250.0225 62.80414 289.2051
## Jul 2023 175.0697 99.59394 250.5454 59.63949 290.4999
## Aug 2023 159.8804 82.97439 236.7865 42.26280 277.4981
plot(previsao_ferro)
previsao_boi <- forecast(modelo_boi,h=24)
previsao_boi
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Sep 2021 124.4645 116.01941 132.9096 111.54884 137.3802
## Oct 2021 125.1356 114.27594 135.9952 108.52720 141.7440
## Nov 2021 127.1802 114.18519 140.1753 107.30602 147.0545
## Dec 2021 128.1442 113.34666 142.9418 105.51331 150.7751
## Jan 2022 128.0152 111.60714 144.4233 102.92124 153.1092
## Feb 2022 126.4497 108.57648 144.3228 99.11499 153.7843
## Mar 2022 126.1963 106.96914 145.4234 96.79091 155.6016
## Apr 2022 123.6783 103.18655 144.1701 92.33886 155.0178
## May 2022 125.0507 103.36788 146.7335 91.88969 158.2117
## Jun 2022 124.9914 102.17961 147.8031 90.10381 159.8789
## Jul 2022 126.5217 102.63435 150.4091 89.98914 163.0543
## Aug 2022 127.1261 102.20945 152.0427 89.01939 165.2327
## Sep 2022 127.7376 101.41548 154.0597 87.48139 167.9938
## Oct 2022 127.4799 99.90466 155.0551 85.30721 169.6526
## Nov 2022 128.4202 99.63167 157.2087 84.39194 172.4485
## Dec 2022 128.9774 99.02736 158.9274 83.17278 174.7820
## Jan 2023 129.2568 98.18822 160.3254 81.74149 176.7721
## Feb 2023 128.7182 96.56997 160.8664 79.55175 177.8846
## Mar 2023 129.8043 96.61153 162.9970 79.04037 180.5681
## Apr 2023 128.6745 94.46919 162.8799 76.36197 180.9871
## May 2023 128.8840 93.69509 164.0728 75.06723 182.7007
## Jun 2023 129.8231 93.67750 165.9687 74.54317 185.1031
## Jul 2023 130.0157 92.93804 167.0934 73.31029 186.7212
## Aug 2023 130.4310 92.44406 168.4179 72.33501 188.5269
plot(previsao_boi)
Características do modelo arima
summary(modelo_ouro)
## Series: ouro
## ARIMA(0,1,0)
##
## sigma^2 estimated as 5026: log likelihood=-721.37
## AIC=1444.75 AICc=1444.78 BIC=1447.59
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 3.575655 70.61547 53.39362 0.122329 3.589525 0.3435969 -0.109594
summary(modelo_boi)
## Series: boi
## ARIMA(1,1,0)(2,0,0)[12]
##
## Coefficients:
## ar1 sar1 sar2
## -0.1916 0.1656 0.1432
## s.e. 0.0885 0.0885 0.0945
##
## sigma^2 estimated as 43.42: log likelihood=-418.64
## AIC=845.29 AICc=845.62 BIC=856.66
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.1443143 6.485973 4.788159 -0.01688264 3.970015 0.3605553
## ACF1
## Training set 0.01845741
summary(modelo_ferro)
## Series: ferro
## ARIMA(0,1,1)(2,0,0)[12]
##
## Coefficients:
## ma1 sar1 sar2
## 0.4050 -0.1257 0.2704
## s.e. 0.1012 0.1030 0.1124
##
## sigma^2 estimated as 87.94: log likelihood=-464.14
## AIC=936.28 AICc=936.61 BIC=947.66
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.1036045 9.230171 6.568188 -0.2270176 6.858008 0.2332703
## ACF1
## Training set -0.03931499