Forecast Arima
Carga de Dados
## [1] 21 2##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.432 -13.759 -6.723 12.350 37.423
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9136.5498 1336.7907 6.835 1.60e-06 ***
## x -4.4818 0.6651 -6.739 1.94e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.45 on 19 degrees of freedom
## Multiple R-squared: 0.705, Adjusted R-squared: 0.6895
## F-statistic: 45.41 on 1 and 19 DF, p-value: 1.938e-06##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.432 -13.759 -6.723 12.350 37.423
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9136.5498 1336.7907 6.835 0.00000160 ***
## x -4.4818 0.6651 -6.739 0.00000194 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.45 on 19 degrees of freedom
## Multiple R-squared: 0.705, Adjusted R-squared: 0.6895
## F-statistic: 45.41 on 1 and 19 DF, p-value: 0.000001938## 1 2 3 4 5 6 7 8
## 172.91342 168.43160 163.94978 159.46797 154.98615 150.50433 146.02251 141.54069
## 9 10 11 12 13 14 15 16
## 137.05887 132.57706 128.09524 123.61342 119.13160 114.64978 110.16797 105.68615
## 17 18 19 20 21
## 101.20433 96.72251 92.24069 87.75887 83.27706## 1 2 3 4 5 6 7 8
## 78.79524 74.31342 69.83160 65.34978 60.86797 56.38615 51.90433 47.42251
## 9 10
## 42.94069 38.45887## [1] 78 74 69 65 60 56 51 47 42 38## fit lwr upr
## 1 78.79524 36.3981942 121.19228
## 2 74.31342 31.3940108 117.23283
## 3 69.83160 26.3515217 113.31168
## 4 65.34978 21.2721886 109.42738
## 5 60.86797 16.1574886 105.57844
## 6 56.38615 11.0089016 101.76339
## 7 51.90433 5.8278986 97.98076
## 8 47.42251 0.6159323 94.22909
## 9 42.94069 -4.6255714 90.50696
## 10 38.45887 -9.8952205 86.81297## fit lwr upr
## 1 78.79524 61.316521 96.27395
## 2 74.31342 55.603212 93.02363
## 3 69.83160 49.868797 89.79441
## 4 65.34978 44.117012 86.58256
## 5 60.86797 38.350796 83.38514
## 6 56.38615 32.572483 80.19981
## 7 51.90433 26.783946 77.02471
## 8 47.42251 20.986702 73.85832
## 9 42.94069 15.181988 70.69940
## 10 38.45887 9.370824 67.54693## Warning: package 'ggplot2' was built under R version 3.6.3## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
Verificando a serie com 10 anos futuros
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
Plotando dados
Fatais de 2000 a 2020
Predição
Predict para 10 anos:
## Warning: package 'forecast' was built under R version 3.6.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 22 50.594582 42.418782 58.770381 38.090775 63.098388
## 23 40.835005 33.282482 48.387528 29.284418 52.385592
## 24 31.075428 23.486780 38.664077 19.469592 42.681265
## 25 21.315852 13.020582 29.611121 8.629332 34.002372
## 26 11.556275 2.025165 21.087385 -3.020300 26.132850
## 27 1.796699 -9.330831 12.924228 -15.221389 18.814786
## 28 -7.962878 -20.928870 5.003113 -27.792651 11.866895
## 29 -17.722455 -32.706697 -2.738212 -40.638876 5.193967
## 30 -27.482031 -44.643061 -10.321002 -53.727561 -1.236501
## 31 -37.241608 -56.744064 -17.739152 -67.068040 -7.415176Auto Arima
## Series: ts(FATAIS, frequency = 1, start = c(2000))
## ARIMA(0,1,1) with drift
##
## Coefficients:
## ma1 drift
## -0.4691 -4.5780
## s.e. 0.1751 2.0038
##
## sigma^2 estimated as 288: log likelihood=-84.08
## AIC=174.16 AICc=175.66 BIC=177.15Projeção h=10
Impressão de gráfico com série temporal e projeção com intervalos de confiança de 80 e 95%
Incluir no gráfico os valores do modelo para dados observados em azul
Verificando os dados
## [1] "forecast"## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2021 62.47874 40.7289693 84.22851 29.215336 95.74215
## 2022 57.90071 33.2763053 82.52511 20.240935 95.56048
## 2023 53.32267 26.1258025 80.51954 11.728650 94.91669
## 2024 48.74463 19.1984313 78.29084 3.557616 93.93165
## 2025 44.16660 12.4445776 75.88862 -4.348046 92.68124
## 2026 39.58856 5.8306732 73.34645 -12.039675 91.21680
## 2027 35.01053 -0.6672476 70.68830 -19.553921 89.57498
## 2028 30.43249 -7.0670034 67.93199 -26.918038 87.78302
## 2029 25.85446 -13.3822695 65.09118 -34.152938 85.86185
## 2030 21.27642 -19.6238135 62.17666 -41.275090 83.82793Verificando os dados residuais
## Warning: package 'pander' was built under R version 3.6.3R version 3.6.2 (2019-12-12)
Platform: x86_64-w64-mingw32/x64 (64-bit)
locale: LC_COLLATE=Portuguese_Brazil.1252, LC_CTYPE=Portuguese_Brazil.1252, LC_MONETARY=Portuguese_Brazil.1252, LC_NUMERIC=C and LC_TIME=Portuguese_Brazil.1252
attached base packages:
- stats
- graphics
- grDevices
- utils
- datasets
- methods
- base
other attached packages:
- pander(v.0.6.3)
- forecast(v.8.12)
- ggplot2(v.3.3.2)
loaded via a namespace (and not attached):
- Rcpp(v.1.0.4.6)
- urca(v.1.3-0)
- pillar(v.1.4.3)
- compiler(v.3.6.2)
- xts(v.0.12.1)
- tseries(v.0.10-47)
- tools(v.3.6.2)
- digest(v.0.6.27)
- jsonlite(v.1.6.1)
- evaluate(v.0.14)
- lifecycle(v.0.2.0)
- tibble(v.3.0.4)
- gtable(v.0.3.0)
- nlme(v.3.1-142)
- lattice(v.0.20-38)
- mgcv(v.1.8-31)
- pkgconfig(v.2.0.3)
- rlang(v.0.4.10)
- Matrix(v.1.2-18)
- curl(v.4.3)
- parallel(v.3.6.2)
- yaml(v.2.2.0)
- xfun(v.0.19)
- withr(v.2.3.0)
- stringr(v.1.4.0)
- dplyr(v.0.8.5)
- knitr(v.1.30)
- vctrs(v.0.3.6)
- nnet(v.7.3-12)
- lmtest(v.0.9-37)
- grid(v.3.6.2)
- tidyselect(v.0.2.5)
- glue(v.1.4.2)
- R6(v.2.4.1)
- rmarkdown(v.2.2.2)
- TTR(v.0.23-6)
- farver(v.2.0.1)
- purrr(v.0.3.3)
- magrittr(v.1.5)
- scales(v.1.1.1)
- ellipsis(v.0.3.0)
- htmltools(v.0.4.0)
- splines(v.3.6.2)
- quantmod(v.0.4.17)
- assertthat(v.0.2.1)
- timeDate(v.3043.102)
- colorspace(v.1.4-1)
- fracdiff(v.1.5-1)
- quadprog(v.1.5-8)
- labeling(v.0.3)
- stringi(v.1.4.4)
- munsell(v.0.5.0)
- crayon(v.1.3.4)
- zoo(v.1.8-6)