library(tidyverse)
library(tsibble)
library(feasts)
library(fable)
library(tsibbledata)
library(fpp3)
library(patchwork)
library(timetk) # manejo de series de tiempo modeltimeDemanda de energía en Victoria, Australia
Las paqueterías necesarias para el análisis:
1 Pre-procesamiento de los datos
Los datos tienen una periodicidad de cada media hora. Nos interesa tenerlos por hora.
vic_elec# A tsibble: 52,608 x 5 [30m] <Australia/Melbourne>
Time Demand Temperature Date Holiday
<dttm> <dbl> <dbl> <date> <lgl>
1 2012-01-01 00:00:00 4383. 21.4 2012-01-01 TRUE
2 2012-01-01 00:30:00 4263. 21.0 2012-01-01 TRUE
3 2012-01-01 01:00:00 4049. 20.7 2012-01-01 TRUE
4 2012-01-01 01:30:00 3878. 20.6 2012-01-01 TRUE
5 2012-01-01 02:00:00 4036. 20.4 2012-01-01 TRUE
6 2012-01-01 02:30:00 3866. 20.2 2012-01-01 TRUE
7 2012-01-01 03:00:00 3694. 20.1 2012-01-01 TRUE
8 2012-01-01 03:30:00 3562. 19.6 2012-01-01 TRUE
9 2012-01-01 04:00:00 3433. 19.1 2012-01-01 TRUE
10 2012-01-01 04:30:00 3359. 19.0 2012-01-01 TRUE
# … with 52,598 more rowsCon el tidyverts, podemos utilizar index_by() y summarise():
vic_elec_hourly <- vic_elec %>%
index_by(hora = ~ floor_date(., "hour")) %>%
summarise(
Demand = sum(Demand),
Temperature = mean(Temperature),
Holiday = mean(Holiday)
)
vic_elec_hourly# A tsibble: 26,304 x 4 [1h] <Australia/Melbourne>
hora Demand Temperature Holiday
<dttm> <dbl> <dbl> <dbl>
1 2012-01-01 00:00:00 8646. 21.2 1
2 2012-01-01 01:00:00 7927. 20.6 1
3 2012-01-01 02:00:00 7902. 20.3 1
4 2012-01-01 03:00:00 7256. 19.8 1
5 2012-01-01 04:00:00 6793. 19.0 1
6 2012-01-01 05:00:00 6636. 18.7 1
7 2012-01-01 06:00:00 6548. 18.7 1
8 2012-01-01 07:00:00 6865. 19.6 1
9 2012-01-01 08:00:00 7300. 21.8 1
10 2012-01-01 09:00:00 8002. 24.6 1
# … with 26,294 more rowsHaciendo esto mismo, pero con la paquetería timetk, tendríamos primero que convertir los datos a una tibble, y posteriormente podríamos utilizar la función summarise_by_time()
vic_elec %>%
as_tibble() %>%
summarise_by_time(
.date_var = Time,
.by = "hour",
Demand = sum(Demand),
Temperature = mean(Temperature)
) %>%
as_tsibble(index = Time)# A tsibble: 26,304 x 3 [1h] <Australia/Melbourne>
Time Demand Temperature
<dttm> <dbl> <dbl>
1 2012-01-01 00:00:00 8646. 21.2
2 2012-01-01 01:00:00 7927. 20.6
3 2012-01-01 02:00:00 7902. 20.3
4 2012-01-01 03:00:00 7256. 19.8
5 2012-01-01 04:00:00 6793. 19.0
6 2012-01-01 05:00:00 6636. 18.7
7 2012-01-01 06:00:00 6548. 18.7
8 2012-01-01 07:00:00 6865. 19.6
9 2012-01-01 08:00:00 7300. 21.8
10 2012-01-01 09:00:00 8002. 24.6
# … with 26,294 more rows2 Análisis exploratorio
p <- vic_elec_hourly %>%
autoplot(Demand)
plotly::ggplotly(p)Al observar la gráfica, parece exhibir tres tipos de estacionalidad:
- Anual
- Semanal
- Diaria
s_y <- vic_elec_hourly %>%
gg_season(Demand, period = "year")
s_w <- vic_elec_hourly %>%
gg_season(Demand, period = "week")
s_d <- vic_elec_hourly %>%
gg_season(Demand, period = "day")
s_y / s_w / s_d
s_y / (s_w | s_d)
3 Descomposición STL
Realizamos una descomposición STL de la serie:
comp_stl <- vic_elec_hourly %>%
model(
STL(Demand, robust = TRUE)
) %>%
components()
comp_stl %>%
autoplot()
comp_stl %>%
autoplot(season_year)
comp_stl %>%
autoplot(season_week)
comp_stl %>%
autoplot(season_day)
comp_stl %>%
ggplot(aes(x = hora, y = season_adjust)) +
geom_line()
4 Flujo de pronóstico
4.1 Conjuntos de entrenamiento y prueba
vic_train <- vic_elec_hourly %>%
filter_index(. ~ "2014-09-30")
vic_test <- vic_elec_hourly %>%
filter_index("2014-10-01"~.)4.2 Modelado
4.2.1 Suavización exponencial
Ajustamos un Holt-Winters aditivo y con tendencia amortiguada:
fit1 <- vic_train %>%
model(ets = ETS(Demand ~ error("A") + trend("Ad") + season("A")))
report(fit1)Series: Demand
Model: ETS(A,Ad,A)
Smoothing parameters:
alpha = 0.8429999
beta = 0.0005046006
gamma = 0.156982
phi = 0.9795556
Initial states:
l[0] b[0] s[0] s[-1] s[-2] s[-3] s[-4] s[-5]
8643.489 82.40267 -642.5048 -73.45193 680.717 1153.295 1486.505 1405.408
s[-6] s[-7] s[-8] s[-9] s[-10] s[-11] s[-12] s[-13]
1099.634 987.357 842.7851 802.8814 767.5777 790.5029 828.9911 866.8354
s[-14] s[-15] s[-16] s[-17] s[-18] s[-19] s[-20] s[-21]
752.8551 270.4595 -464.1822 -1644.818 -2270.221 -2366.422 -2091.133 -1542.735
s[-22] s[-23]
-1132.932 -507.4028
sigma^2: 80822.89
AIC AICc BIC
515462.4 515462.5 515705.1 p <- vic_train %>%
autoplot(Demand) +
geom_line(aes(y = .fitted), data = fit1 %>% augment(), color = "firebrick")
plotly::ggplotly(p)Las métricas de error en el entrenamiento:
accuracy(fit1) %>%
select(.model, .type, RMSE, MAE, MAPE, MASE)# A tibble: 1 × 6
.model .type RMSE MAE MAPE MASE
<chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 ets Training 284. 210. 2.32 0.282Los pronósticos a tres meses.
fc1 <- fit1 %>%
forecast(h = "3 months")
fc1 %>%
autoplot(vic_elec_hourly %>% filter_index("2014-10-01"~.), level = NULL)
fc1 %>%
accuracy(vic_elec_hourly)# A tibble: 1 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 ets Test 41.1 1137. 949. -0.847 10.8 1.27 0.985 0.943El diagnóstico de residuos:
fit1 %>%
gg_tsresiduals()
Dado que los periodos estacionales de esta serie son:
- Anual: 8760
- Semanal: 168
- Diaria: 24
No podemos modelar la estacionalidad a partir de ETS, ya que permite máximo periodos estacionales = 24.
4.2.2 Pronóstico con descomposición y ETS
Vamos a hacer un modelo de descomposición, modelando con SNAIVE las estacionalidades, y con ETS la serie desestacionalizada.
fit2 <- vic_train %>%
model(
dcmp = decomposition_model(
STL(Demand, robust = TRUE),
ETS(season_adjust ~ error("A") + trend("Ad") + season("N"))
)
)
fit2 %>% report()Series: Demand
Model: STL decomposition model
Combination: season_adjust + season_year + season_week + season_day
===================================================================
Series: season_adjust + season_year + season_week
Model: COMBINATION
Combination: season_adjust + season_year + season_week
======================================================
Series: season_adjust + season_year
Model: COMBINATION
Combination: season_adjust + season_year
========================================
Series: season_adjust
Model: ETS(A,Ad,N)
Smoothing parameters:
alpha = 0.9490909
beta = 0.0001000419
phi = 0.8390464
Initial states:
l[0] b[0]
10495.53 114.8676
sigma^2: 84379.73
AIC AICc BIC
516476.2 516476.2 516524.7
Series: season_year
Model: SNAIVE
sigma^2: 150953.5072
Series: season_week
Model: SNAIVE
sigma^2: 571.2532
Series: season_day
Model: SNAIVE
sigma^2: 2131.6242 accuracy(fit2)# A tibble: 1 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 dcmp Training 3.48 470. 167. -0.0777 1.73 0.224 0.407 0.623fc2 <- fit2 %>%
forecast(h = "3 months")
fc2 %>%
autoplot(vic_elec_hourly %>% filter_index("2014-10-01"~.), level = NULL)
fc2 %>%
accuracy(vic_elec_hourly)# A tibble: 1 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 dcmp Test 192. 995. 700. 1.95 8.02 0.938 0.862 0.896fit2 %>%
gg_tsresiduals()Warning: Removed 8766 row(s) containing missing values (geom_path).Warning: Removed 8766 rows containing missing values (geom_point).Warning: Removed 8766 rows containing non-finite values (stat_bin).
4.2.3 Regresión armónica dinámica
tictoc::tic()
fit3 <- vic_train %>%
model(
harmonic = ARIMA(Demand ~ fourier(period = "year", K = 5) +
fourier(period = "week", K = 3) +
fourier(period = "day", K = 3) + pdq(2,0,2) + PDQ(0,0,0))
)
tictoc::toc()34.35 sec elapsedreport(fit3)Series: Demand
Model: LM w/ ARIMA(2,0,2) errors
Coefficients:
ar1 ar2 ma1 ma2 fourier(period = "year", K = 5)C1_8766
0.8709 -0.0137 0.4393 0.1211 -372.1854
s.e. 0.0359 0.0319 0.0353 0.0161 35.1763
fourier(period = "year", K = 5)S1_8766
132.2054
s.e. 35.2763
fourier(period = "year", K = 5)C2_8766
375.1088
s.e. 35.1598
fourier(period = "year", K = 5)S2_8766
322.8801
s.e. 35.2795
fourier(period = "year", K = 5)C3_8766
-178.5210
s.e. 35.1378
fourier(period = "year", K = 5)S3_8766
122.8226
s.e. 35.2509
fourier(period = "year", K = 5)C4_8766
-192.5261
s.e. 35.0181
fourier(period = "year", K = 5)S4_8766
59.3766
s.e. 35.2105
fourier(period = "year", K = 5)C5_8766
-41.3890
s.e. 34.9357
fourier(period = "year", K = 5)S5_8766
-3.1212
s.e. 35.0062
fourier(period = "week", K = 3)C1_168
592.4026
s.e. 33.7797
fourier(period = "week", K = 3)S1_168
-520.2649
s.e. 33.7890
fourier(period = "week", K = 3)C2_168
-24.7762
s.e. 31.3337
fourier(period = "week", K = 3)S2_168
455.9899
s.e. 31.3294
fourier(period = "week", K = 3)C3_168
-43.9442
s.e. 28.2006
fourier(period = "week", K = 3)S3_168
-103.9370
s.e. 28.1992
fourier(period = "day", K = 3)C1_24 fourier(period = "day", K = 3)S1_24
562.4180 1408.5068
s.e. 17.6527 17.6545
fourier(period = "day", K = 3)C2_24 fourier(period = "day", K = 3)S2_24
380.9742 -543.3201
s.e. 9.5259 9.5264
fourier(period = "day", K = 3)C3_24 fourier(period = "day", K = 3)S3_24
69.9436 -296.9114
s.e. 6.1454 6.1454
intercept
9341.1353
s.e. 24.9025
sigma^2 estimated as 122038: log likelihood=-175292.9
AIC=350641.9 AICc=350641.9 BIC=350868.4p <- vic_train %>%
autoplot(Demand) +
geom_line(aes(y = .fitted), data = fit3 %>% augment(), color = "firebrick")
plotly::ggplotly(p)fc3 <- fit3 %>%
forecast(h = "3 months")
fc3 %>%
autoplot(vic_elec_hourly %>% filter_index("2014-10-01"~.), level = NULL)
fc3 %>%
autoplot(vic_elec_hourly %>% filter_index("2014-10-01"~.))
fc3 %>%
accuracy(vic_elec_hourly)# A tibble: 1 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 harmonic Test -111. 880. 673. -1.65 7.90 0.902 0.762 0.9084.2.4 Regresión armónica + predictoras exógenas
tictoc::tic()
fit4 <- vic_train %>%
model(
harmonic = ARIMA(Demand ~ Temperature + I(Temperature^2) + fourier(period = "year", K = 7) +
fourier(period = "week", K = 5) +
fourier(period = "day", K = 4) + PDQ(0,0,0) + pdq(2,0,2))
)
tictoc::toc()113 sec elapsedreport(fit4)Series: Demand
Model: LM w/ ARIMA(2,0,2) errors
Coefficients:
ar1 ar2 ma1 ma2 Temperature I(Temperature^2)
1.5044 -0.5668 -0.3417 -0.1170 -279.5698 7.5088
s.e. 0.0372 0.0321 0.0379 0.0139 7.7654 0.1837
fourier(period = "year", K = 7)C1_8766
-286.9762
s.e. 29.0917
fourier(period = "year", K = 7)S1_8766
161.6119
s.e. 26.0699
fourier(period = "year", K = 7)C2_8766
278.0314
s.e. 25.4613
fourier(period = "year", K = 7)S2_8766
265.3362
s.e. 25.5440
fourier(period = "year", K = 7)C3_8766
-147.4291
s.e. 25.3447
fourier(period = "year", K = 7)S3_8766
106.8796
s.e. 25.4146
fourier(period = "year", K = 7)C4_8766
-200.4560
s.e. 25.3352
fourier(period = "year", K = 7)S4_8766
29.0285
s.e. 25.4230
fourier(period = "year", K = 7)C5_8766
-58.3848
s.e. 25.3064
fourier(period = "year", K = 7)S5_8766
-12.5391
s.e. 25.3883
fourier(period = "year", K = 7)C6_8766
-92.0476
s.e. 25.2398
fourier(period = "year", K = 7)S6_8766
23.1517
s.e. 25.3465
fourier(period = "year", K = 7)C7_8766
-113.5976
s.e. 25.1573
fourier(period = "year", K = 7)S7_8766
68.9044
s.e. 25.2367
fourier(period = "week", K = 5)C1_168
585.2528
s.e. 24.6627
fourier(period = "week", K = 5)S1_168
-525.6332
s.e. 24.6747
fourier(period = "week", K = 5)C2_168
-35.4893
s.e. 23.6637
fourier(period = "week", K = 5)S2_168
451.2795
s.e. 23.6651
fourier(period = "week", K = 5)C3_168
-48.3112
s.e. 22.1794
fourier(period = "week", K = 5)S3_168
-111.9848
s.e. 22.1797
fourier(period = "week", K = 5)C4_168
-82.5628
s.e. 20.4075
fourier(period = "week", K = 5)S4_168
88.5390
s.e. 20.4108
fourier(period = "week", K = 5)C5_168
97.4267
s.e. 18.5450
fourier(period = "week", K = 5)S5_168
-214.5934
s.e. 18.5468
fourier(period = "day", K = 4)C1_24 fourier(period = "day", K = 4)S1_24
553.8125 1465.3068
s.e. 15.2370 17.5365
fourier(period = "day", K = 4)C2_24 fourier(period = "day", K = 4)S2_24
419.3109 -534.7655
s.e. 7.7587 7.9637
fourier(period = "day", K = 4)C3_24 fourier(period = "day", K = 4)S3_24
81.8289 -291.6448
s.e. 4.8385 4.8306
fourier(period = "day", K = 4)C4_24 fourier(period = "day", K = 4)S4_24
-188.4723 100.2865
s.e. 3.4588 3.4473
intercept
11659.4246
s.e. 80.2433
sigma^2 estimated as 100188: log likelihood=-172909.7
AIC=345899.4 AICc=345899.5 BIC=346223fc4 <- fit4 %>%
forecast(new_data = vic_elec_hourly %>% filter_index("2014-10-01"~.))
fc4 %>%
autoplot(vic_elec_hourly %>% filter_index("2014-10-01"~.), level = NULL)
fc4 %>%
autoplot(vic_elec_hourly %>% filter_index("2014-10-01"~.))
fc4 %>%
accuracy(vic_elec_hourly)# A tibble: 1 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 harmonic Test -88.7 772. 597. -1.18 7.09 0.800 0.668 0.9034.3 Combinación de modelos
Unimos los modelos estimados anteriormente en una sola mable (tabla de modelos) y creamos un modelo combinado a partir de los modelos anteriores:
fit <- fit1 %>%
mutate(
dcmp = fit2$dcmp,
harmonic = fit3$harmonic,
harmonic_temp = fit4$harmonic,
combinado1 = (ets + dcmp + harmonic + harmonic_temp)/4
)
fit# A mable: 1 x 5
ets dcmp harmonic
<model> <model> <model>
1 <ETS(A,Ad,A)> <STL decomposition model> <LM w/ ARIMA(2,0,2) errors>
# … with 2 more variables: harmonic_temp <model>, combinado1 <model>accuracy(fit) %>% arrange(MAPE)# A tibble: 5 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 dcmp Training 3.48 470. 167. -0.0777 1.73 0.224 0.407 6.23e-1
2 combinado1 Training -3.12 244. 172. -0.144 1.85 0.231 0.211 3.87e-1
3 ets Training -0.186 284. 210. -0.0556 2.32 0.282 0.246 7.68e-1
4 harmonic_temp Training -0.00195 316. 238. -0.120 2.61 0.319 0.274 -2.04e-3
5 harmonic Training 0.00939 349. 262. -0.135 2.83 0.352 0.302 9.99e-5fc <- fit %>%
forecast(new_data = vic_test)
p <-
ggplot()+
geom_line(data = vic_test, aes(x = hora, y = Demand)) +
geom_line(data = fc, aes(x = hora, y = .mean, color = .model))
plotly::ggplotly(p)fc %>%
accuracy(vic_elec_hourly) %>% arrange(MAPE)# A tibble: 5 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 combinado1 Test 2.12 768. 578. -0.507 6.58 0.775 0.665 0.911
2 harmonic_temp Test -88.7 772. 597. -1.18 7.09 0.800 0.668 0.903
3 dcmp Test 188. 993. 698. 1.90 8.00 0.936 0.859 0.897
4 harmonic Test -124. 894. 682. -1.82 8.03 0.915 0.774 0.910
5 ets Test 33.3 1138. 950. -0.936 10.8 1.27 0.986 0.943fc %>%
filter(.model == "combinado1") %>%
autoplot(vic_test)
4.3.1 Regresión armónica + predictoras exógenas y dummy festivos
tictoc::tic()
fit5 <- vic_train %>%
model(
harmonic_temp_h = ARIMA(Demand ~ Temperature + I(Temperature^2) + fourier(period = "year", K = 7) + Holiday +
fourier(period = "week", K = 5) +
fourier(period = "day", K = 4) + PDQ(0,0,0) + pdq(2,0,2))
)
tictoc::toc()129.29 sec elapsedreport(fit5)Series: Demand
Model: LM w/ ARIMA(2,0,2) errors
Coefficients:
ar1 ar2 ma1 ma2 Temperature I(Temperature^2)
1.5057 -0.5698 -0.3458 -0.1166 -277.0607 7.4895
s.e. 0.0358 0.0307 0.0366 0.0135 7.7482 0.1841
fourier(period = "year", K = 7)C1_8766
-290.7067
s.e. 28.2610
fourier(period = "year", K = 7)S1_8766
163.3459
s.e. 25.1826
fourier(period = "year", K = 7)C2_8766
279.8746
s.e. 24.5480
fourier(period = "year", K = 7)S2_8766
261.2902
s.e. 24.6468
fourier(period = "year", K = 7)C3_8766
-144.0639
s.e. 24.4367
fourier(period = "year", K = 7)S3_8766
104.1295
s.e. 24.5107
fourier(period = "year", K = 7)C4_8766
-195.0305
s.e. 24.4444
fourier(period = "year", K = 7)S4_8766
30.4333
s.e. 24.5118
fourier(period = "year", K = 7)C5_8766
-55.6505
s.e. 24.4109
fourier(period = "year", K = 7)S5_8766
-9.2727
s.e. 24.4798
fourier(period = "year", K = 7)C6_8766
-88.7195
s.e. 24.3423
fourier(period = "year", K = 7)S6_8766
19.7732
s.e. 24.4441
fourier(period = "year", K = 7)C7_8766
-108.1952
s.e. 24.2762
fourier(period = "year", K = 7)S7_8766 Holiday
68.7754 -272.8512
s.e. 24.3355 44.1670
fourier(period = "week", K = 5)C1_168
583.1329
s.e. 23.8272
fourier(period = "week", K = 5)S1_168
-529.9252
s.e. 23.8458
fourier(period = "week", K = 5)C2_168
-33.1550
s.e. 22.9762
fourier(period = "week", K = 5)S2_168
456.8081
s.e. 22.9880
fourier(period = "week", K = 5)C3_168
-49.9360
s.e. 21.6779
fourier(period = "week", K = 5)S3_168
-115.5447
s.e. 21.6874
fourier(period = "week", K = 5)C4_168
-83.9451
s.e. 20.0969
fourier(period = "week", K = 5)S4_168
90.5980
s.e. 20.0961
fourier(period = "week", K = 5)C5_168
98.6771
s.e. 18.3810
fourier(period = "week", K = 5)S5_168
-216.1351
s.e. 18.3816
fourier(period = "day", K = 4)C1_24 fourier(period = "day", K = 4)S1_24
552.4248 1460.0218
s.e. 15.2307 17.5121
fourier(period = "day", K = 4)C2_24 fourier(period = "day", K = 4)S2_24
419.0302 -536.4984
s.e. 7.7888 7.9916
fourier(period = "day", K = 4)C3_24 fourier(period = "day", K = 4)S3_24
81.9913 -291.5046
s.e. 4.8462 4.8384
fourier(period = "day", K = 4)C4_24 fourier(period = "day", K = 4)S4_24
-188.6192 100.2777
s.e. 3.4600 3.4486
intercept
11631.9996
s.e. 79.7767
sigma^2 estimated as 100053: log likelihood=-172893
AIC=345868 AICc=345868.2 BIC=346199.7fc5 <- fit5 %>%
forecast(new_data = vic_test)
fc5 %>%
accuracy(vic_test)# A tibble: 1 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 harmonic_temp_h Test -89.4 755. 589. -1.16 6.99 NaN NaN 0.8994.3.2 Más modelos combinados
Agregamos el nuevo modelo a nuestra tabla, y probamos haciendo otras dos combinaciones distintas:
fit_comb2 <- fit %>%
mutate(harmonic_temp_h = fit5$harmonic_temp_h,
combinado2 = (ets + dcmp + harmonic_temp_h)/3,
combinado3 = (ets + dcmp + harmonic + harmonic_temp + harmonic_temp_h)/5)fit_comb2 %>%
accuracy() %>% arrange(MAPE)# A tibble: 8 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 combinado2 Train… -1.89 241. 157. -0.117 1.69 0.211 0.209 5.55e-1
2 dcmp Train… 3.48 470. 167. -0.0777 1.73 0.224 0.407 6.23e-1
3 combinado1 Train… -3.12 244. 172. -0.144 1.85 0.231 0.211 3.87e-1
4 combinado3 Train… -4.33 249. 181. -0.161 1.95 0.242 0.215 2.80e-1
5 ets Train… -0.186 284. 210. -0.0556 2.32 0.282 0.246 7.68e-1
6 harmonic_temp_h Train… 0.0117 316. 238. -0.120 2.61 0.319 0.274 -2.32e-3
7 harmonic_temp Train… -0.00195 316. 238. -0.120 2.61 0.319 0.274 -2.04e-3
8 harmonic Train… 0.00939 349. 262. -0.135 2.83 0.352 0.302 9.99e-5fc_comb2 <- fit_comb2 %>%
forecast(new_data = vic_test)
fc_comb2 %>%
accuracy(vic_test) %>% arrange(MAPE)# A tibble: 8 × 10
.model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 combinado3 Test -16.2 744. 565. -0.638 6.48 NaN NaN 0.908
2 combinado1 Test 2.12 768. 578. -0.507 6.58 NaN NaN 0.911
3 combinado2 Test 44.0 773. 586. -0.0669 6.61 NaN NaN 0.909
4 harmonic_temp_h Test -89.4 755. 589. -1.16 6.99 NaN NaN 0.899
5 harmonic_temp Test -88.7 772. 597. -1.18 7.09 NaN NaN 0.903
6 dcmp Test 188. 993. 698. 1.90 8.00 NaN NaN 0.897
7 harmonic Test -124. 894. 682. -1.82 8.03 NaN NaN 0.910
8 ets Test 33.3 1138. 950. -0.936 10.8 NaN NaN 0.943p <-
ggplot()+
geom_line(data = vic_test, aes(x = hora, y = Demand)) +
geom_line(data = fc_comb2, aes(x = hora, y = .mean, color = .model))
plotly::ggplotly(p)