O pacote R fable fornece métodos e ferramentas para visualizar e analisar previsões de séries temporais univariadas incluindo os modelos “Exponential smoothing via state space models” e “automatic ARIMA modelling”. Dados, modelos e objetos são todos armazenados em formato tidy(arrumado).

Fable package

O pacote ainda não está no CRAN e foi apresentado recentemente pelo Hyndman no ISF 20181.

Exemplo: Alimentação fora do domicílio - Austrália

remove(list = ls())
library(tidyverse)

if(!require(fpp2)) install.packages("fpp2")
library(fpp2)

head(fpp2::auscafe)
##         Apr    May    Jun    Jul    Aug    Sep
## 1982 0.3424 0.3421 0.3287 0.3385 0.3315 0.3419
if(!require(tsibble)) install.packages("tsibble") # Tidy Temporal Data Frames and Tools
library(tsibble)

cafe <- as_tsibble(fpp2::auscafe)
cafe
## # A tsibble: 426 x 2 [1MONTH]
##       index value
##       <mth> <dbl>
##  1 1982 abr 0.342
##  2 1982 mai 0.342
##  3 1982 jun 0.329
##  4 1982 jul 0.338
##  5 1982 ago 0.332
##  6 1982 set 0.342
##  7 1982 out 0.358
##  8 1982 nov 0.375
##  9 1982 dez 0.433
## 10 1983 jan 0.369
## # ... with 416 more rows
if(!require(devtools)) install.packages("devtools")
library(devtools)
if(!require(fable)) install_github("tidyverts/fable", force = TRUE) # antes de instala-lom instale o pacote tidyverse
library(fable)

cafe %>% ETS(formula = value)
## # A mable: 1 model [1MONTH]
##   data                model     
##   <list>              <model>   
## 1 <tsibble [426 x 2]> ETS(M,A,M)
cafe %>% ETS(value) %>% summary()
## ETS(M,A,M) 
## 
## Call:
##  ETS(data = ., formula = value) 
## 
##   Smoothing parameters:
##     alpha = 0.6263 
##     beta  = 0.0065 
##     gamma = 0.0755 
## 
##   Initial states:
##     l = 0.3477 
##     b = 0.0038 
##     s = 0.996 0.9357 1.0124 1.1498 1.0105 1.0106
##            0.9831 0.9911 0.9918 0.9509 0.9968 0.9714
## 
##   sigma:  0.0249
## 
##       AIC      AICc       BIC 
## -319.1016 -317.6016 -250.1762 
## 
## Training set error measures:
##                       ME       RMSE        MAE       MPE     MAPE
## Training set 0.002601818 0.03997611 0.02952838 0.1121434 1.982609
##                   MASE      ACF1
## Training set 0.2826048 0.1249781
cafe %>% ETS(value) %>% forecast() %>% summary()
## # A tsibble: 24 x 4 [1MONTH]
##       index  mean                  `80%`                  `95%`
##       <mth> <dbl>                 <hilo>                 <hilo>
##  1 2017 out  3.83 [3.710682, 3.955486]80 [3.645886, 4.020282]95
##  2 2017 nov  3.81 [3.669399, 3.957380]80 [3.593176, 4.033603]95
##  3 2017 dez  4.22 [4.036861, 4.398464]80 [3.941150, 4.494175]95
##  4 2018 jan  3.83 [3.644415, 4.007830]80 [3.548225, 4.104020]95
##  5 2018 fev  3.51 [3.332694, 3.696526]80 [3.236394, 3.792827]95
##  6 2018 mar  3.87 [3.654231, 4.085779]80 [3.540007, 4.200003]95
##  7 2018 abr  3.78 [3.558549, 4.009072]80 [3.439302, 4.128318]95
##  8 2018 mai  3.81 [3.570956, 4.052222]80 [3.443573, 4.179605]95
##  9 2018 jun  3.68 [3.433373, 3.923180]80 [3.303729, 4.052825]95
## 10 2018 jul  3.88 [3.604236, 4.146000]80 [3.460840, 4.289396]95
## # ... with 14 more rows
cafe %>% ETS(value) %>% forecast() %>% summary(level = 90)
## # A tsibble: 24 x 3 [1MONTH]
##       index  mean                  `90%`
##       <mth> <dbl>                 <hilo>
##  1 2017 out  3.83 [3.675982, 3.990186]90
##  2 2017 nov  3.81 [3.628580, 3.998199]90
##  3 2017 dez  4.22 [3.985606, 4.449719]90
##  4 2018 jan  3.83 [3.592904, 4.059341]90
##  5 2018 fev  3.51 [3.281124, 3.748097]90
##  6 2018 mar  3.87 [3.593062, 4.146948]90
##  7 2018 abr  3.78 [3.494690, 4.072931]90
##  8 2018 mai  3.81 [3.502740, 4.120438]90
##  9 2018 jun  3.68 [3.363946, 3.992607]90
## 10 2018 jul  3.88 [3.527445, 4.222791]90
## # ... with 14 more rows
cafe %>% ETS(value) %>% forecast() %>% autoplot()

cafe %>% ETS(value) %>% forecast() %>% autoplot()

cafe %>% ARIMA(log(value)) %>% forecast() %>% summary()
## # A tsibble: 24 x 4 [1MONTH]
##       index  mean                  `80%`                  `95%`
##       <mth> <dbl>                 <hilo>                 <hilo>
##  1 2017 out  3.81 [3.695757, 3.925596]80 [3.637208, 3.988787]95
##  2 2017 nov  3.79 [3.652255, 3.926338]80 [3.582969, 4.002265]95
##  3 2017 dez  4.17 [3.994774, 4.338391]80 [3.908470, 4.434187]95
##  4 2018 jan  3.73 [3.550551, 3.903099]80 [3.462690, 4.002135]95
##  5 2018 fev  3.40 [3.222464, 3.571614]80 [3.135906, 3.670200]95
##  6 2018 mar  3.77 [3.563436, 3.984984]80 [3.459526, 4.104676]95
##  7 2018 abr  3.70 [3.483283, 3.925831]80 [3.374741, 4.052098]95
##  8 2018 mai  3.76 [3.520066, 3.996561]80 [3.403747, 4.133139]95
##  9 2018 jun  3.66 [3.413722, 3.903254]80 [3.294761, 4.044185]95
## 10 2018 jul  3.88 [3.607122, 4.151691]80 [3.475347, 4.309111]95
## # ... with 14 more rows

Exemplo: População carcerária da Austrália

Quarterly time series of prisoner numbers in Australia from 2005 to 2016, split by sex, state and legal status2.

fpp2::prisonLF
## # A tibble: 1,536 x 5
##    state gender legal    t          count
##    <fct> <fct>  <fct>    <date>     <dbl>
##  1 ACT   Female Remanded 2005-03-01     2
##  2 ACT   Female Remanded 2005-06-01     4
##  3 ACT   Female Remanded 2005-09-01     1
##  4 ACT   Female Remanded 2005-12-01     4
##  5 ACT   Female Remanded 2006-03-01     4
##  6 ACT   Female Remanded 2006-06-01     6
##  7 ACT   Female Remanded 2006-09-01     9
##  8 ACT   Female Remanded 2006-12-01     6
##  9 ACT   Female Remanded 2007-03-01     4
## 10 ACT   Female Remanded 2007-06-01     4
## # ... with 1,526 more rows
autoplot(prison)

head(fpp2::prisonLF)
## # A tibble: 6 x 5
##   state gender legal    t          count
##   <fct> <fct>  <fct>    <date>     <dbl>
## 1 ACT   Female Remanded 2005-03-01     2
## 2 ACT   Female Remanded 2005-06-01     4
## 3 ACT   Female Remanded 2005-09-01     1
## 4 ACT   Female Remanded 2005-12-01     4
## 5 ACT   Female Remanded 2006-03-01     4
## 6 ACT   Female Remanded 2006-06-01     6
prison <- fpp2::prisonLF %>% 
  mutate(qtr = yearquarter(t)) %>% 
  select(-t) %>% 
  as_tsibble(index = qtr, key = id(state, gender,legal))
prison
## # A tsibble: 1,536 x 5 [1QUARTER]
## # Key:       state, gender, legal [32]
##    state gender legal    count     qtr
##    <fct> <fct>  <fct>    <dbl>   <qtr>
##  1 ACT   Female Remanded     2 2005 Q1
##  2 ACT   Female Remanded     4 2005 Q2
##  3 ACT   Female Remanded     1 2005 Q3
##  4 ACT   Female Remanded     4 2005 Q4
##  5 ACT   Female Remanded     4 2006 Q1
##  6 ACT   Female Remanded     6 2006 Q2
##  7 ACT   Female Remanded     9 2006 Q3
##  8 ACT   Female Remanded     6 2006 Q4
##  9 ACT   Female Remanded     4 2007 Q1
## 10 ACT   Female Remanded     4 2007 Q2
## # ... with 1,526 more rows
prison %>% ETS(formula = count) # cria um modelo para cada uma das possíveis combinações (e.g. estado ACT, mulher e reencarcerada)
## # A mable: 32 models [1QUARTER]
## # Key:     state, gender, legal [32]
##    state gender legal     data               model     
##    <fct> <fct>  <fct>     <list>             <model>   
##  1 ACT   Female Remanded  <tsibble [48 x 2]> ETS(M,A,N)
##  2 ACT   Female Sentenced <tsibble [48 x 2]> ETS(A,A,N)
##  3 ACT   Male   Remanded  <tsibble [48 x 2]> ETS(M,N,N)
##  4 ACT   Male   Sentenced <tsibble [48 x 2]> ETS(A,N,N)
##  5 NSW   Female Remanded  <tsibble [48 x 2]> ETS(M,N,M)
##  6 NSW   Female Sentenced <tsibble [48 x 2]> ETS(M,N,M)
##  7 NSW   Male   Remanded  <tsibble [48 x 2]> ETS(M,A,A)
##  8 NSW   Male   Sentenced <tsibble [48 x 2]> ETS(M,A,A)
##  9 NT    Female Remanded  <tsibble [48 x 2]> ETS(M,N,N)
## 10 NT    Female Sentenced <tsibble [48 x 2]> ETS(M,A,A)
## # ... with 22 more rows
prison %>% ETS(count) %>% forecast()
## # A fable: 32 forecasts [1QUARTER]
## # Key:     state, gender, legal [32]
##    state gender legal     data               model      forecast
##    <fct> <fct>  <fct>     <list>             <model>    <fc>    
##  1 ACT   Female Remanded  <tsibble [48 x 2]> ETS(M,A,N) ~N [h=8]
##  2 ACT   Female Sentenced <tsibble [48 x 2]> ETS(A,A,N) ~N [h=8]
##  3 ACT   Male   Remanded  <tsibble [48 x 2]> ETS(M,N,N) ~N [h=8]
##  4 ACT   Male   Sentenced <tsibble [48 x 2]> ETS(A,N,N) ~N [h=8]
##  5 NSW   Female Remanded  <tsibble [48 x 2]> ETS(M,N,M) ~N [h=8]
##  6 NSW   Female Sentenced <tsibble [48 x 2]> ETS(M,N,M) ~N [h=8]
##  7 NSW   Male   Remanded  <tsibble [48 x 2]> ETS(M,A,A) ~N [h=8]
##  8 NSW   Male   Sentenced <tsibble [48 x 2]> ETS(M,A,A) ~N [h=8]
##  9 NT    Female Remanded  <tsibble [48 x 2]> ETS(M,N,N) ~N [h=8]
## 10 NT    Female Sentenced <tsibble [48 x 2]> ETS(M,A,A) ~N [h=8]
## # ... with 22 more rows

Exemplo: Demanda de eletricidade - 30 em 30 minutos

prison <- fpp2::prisonLF %>% 
  mutate(qtr = yearquarter(t)) %>% 
  select(-t) %>% 
  as_tsibble(index = qtr, key = id(state, gender,legal))
prison
## # A tsibble: 1,536 x 5 [1QUARTER]
## # Key:       state, gender, legal [32]
##    state gender legal    count     qtr
##    <fct> <fct>  <fct>    <dbl>   <qtr>
##  1 ACT   Female Remanded     2 2005 Q1
##  2 ACT   Female Remanded     4 2005 Q2
##  3 ACT   Female Remanded     1 2005 Q3
##  4 ACT   Female Remanded     4 2005 Q4
##  5 ACT   Female Remanded     4 2006 Q1
##  6 ACT   Female Remanded     6 2006 Q2
##  7 ACT   Female Remanded     9 2006 Q3
##  8 ACT   Female Remanded     6 2006 Q4
##  9 ACT   Female Remanded     4 2007 Q1
## 10 ACT   Female Remanded     4 2007 Q2
## # ... with 1,526 more rows
if(!require(tsibbledata)) install_github("tidyverts/tsibbledata", force = TRUE) # antes de instala-lom instale o pacote tidyverse
## Loading required package: tsibbledata
## 
## Attaching package: 'tsibbledata'
## The following object is masked from 'package:fpp2':
## 
##     elecdemand
library(tsibbledata)

tsibbledata::elecdemand
## # A tsibble: 17,520 x 4 [30MINUTE]
##    index               Demand WorkDay Temperature
##    <dttm>               <dbl>   <dbl>       <dbl>
##  1 2014-01-01 00:00:00   3.91       0        18.2
##  2 2014-01-01 00:30:00   3.67       0        17.9
##  3 2014-01-01 01:00:00   3.50       0        17.6
##  4 2014-01-01 01:30:00   3.34       0        16.8
##  5 2014-01-01 02:00:00   3.20       0        16.3
##  6 2014-01-01 02:30:00   3.10       0        16.6
##  7 2014-01-01 03:00:00   3.04       0        16.6
##  8 2014-01-01 03:30:00   3.01       0        16.7
##  9 2014-01-01 04:00:00   3.02       0        16.2
## 10 2014-01-01 04:30:00   3.03       0        16.6
## # ... with 17,510 more rows
fit2 <- ARIMA(tsibbledata::elecdemand, formula = Demand ~ Temperature + I(Temperature^2) + WorkDay)
summary(fit2)
## Series: Demand 
## Regression with ARIMA(1,1,0)(2,0,2)[2] errors 
## 
## Coefficients:
##          ar1     sar1    sar2     sma1     sma2  Temperature
##       0.8527  -0.1809  0.5231  -0.0657  -0.7922      -0.0086
## s.e.  0.0048   0.0153  0.0125   0.0120   0.0112       0.0025
##       I(Temperature^2)  WorkDay
##                  2e-04   0.0163
## s.e.             1e-04   0.0055
## 
## sigma^2 estimated as 0.008459:  log likelihood=16949.3
## AIC=-33880.61   AICc=-33880.6   BIC=-33810.67
## 
## Training set error measures:
##                        ME       RMSE        MAE         MPE     MAPE
## Training set 6.509344e-06 0.09195127 0.06338631 0.006327664 1.390059
##                   MASE      ACF1
## Training set 0.2918306 0.1027364

  1. Para assistir a apresentação, acesse aqui↩

  2. prisonLF is a long-form version of the data of class data.frame, while prison is in wide form and of class mts.↩