#Removing all the objects in the memory
rm(list = ls())
#Loading the libraries
library(fpp2)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v ggplot2 3.3.3 v fma 2.4
## v forecast 8.14 v expsmooth 2.3
##
library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v tibble 3.1.1 v dplyr 1.0.6
## v tidyr 1.1.3 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.1
## v purrr 0.3.4
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
library(dplyr)
library(readr)
library(psych)
##
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
library(caret)
## Loading required package: lattice
##
## Attaching package: 'caret'
## The following object is masked from 'package:purrr':
##
## lift
library(neuralnet)
##
## Attaching package: 'neuralnet'
## The following object is masked from 'package:dplyr':
##
## compute
library(neuralnet)
library(knitr)
#Importing the test and train dataset
dengue_features_test <- read_csv("C:/Users/HP/Desktop/dengue_features_test.csv")
##
## -- Column specification --------------------------------------------------------
## cols(
## .default = col_double(),
## city = col_character(),
## week_start_date = col_date(format = "")
## )
## i Use `spec()` for the full column specifications.
View(dengue_features_test)
attach(dengue_features_test)
dim(dengue_features_test)
## [1] 416 24
#Selecting only important variables
dengue_features_test <- select(dengue_features_test,
city, year, week_start_date, precipitation_amt_mm,
reanalysis_air_temp_k ,reanalysis_avg_temp_k,
reanalysis_relative_humidity_percent,
reanalysis_sat_precip_amt_mm)
view(dengue_features_test)
attach(dengue_features_test)
## The following objects are masked from dengue_features_test (pos = 3):
##
## city, precipitation_amt_mm, reanalysis_air_temp_k,
## reanalysis_avg_temp_k, reanalysis_relative_humidity_percent,
## reanalysis_sat_precip_amt_mm, week_start_date, year
#Checking for missing values and removing them
sum(is.na(dengue_features_test))
## [1] 10
#Removing missing observation
dengue_features_test <- na.omit(dengue_features_test)
dengue_features_test
## # A tibble: 414 x 8
## city year week_start_date precipitation_amt_mm reanalysis_air_temp_k
## <chr> <dbl> <date> <dbl> <dbl>
## 1 sj 2008 2008-04-29 78.6 298.
## 2 sj 2008 2008-05-06 12.6 298.
## 3 sj 2008 2008-05-13 3.66 299.
## 4 sj 2008 2008-05-20 0 300.
## 5 sj 2008 2008-05-27 0.76 300.
## 6 sj 2008 2008-06-03 71.2 300.
## 7 sj 2008 2008-06-10 49.0 300.
## 8 sj 2008 2008-06-17 30.8 300.
## 9 sj 2008 2008-06-24 8.02 301.
## 10 sj 2008 2008-07-01 17.5 300.
## # ... with 404 more rows, and 3 more variables: reanalysis_avg_temp_k <dbl>,
## # reanalysis_relative_humidity_percent <dbl>,
## # reanalysis_sat_precip_amt_mm <dbl>
#Train dataset
dengue_features_train <- read_csv("C:/Users/HP/Desktop/dengue_features_train.csv")
##
## -- Column specification --------------------------------------------------------
## cols(
## .default = col_double(),
## city = col_character(),
## week_start_date = col_date(format = "")
## )
## i Use `spec()` for the full column specifications.
View(dengue_features_train)
attach(dengue_features_train) #Attaching the variables in the dataset
## The following objects are masked from dengue_features_test (pos = 3):
##
## city, precipitation_amt_mm, reanalysis_air_temp_k,
## reanalysis_avg_temp_k, reanalysis_relative_humidity_percent,
## reanalysis_sat_precip_amt_mm, week_start_date, year
## The following objects are masked from dengue_features_test (pos = 4):
##
## city, ndvi_ne, ndvi_nw, ndvi_se, ndvi_sw, precipitation_amt_mm,
## reanalysis_air_temp_k, reanalysis_avg_temp_k,
## reanalysis_dew_point_temp_k, reanalysis_max_air_temp_k,
## reanalysis_min_air_temp_k, reanalysis_precip_amt_kg_per_m2,
## reanalysis_relative_humidity_percent, reanalysis_sat_precip_amt_mm,
## reanalysis_specific_humidity_g_per_kg, reanalysis_tdtr_k,
## station_avg_temp_c, station_diur_temp_rng_c, station_max_temp_c,
## station_min_temp_c, station_precip_mm, week_start_date, weekofyear,
## year
#Selecting only important variables
dengue_features_train <- select(dengue_features_train, city,
year, week_start_date,precipitation_amt_mm,
reanalysis_air_temp_k,reanalysis_avg_temp_k,
reanalysis_relative_humidity_percent,reanalysis_sat_precip_amt_mm
)
dengue_features_train <- as_tibble(dengue_features_train)
view(dengue_features_train)
attach(dengue_features_train)
## The following objects are masked from dengue_features_train (pos = 3):
##
## city, precipitation_amt_mm, reanalysis_air_temp_k,
## reanalysis_avg_temp_k, reanalysis_relative_humidity_percent,
## reanalysis_sat_precip_amt_mm, week_start_date, year
## The following objects are masked from dengue_features_test (pos = 4):
##
## city, precipitation_amt_mm, reanalysis_air_temp_k,
## reanalysis_avg_temp_k, reanalysis_relative_humidity_percent,
## reanalysis_sat_precip_amt_mm, week_start_date, year
## The following objects are masked from dengue_features_test (pos = 5):
##
## city, precipitation_amt_mm, reanalysis_air_temp_k,
## reanalysis_avg_temp_k, reanalysis_relative_humidity_percent,
## reanalysis_sat_precip_amt_mm, week_start_date, year
#Checking for missing values and removing them
sum(is.na(dengue_features_train))
## [1] 56
#Removing missing observation
dengue_features_train <- na.omit(dengue_features_train)
dengue_features_train
## # A tibble: 1,443 x 8
## city year week_start_date precipitation_amt_mm reanalysis_air_temp_k
## <chr> <dbl> <date> <dbl> <dbl>
## 1 sj 1990 1990-04-30 12.4 298.
## 2 sj 1990 1990-05-07 22.8 298.
## 3 sj 1990 1990-05-14 34.5 299.
## 4 sj 1990 1990-05-21 15.4 299.
## 5 sj 1990 1990-05-28 7.52 300.
## 6 sj 1990 1990-06-04 9.58 300.
## 7 sj 1990 1990-06-11 3.48 299.
## 8 sj 1990 1990-06-18 151. 300.
## 9 sj 1990 1990-06-25 19.3 300.
## 10 sj 1990 1990-07-02 14.4 300.
## # ... with 1,433 more rows, and 3 more variables: reanalysis_avg_temp_k <dbl>,
## # reanalysis_relative_humidity_percent <dbl>,
## # reanalysis_sat_precip_amt_mm <dbl>
sum(is.na(dengue_features_train)) #There are no missing observation
## [1] 0
#Data Description
describe(dengue_features_train[-c(1:4)])
## vars n mean sd median trimmed
## reanalysis_air_temp_k 1 1443 298.70 1.36 298.65 298.72
## reanalysis_avg_temp_k 2 1443 299.23 1.26 299.29 299.26
## reanalysis_relative_humidity_percent 3 1443 82.17 7.16 80.30 81.70
## reanalysis_sat_precip_amt_mm 4 1443 45.76 43.72 38.34 40.16
## mad min max range skew kurtosis
## reanalysis_air_temp_k 1.57 294.64 302.20 7.56 -0.08 -0.69
## reanalysis_avg_temp_k 1.43 294.89 302.93 8.04 -0.19 -0.53
## reanalysis_relative_humidity_percent 5.68 57.79 98.61 40.82 0.57 -0.40
## reanalysis_sat_precip_amt_mm 44.23 0.00 390.60 390.60 1.73 6.74
## se
## reanalysis_air_temp_k 0.04
## reanalysis_avg_temp_k 0.03
## reanalysis_relative_humidity_percent 0.19
## reanalysis_sat_precip_amt_mm 1.15
knitr::kable(describe(dengue_features_train[-c(1:4)]))
| reanalysis_air_temp_k |
1 |
1443 |
298.70389 |
1.363079 |
298.64857 |
298.71992 |
1.573674 |
294.63571 |
302.2000 |
7.564286 |
-0.0845621 |
-0.6865367 |
0.0358829 |
| reanalysis_avg_temp_k |
2 |
1443 |
299.22823 |
1.261648 |
299.29286 |
299.25639 |
1.429650 |
294.89286 |
302.9286 |
8.035714 |
-0.1935768 |
-0.5309318 |
0.0332128 |
| reanalysis_relative_humidity_percent |
3 |
1443 |
82.16908 |
7.158343 |
80.30286 |
81.70087 |
5.682594 |
57.78714 |
98.6100 |
40.822857 |
0.5705195 |
-0.4022083 |
0.1884427 |
| reanalysis_sat_precip_amt_mm |
4 |
1443 |
45.76039 |
43.715537 |
38.34000 |
40.15939 |
44.225958 |
0.00000 |
390.6000 |
390.600000 |
1.7338384 |
6.7388910 |
1.1508074 |
#Data description in San Juan
San_Juan_dengue_train <- filter(dengue_features_train,
city == "sj")
view(San_Juan_dengue_train)
knitr::kable(describe(San_Juan_dengue_train[-c(1:4)]))
| reanalysis_air_temp_k |
1 |
927 |
299.16831 |
1.235662 |
299.27000 |
299.20093 |
1.459302 |
295.93857 |
302.20000 |
6.261429 |
-0.2241410 |
-0.8722457 |
0.0405845 |
| reanalysis_avg_temp_k |
2 |
927 |
299.28122 |
1.218206 |
299.38571 |
299.31410 |
1.408470 |
296.11429 |
302.16429 |
6.050000 |
-0.2307338 |
-0.8159498 |
0.0400111 |
| reanalysis_relative_humidity_percent |
3 |
927 |
78.56764 |
3.390744 |
78.66857 |
78.62003 |
3.486228 |
66.73571 |
87.57571 |
20.840000 |
-0.1930726 |
-0.0833090 |
0.1113666 |
| reanalysis_sat_precip_amt_mm |
4 |
927 |
35.47081 |
44.606137 |
20.80000 |
27.51576 |
30.838080 |
0.00000 |
390.60000 |
390.600000 |
2.6102012 |
11.6922106 |
1.4650578 |
#San Juan test data
San_Juan_dengue_test <- filter(dengue_features_test,
city == "sj")
view(San_Juan_dengue_test)
#converting the dataset into a timeseries data
#Precipitation
San_Juan_dengue_train_precipitation.ts <- ts(San_Juan_dengue_train$precipitation_amt_mm, start = 1990, frequency = 52)
view(San_Juan_dengue_train_precipitation.ts)
#Datavisualization
autoplot(San_Juan_dengue_train_precipitation.ts)+
ggtitle("San Juan Precipitation amount (mm)")+
ylab("Precipitation amount (mm)")+
xlab("Time") +
theme_light()
#Humidity
San_Juan_dengue_train_humidity.ts <- ts(San_Juan_dengue_train$reanalysis_relative_humidity_percent, start = 1990, frequency = 52)
view(San_Juan_dengue_train_humidity.ts)
#Datavisualization
autoplot(San_Juan_dengue_train_humidity.ts)+
ggtitle("San Juan Relative Humidity percent")+
ylab("Relative Humidity")+
xlab("Time") +
theme_light()
#Temperature
San_Juan_dengue_train_temp.ts <- ts(San_Juan_dengue_train$reanalysis_air_temp_k, start = 1990, frequency = 52)
view(San_Juan_dengue_train_temp.ts)
#Datavisualization
autoplot(San_Juan_dengue_train_temp.ts)+
ggtitle("San Juan Air Temperature (k)")+
ylab("Air Temperature")+
xlab("Time") +
theme_grey()
#Data description in Iquitos
iquitos_dengue_train <- filter(dengue_features_train,
city == "iq")
view(iquitos_dengue_train)
knitr::kable(describe(iquitos_dengue_train[-c(1:4)]))
| reanalysis_air_temp_k |
1 |
516 |
297.86954 |
1.170997 |
297.82286 |
297.86236 |
1.131012 |
294.63571 |
301.6371 |
7.001429 |
0.1056252 |
-0.0381419 |
0.0515503 |
| reanalysis_avg_temp_k |
2 |
516 |
299.13304 |
1.332073 |
299.12143 |
299.15093 |
1.408470 |
294.89286 |
302.9286 |
8.035714 |
-0.1077805 |
-0.2133632 |
0.0586412 |
| reanalysis_relative_humidity_percent |
3 |
516 |
88.63912 |
7.583889 |
90.91714 |
89.58349 |
6.321171 |
57.78714 |
98.6100 |
40.822857 |
-1.0992274 |
0.7842504 |
0.3338621 |
| reanalysis_sat_precip_amt_mm |
4 |
516 |
64.24574 |
35.218995 |
60.47000 |
62.24196 |
33.944127 |
0.00000 |
210.8300 |
210.830000 |
0.5973640 |
0.3969977 |
1.5504298 |
#Iquitos test data data
iquitos_dengue_test <- filter(dengue_features_test,
city == "sj")
view(iquitos_dengue_test)
#converting the dataset into a timeseries data
#Precipitation
iquitos_dengue_train_precipitation.ts <- ts(iquitos_dengue_train $precipitation_amt_mm, start = 1990, frequency = 52)
view(iquitos_dengue_train_precipitation.ts)
#Datavisualization
autoplot(iquitos_dengue_train_precipitation.ts)+
ggtitle("Iquitos Precipitation amount (mm)")+
ylab("Precipitation amount (mm)")+
xlab("Time") +
theme_gray()
#Humidity
iquitos_dengue_train_humidity.ts <- ts(iquitos_dengue_train$reanalysis_relative_humidity_percent, start = 1990, frequency = 52)
view(iquitos_dengue_train_humidity.ts)
#Datavisualization
autoplot(iquitos_dengue_train_humidity.ts)+
ggtitle("Iquitos Relative Humidity percent")+
ylab("Relative Humidity")+
xlab("Time") +
theme_light()
#Temperature
iquitos_train_temp.ts <- ts(iquitos_dengue_train$reanalysis_air_temp_k, start = 1990, frequency = 52)
view(iquitos_train_temp.ts)
#Datavisualization
autoplot(iquitos_train_temp.ts)+
ggtitle("Iquitos Air Temperature (k)")+
ylab("Air Temperature")+
xlab("Time") +
theme_grey()
#total dengue cases
#importing the dataset
dengue_labels_train <- read_csv("C:/Users/HP/Desktop/dengue_labels_train.csv")
##
## -- Column specification --------------------------------------------------------
## cols(
## city = col_character(),
## year = col_double(),
## weekofyear = col_double(),
## total_cases = col_double()
## )
View(dengue_labels_train)
attach(dengue_labels_train)
## The following objects are masked from dengue_features_train (pos = 3):
##
## city, year
## The following objects are masked from dengue_features_train (pos = 4):
##
## city, weekofyear, year
## The following objects are masked from dengue_features_test (pos = 5):
##
## city, year
## The following objects are masked from dengue_features_test (pos = 6):
##
## city, weekofyear, year
#data description
aggregate((total_cases) ~ city, data = dengue_labels_train, FUN = sum)
## city (total_cases)
## 1 iq 3934
## 2 sj 31993
san.juan.cases <- filter(dengue_labels_train, city == "sj")
san.juan.cases
## # A tibble: 936 x 4
## city year weekofyear total_cases
## <chr> <dbl> <dbl> <dbl>
## 1 sj 1990 18 4
## 2 sj 1990 19 5
## 3 sj 1990 20 4
## 4 sj 1990 21 3
## 5 sj 1990 22 6
## 6 sj 1990 23 2
## 7 sj 1990 24 4
## 8 sj 1990 25 5
## 9 sj 1990 26 10
## 10 sj 1990 27 6
## # ... with 926 more rows
San_Juan.cases.ts <- ts(san.juan.cases$total_cases, start = 1990, frequency = 52)
view(San_Juan.cases.ts)
#Datavisualization
autoplot(San_Juan.cases.ts)+
ggtitle("San Juan total dengue cases")+
ylab("dengue cases")+
xlab("Time") +
theme_light()
iquitos.cases <- filter(dengue_labels_train, city == "iq")
iquitos.cases
## # A tibble: 520 x 4
## city year weekofyear total_cases
## <chr> <dbl> <dbl> <dbl>
## 1 iq 2000 26 0
## 2 iq 2000 27 0
## 3 iq 2000 28 0
## 4 iq 2000 29 0
## 5 iq 2000 30 0
## 6 iq 2000 31 0
## 7 iq 2000 32 0
## 8 iq 2000 33 0
## 9 iq 2000 34 0
## 10 iq 2000 35 0
## # ... with 510 more rows
attach(iquitos.cases)
## The following objects are masked from dengue_labels_train:
##
## city, total_cases, weekofyear, year
## The following objects are masked from dengue_features_train (pos = 4):
##
## city, year
## The following objects are masked from dengue_features_train (pos = 5):
##
## city, weekofyear, year
## The following objects are masked from dengue_features_test (pos = 6):
##
## city, year
## The following objects are masked from dengue_features_test (pos = 7):
##
## city, weekofyear, year
iquitos.ts <- ts(iquitos.cases$total_cases, start = 1990, frequency = 52)
iquitos.ts
## Time Series:
## Start = c(1990, 1)
## End = c(1999, 52)
## Frequency = 52
## [1] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0
## [19] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0
## [55] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 1 1 1 2 4 1 4 11 16 23 12 14 18 8 7 10 7 10
## [91] 5 11 8 18 13 9 22 10 5 13 2 11 11 3 7 7 4 5
## [109] 6 7 7 4 9 17 8 22 18 21 16 31 25 28 26 18 27 11
## [127] 38 29 21 11 10 5 6 2 1 2 2 3 5 1 4 2 4 0
## [145] 0 0 0 1 1 1 1 1 2 3 4 6 2 2 5 1 1 0
## [163] 0 0 0 2 0 3 0 0 0 2 2 3 3 3 1 2 3 6
## [181] 5 1 4 5 8 5 2 3 3 1 6 4 1 2 3 1 8 4
## [199] 6 7 5 8 6 5 6 6 13 2 10 3 12 7 6 5 6 6
## [217] 6 8 6 9 12 19 8 16 21 6 22 37 33 18 83 116 32 7
## [235] 9 10 5 8 7 8 11 6 7 7 14 7 9 13 16 7 9 2
## [253] 13 8 3 5 4 8 2 3 5 7 3 5 6 5 5 4 0 0
## [271] 0 0 0 2 4 4 3 3 5 6 14 3 7 11 2 6 8 25
## [289] 21 10 28 39 20 24 28 26 8 9 12 18 9 9 6 6 8 5
## [307] 7 6 5 3 1 0 1 2 3 2 2 2 2 2 4 0 6 3
## [325] 2 6 2 7 4 6 6 2 13 10 5 2 0 1 0 14 6 10
## [343] 5 12 9 5 11 2 6 7 6 5 9 5 8 3 4 11 5 8
## [361] 4 3 1 2 3 4 1 8 5 3 2 7 1 6 7 5 2 6
## [379] 11 6 3 11 11 5 4 9 23 28 26 7 29 58 26 38 35 37
## [397] 20 29 25 23 9 3 6 6 3 1 3 1 1 0 2 1 1 0
## [415] 0 1 0 3 3 1 5 2 5 5 5 9 17 19 25 45 34 63
## [433] 44 50 35 16 16 13 9 15 4 0 1 10 11 29 35 30 20 21
## [451] 12 9 11 9 5 11 3 5 5 4 4 1 0 2 3 3 5 2
## [469] 1 2 0 0 3 5 5 7 5 2 2 2 0 2 1 1 2 2
## [487] 3 9 5 5 4 4 1 0 0 10 9 17 16 11 12 19 15 12
## [505] 12 16 9 4 9 6 8 4 2 7 6 5 8 1 1 4
autoplot(iquitos.ts)+
ggtitle("iquitos total dengue cases")+
ylab("Iquitos cases")+
xlab("Time") +
theme_light()
#ETS model
Ets_San.Juan_train.model <- ets(San_Juan.cases.ts)
Ets_San.Juan_train.model
## ETS(A,Ad,N)
##
## Call:
## ets(y = San_Juan.cases.ts)
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.1355
## phi = 0.8
##
## Initial states:
## l = 3.0767
## b = 0.2624
##
## sigma: 13.4753
##
## AIC AICc BIC
## 11279.55 11279.64 11308.60
summary(Ets_San.Juan_train.model)
## ETS(A,Ad,N)
##
## Call:
## ets(y = San_Juan.cases.ts)
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.1355
## phi = 0.8
##
## Initial states:
## l = 3.0767
## b = 0.2624
##
## sigma: 13.4753
##
## AIC AICc BIC
## 11279.55 11279.64 11308.60
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.00139911 13.43929 8.026055 NaN Inf 0.2196945 0.01271293
#forecasting for the total cases using ETS Model
forecast_ets.san.juan <- forecast(Ets_San.Juan_train.model)
forecast_ets.san.juan
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2008.000 5.228984 -12.04034 22.49831 -21.18217 31.64014
## 2008.019 5.412350 -20.36663 31.19133 -34.01320 44.83790
## 2008.038 5.559044 -27.46309 38.58118 -44.94396 56.06204
## 2008.058 5.676398 -33.91225 45.26505 -54.86921 66.22201
## 2008.077 5.770282 -39.91170 51.45226 -64.09428 75.63484
## 2008.096 5.845390 -45.55476 57.24554 -72.76435 84.45513
## 2008.115 5.905476 -50.89588 62.70683 -80.96470 92.77565
## 2008.135 5.953544 -55.97209 67.87917 -88.75353 100.66062
## 2008.154 5.992000 -60.81143 72.79542 -96.17502 108.15902
## 2008.173 6.022764 -65.43668 77.48221 -103.26503 115.31056
## 2008.192 6.047375 -69.86720 81.96195 -110.05395 122.14870
## 2008.212 6.067064 -74.11982 86.25395 -116.56819 128.70232
## 2008.231 6.082816 -78.20943 90.37506 -122.83105 134.99668
## 2008.250 6.095417 -82.14931 94.34014 -128.86325 141.05408
## 2008.269 6.105498 -85.95137 98.16237 -134.68334 146.89433
## 2008.288 6.113562 -89.62634 101.85346 -140.30798 152.53510
## 2008.308 6.120014 -93.18385 105.42388 -145.75214 157.99217
## 2008.327 6.125176 -96.63264 108.88299 -151.02935 163.27970
## 2008.346 6.129305 -99.98059 112.23920 -156.15178 168.41039
## 2008.365 6.132608 -103.23483 115.50005 -161.13046 173.39568
## 2008.385 6.135251 -106.40183 118.67233 -165.97536 178.24587
## 2008.404 6.137365 -109.48745 121.76218 -170.69553 182.97026
## 2008.423 6.139056 -112.49702 124.77513 -175.29916 187.57727
## 2008.442 6.140409 -115.43538 127.71620 -179.79371 192.07453
## 2008.462 6.141492 -118.30695 130.58993 -184.18597 196.46895
## 2008.481 6.142358 -121.11575 133.40046 -188.48212 200.76684
## 2008.500 6.143051 -123.86546 136.15156 -192.68781 204.97391
## 2008.519 6.143605 -126.55946 138.84667 -196.80822 209.09543
## 2008.538 6.144048 -129.20082 141.48891 -200.84806 213.13616
## 2008.558 6.144403 -131.79238 144.08118 -204.81170 217.10051
## 2008.577 6.144687 -134.33675 146.62612 -208.70312 220.99250
## 2008.596 6.144914 -136.83632 149.12615 -212.52601 224.81584
## 2008.615 6.145095 -139.29332 151.58351 -216.28377 228.57396
## 2008.635 6.145241 -141.70979 154.00027 -219.97952 232.27000
## 2008.654 6.145357 -144.08764 156.37835 -223.61618 235.90689
## 2008.673 6.145450 -146.42861 158.71951 -227.19644 239.48734
## 2008.692 6.145524 -148.73435 161.02540 -230.72281 243.01386
## 2008.712 6.145584 -151.00639 163.29755 -234.19761 246.48878
## 2008.731 6.145631 -153.24613 165.53739 -237.62302 249.91429
## 2008.750 6.145669 -155.45490 167.74624 -241.00107 253.29241
## 2008.769 6.145700 -157.63394 169.92534 -244.33365 256.62505
## 2008.788 6.145724 -159.78442 172.07587 -247.62253 259.91398
## 2008.808 6.145744 -161.90742 174.19890 -250.86938 263.16087
## 2008.827 6.145759 -164.00395 176.29547 -254.07577 266.36729
## 2008.846 6.145772 -166.07499 178.36654 -257.24316 269.53470
## 2008.865 6.145782 -168.12144 180.41300 -260.37293 272.66450
## 2008.885 6.145790 -170.14415 182.43572 -263.46640 275.75798
## 2008.904 6.145796 -172.14392 184.43551 -266.52479 278.81638
## 2008.923 6.145801 -174.12151 186.41312 -269.54926 281.84087
## 2008.942 6.145805 -176.07766 188.36927 -272.54093 284.83254
## 2008.962 6.145809 -178.01303 190.30464 -275.50083 287.79244
## 2008.981 6.145811 -179.92827 192.21990 -278.42995 290.72157
## 2009.000 6.145813 -181.82401 194.11564 -281.32923 293.62085
## 2009.019 6.145815 -183.70082 195.99245 -284.19956 296.49119
## 2009.038 6.145816 -185.55926 197.85089 -287.04180 299.33343
## 2009.058 6.145817 -187.39986 199.69149 -289.85675 302.14839
## 2009.077 6.145818 -189.22312 201.51475 -292.64519 304.93682
## 2009.096 6.145819 -191.02952 203.32116 -295.40784 307.69948
## 2009.115 6.145820 -192.81952 205.11116 -298.14541 310.43705
## 2009.135 6.145820 -194.59356 206.88520 -300.85857 313.15021
## 2009.154 6.145820 -196.35207 208.64371 -303.54797 315.83961
## 2009.173 6.145821 -198.09543 210.38707 -306.21421 318.50585
## 2009.192 6.145821 -199.82403 212.11568 -308.85789 321.14953
## 2009.212 6.145821 -201.53825 213.82990 -311.47956 323.77120
## 2009.231 6.145821 -203.23844 215.53008 -314.07977 326.37141
## 2009.250 6.145821 -204.92493 217.21657 -316.65904 328.95068
## 2009.269 6.145821 -206.59805 218.88970 -319.21786 331.50950
## 2009.288 6.145821 -208.25812 220.54976 -321.75671 334.04836
## 2009.308 6.145821 -209.90543 222.19708 -324.27606 336.56770
## 2009.327 6.145822 -211.54028 223.83192 -326.77634 339.06798
## 2009.346 6.145822 -213.16294 225.45458 -329.25799 341.54963
## 2009.365 6.145822 -214.77368 227.06533 -331.72140 344.01305
## 2009.385 6.145822 -216.37276 228.66441 -334.16699 346.45863
## 2009.404 6.145822 -217.96044 230.25208 -336.59513 348.88677
## 2009.423 6.145822 -219.53694 231.82859 -339.00618 351.29782
## 2009.442 6.145822 -221.10251 233.39415 -341.40051 353.69215
## 2009.462 6.145822 -222.65736 234.94901 -343.77846 356.07010
## 2009.481 6.145822 -224.20173 236.49337 -346.14035 358.43199
## 2009.500 6.145822 -225.73580 238.02744 -348.48652 360.77816
## 2009.519 6.145822 -227.25979 239.55144 -350.81726 363.10890
## 2009.538 6.145822 -228.77390 241.06554 -353.13289 365.42453
## 2009.558 6.145822 -230.27831 242.56995 -355.43368 367.72533
## 2009.577 6.145822 -231.77321 244.06485 -357.71993 370.01157
## 2009.596 6.145822 -233.25877 245.55041 -359.99190 372.28355
## 2009.615 6.145822 -234.73517 247.02681 -362.24986 374.54151
## 2009.635 6.145822 -236.20258 248.49422 -364.49407 376.78571
## 2009.654 6.145822 -237.66115 249.95279 -366.72477 379.01641
## 2009.673 6.145822 -239.11105 251.40270 -368.94220 381.23384
## 2009.692 6.145822 -240.55243 252.84408 -371.14660 383.43824
## 2009.712 6.145822 -241.98544 254.27708 -373.33819 385.62984
## 2009.731 6.145822 -243.41022 255.70186 -375.51721 387.80885
## 2009.750 6.145822 -244.82691 257.11855 -377.68385 389.97549
## 2009.769 6.145822 -246.23565 258.52729 -379.83833 392.12997
## 2009.788 6.145822 -247.63656 259.92821 -381.98084 394.27249
## 2009.808 6.145822 -249.02979 261.32144 -384.11160 396.40325
## 2009.827 6.145822 -250.41545 262.70710 -386.23079 398.52243
## 2009.846 6.145822 -251.79367 264.08532 -388.33859 400.63023
## 2009.865 6.145822 -253.16456 265.45621 -390.43519 402.72683
## 2009.885 6.145822 -254.52825 266.81989 -392.52077 404.81241
## 2009.904 6.145822 -255.88483 268.17648 -394.59549 406.88713
## 2009.923 6.145822 -257.23443 269.52608 -396.65952 408.95116
## 2009.942 6.145822 -258.57715 270.86880 -398.71303 411.00467
## 2009.962 6.145822 -259.91310 272.20474 -400.75618 413.04782
## 2009.981 6.145822 -261.24236 273.53401 -402.78912 415.08076
#Visualizing
autoplot(forecast_ets.san.juan,
main = "San Juan Total Dengue Fever Cases",
ylab = " Total cases")
#modellin ETS in Iquitos
Ets_iquitos_train.model <- ets(iquitos.ts)
## Warning in ets(iquitos.ts): I can't handle data with frequency greater than 24.
## Seasonality will be ignored. Try stlf() if you need seasonal forecasts.
Ets_iquitos_train.model
## ETS(A,N,N)
##
## Call:
## ets(y = iquitos.ts)
##
## Smoothing parameters:
## alpha = 0.6543
##
## Initial states:
## l = 0.0744
##
## sigma: 7.4063
##
## AIC AICc BIC
## 5338.417 5338.463 5351.178
summary(Ets_iquitos_train.model)
## ETS(A,N,N)
##
## Call:
## ets(y = iquitos.ts)
##
## Smoothing parameters:
## alpha = 0.6543
##
## Initial states:
## l = 0.0744
##
## sigma: 7.4063
##
## AIC AICc BIC
## 5338.417 5338.463 5351.178
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.009226816 7.392083 3.699635 -Inf Inf 0.3919034 0.0713476
#forecasting for the total cases using ETS Model
forecast_ets.iquitos <- forecast(Ets_iquitos_train.model)
forecast_ets.iquitos
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2000.000 3.213589 -6.278017 12.70520 -11.30257 17.72975
## 2000.019 3.213589 -8.129126 14.55630 -14.13360 20.56078
## 2000.038 3.213589 -9.717915 16.14509 -16.56344 22.99062
## 2000.058 3.213589 -11.131807 17.55899 -18.72580 25.15298
## 2000.077 3.213589 -12.418334 18.84551 -20.69337 27.12055
## 2000.096 3.213589 -13.606744 20.03392 -22.51089 28.93807
## 2000.115 3.213589 -14.716559 21.14374 -24.20821 30.63539
## 2000.135 3.213589 -15.761575 22.18875 -25.80642 32.23360
## 2000.154 3.213589 -16.751967 23.17915 -27.32109 33.74827
## 2000.173 3.213589 -17.695501 24.12268 -28.76411 35.19128
## 2000.192 3.213589 -18.598258 25.02544 -30.14475 36.57193
## 2000.212 3.213589 -19.465107 25.89229 -31.47048 37.89766
## 2000.231 3.213589 -20.300021 26.72720 -32.74738 39.17455
## 2000.250 3.213589 -21.106289 27.53347 -33.98046 40.40763
## 2000.269 3.213589 -21.886672 28.31385 -35.17395 41.60113
## 2000.288 3.213589 -22.643513 29.07069 -36.33144 42.75861
## 2000.308 3.213589 -23.378822 29.80600 -37.45599 43.88317
## 2000.327 3.213589 -24.094339 30.52152 -38.55028 44.97746
## 2000.346 3.213589 -24.791581 31.21876 -39.61662 46.04380
## 2000.365 3.213589 -25.471880 31.89906 -40.65705 47.08423
## 2000.385 3.213589 -26.136415 32.56359 -41.67337 48.10055
## 2000.404 3.213589 -26.786234 33.21341 -42.66718 49.09436
## 2000.423 3.213589 -27.422272 33.84945 -43.63992 50.06710
## 2000.442 3.213589 -28.045371 34.47255 -44.59286 51.02004
## 2000.462 3.213589 -28.656290 35.08347 -45.52718 51.95436
## 2000.481 3.213589 -29.255716 35.68290 -46.44393 52.87111
## 2000.500 3.213589 -29.844275 36.27145 -47.34405 53.77123
## 2000.519 3.213589 -30.422537 36.84972 -48.22843 54.65561
## 2000.538 3.213589 -30.991025 37.41820 -49.09785 55.52503
## 2000.558 3.213589 -31.550217 37.97740 -49.95306 56.38024
## 2000.577 3.213589 -32.100556 38.52773 -50.79474 57.22191
## 2000.596 3.213589 -32.642449 39.06963 -51.62349 58.05067
## 2000.615 3.213589 -33.176273 39.60345 -52.43990 58.86708
## 2000.635 3.213589 -33.702378 40.12956 -53.24451 59.67169
## 2000.654 3.213589 -34.221091 40.64827 -54.03781 60.46499
## 2000.673 3.213589 -34.732714 41.15989 -54.82027 61.24745
## 2000.692 3.213589 -35.237529 41.66471 -55.59232 62.01950
## 2000.712 3.213589 -35.735802 42.16298 -56.35437 62.78154
## 2000.731 3.213589 -36.227781 42.65496 -57.10678 63.53396
## 2000.750 3.213589 -36.713699 43.14088 -57.84993 64.27711
## 2000.769 3.213589 -37.193773 43.62095 -58.58414 65.01132
## 2000.788 3.213589 -37.668210 44.09539 -59.30973 65.73691
## 2000.808 3.213589 -38.137205 44.56438 -60.02699 66.45417
## 2000.827 3.213589 -38.600939 45.02812 -60.73621 67.16339
## 2000.846 3.213589 -39.059586 45.48677 -61.43765 67.86483
## 2000.865 3.213589 -39.513311 45.94049 -62.13157 68.55874
## 2000.885 3.213589 -39.962267 46.38945 -62.81819 69.24536
## 2000.904 3.213589 -40.406603 46.83378 -63.49774 69.92492
## 2000.923 3.213589 -40.846459 47.27364 -64.17044 70.59762
## 2000.942 3.213589 -41.281966 47.70914 -64.83649 71.26367
## 2000.962 3.213589 -41.713252 48.14043 -65.49608 71.92326
## 2000.981 3.213589 -42.140436 48.56762 -66.14941 72.57659
## 2001.000 3.213589 -42.563635 48.99081 -66.79663 73.22381
## 2001.019 3.213589 -42.982957 49.41014 -67.43793 73.86511
## 2001.038 3.213589 -43.398506 49.82569 -68.07346 74.50064
## 2001.058 3.213589 -43.810384 50.23756 -68.70337 75.13055
## 2001.077 3.213589 -44.218685 50.64586 -69.32782 75.75499
## 2001.096 3.213589 -44.623502 51.05068 -69.94693 76.37411
## 2001.115 3.213589 -45.024921 51.45210 -70.56085 76.98803
## 2001.135 3.213589 -45.423028 51.85021 -71.16970 77.59688
## 2001.154 3.213589 -45.817902 52.24508 -71.77361 78.20078
## 2001.173 3.213589 -46.209621 52.63680 -72.37269 78.79987
## 2001.192 3.213589 -46.598260 53.02544 -72.96706 79.39424
## 2001.212 3.213589 -46.983890 53.41107 -73.55683 79.98401
## 2001.231 3.213589 -47.366580 53.79376 -74.14210 80.56928
## 2001.250 3.213589 -47.746397 54.17358 -74.72298 81.15016
## 2001.269 3.213589 -48.123403 54.55058 -75.29957 81.72674
## 2001.288 3.213589 -48.497661 54.92484 -75.87194 82.29912
## 2001.308 3.213589 -48.869229 55.29641 -76.44021 82.86739
## 2001.327 3.213589 -49.238166 55.66534 -77.00445 83.43163
## 2001.346 3.213589 -49.604525 56.03170 -77.56475 83.99193
## 2001.365 3.213589 -49.968361 56.39554 -78.12118 84.54836
## 2001.385 3.213589 -50.329724 56.75690 -78.67384 85.10102
## 2001.404 3.213589 -50.688665 57.11584 -79.22280 85.64997
## 2001.423 3.213589 -51.045232 57.47241 -79.76812 86.19530
## 2001.442 3.213589 -51.399470 57.82665 -80.30988 86.73706
## 2001.462 3.213589 -51.751426 58.17860 -80.84815 87.27533
## 2001.481 3.213589 -52.101142 58.52832 -81.38299 87.81017
## 2001.500 3.213589 -52.448661 58.87584 -81.91448 88.34166
## 2001.519 3.213589 -52.794024 59.22120 -82.44266 88.86984
## 2001.538 3.213589 -53.137270 59.56445 -82.96761 89.39479
## 2001.558 3.213589 -53.478438 59.90562 -83.48938 89.91656
## 2001.577 3.213589 -53.817565 60.24474 -84.00803 90.43521
## 2001.596 3.213589 -54.154687 60.58187 -84.52362 90.95080
## 2001.615 3.213589 -54.489840 60.91702 -85.03619 91.46337
## 2001.635 3.213589 -54.823057 61.25024 -85.54580 91.97298
## 2001.654 3.213589 -55.154372 61.58155 -86.05251 92.47968
## 2001.673 3.213589 -55.483818 61.91100 -86.55635 92.98353
## 2001.692 3.213589 -55.811424 62.23860 -87.05738 93.48456
## 2001.712 3.213589 -56.137222 62.56440 -87.55564 93.98282
## 2001.731 3.213589 -56.461241 62.88842 -88.05119 94.47837
## 2001.750 3.213589 -56.783511 63.21069 -88.54406 94.97124
## 2001.769 3.213589 -57.104058 63.53124 -89.03429 95.46147
## 2001.788 3.213589 -57.422911 63.85009 -89.52194 95.94912
## 2001.808 3.213589 -57.740097 64.16728 -90.00703 96.43421
## 2001.827 3.213589 -58.055640 64.48282 -90.48961 96.91679
## 2001.846 3.213589 -58.369566 64.79675 -90.96972 97.39690
## 2001.865 3.213589 -58.681901 65.10908 -91.44739 97.87457
## 2001.885 3.213589 -58.992667 65.41985 -91.92267 98.34985
## 2001.904 3.213589 -59.301888 65.72907 -92.39558 98.82276
## 2001.923 3.213589 -59.609587 66.03677 -92.86617 99.29335
## 2001.942 3.213589 -59.915787 66.34297 -93.33446 99.76164
## 2001.962 3.213589 -60.220508 66.64769 -93.80049 100.22767
## 2001.981 3.213589 -60.523773 66.95095 -94.26429 100.69147
#Visualizing
autoplot(forecast_ets.iquitos,
main = "Iquitos Total Dengue Fever Cases",
ylab = " Total cases")
#ARIMA Model
arima_iquitos_model <- auto.arima(iquitos.ts)
arima_iquitos_model
## Series: iquitos.ts
## ARIMA(0,1,2)(0,0,1)[52]
##
## Coefficients:
## ma1 ma2 sma1
## -0.2508 -0.2322 0.0568
## s.e. 0.0430 0.0449 0.0375
##
## sigma^2 estimated as 52.12: log likelihood=-1761.09
## AIC=3530.18 AICc=3530.26 BIC=3547.19
forecast.iquitos <- forecast(arima_iquitos_model)
autoplot(forecast.iquitos,
main = "Iquitos Total Dengue Fever Cases",
ylab = " Total cases")
#ARIMA Model
arima_san.juan_model <- auto.arima(San_Juan.cases.ts)
arima_san.juan_model
## Series: San_Juan.cases.ts
## ARIMA(1,1,1)
##
## Coefficients:
## ar1 ma1
## 0.7116 -0.5929
## s.e. 0.0948 0.1078
##
## sigma^2 estimated as 180.9: log likelihood=-3755.85
## AIC=7517.71 AICc=7517.73 BIC=7532.23
forecast.san.juan.model <- forecast(arima_san.juan_model)
autoplot(forecast.san.juan.model,
main = "San Juan Total Dengue Fever Cases",
ylab = " Total cases")
#data transformation
library(MASS)
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
## The following objects are masked from 'package:fma':
##
## cement, housing, petrol
lambda_san.juan <- BoxCox.lambda(San_Juan.cases.ts)
## Warning in guerrero(x, lower, upper): Guerrero's method for selecting a Box-Cox
## parameter (lambda) is given for strictly positive data.
lambda_san.juan
## [1] 4.102259e-05
transformed_san.juan <- BoxCox(San_Juan.cases.ts, lambda = lambda_san.juan)
transformed_san.juan
## Time Series:
## Start = c(1990, 1)
## End = c(2007, 52)
## Frequency = 52
## [1] 1.386334 1.609491 1.386334 1.098637 1.791825
## [6] 0.693157 1.386334 1.609491 2.302694 1.791825
## [11] 2.079530 0.693157 1.791825 2.833378 3.135696
## [16] 2.565084 3.044713 3.332432 3.178261 2.995916
## [21] 3.689159 3.296060 3.737956 3.496758 3.761490
## [26] 3.611185 4.043387 4.263053 3.784483 4.025684
## [31] 3.970615 3.951564 3.850452 3.258314 3.296060
## [36] 3.044713 3.044713 3.258314 3.526616 3.611185
## [41] 2.833378 2.944617 3.219088 2.890543 3.044713
## [46] 2.833378 2.833378 2.772746 2.772746 2.708201
## [51] 3.135696 2.772746 2.833378 2.485033 2.833378
## [56] 2.302694 2.708201 2.944617 3.044713 2.639200
## [61] 2.890543 2.565084 2.639200 2.890543 3.135696
## [66] 3.219088 4.127484 4.094688 4.331118 4.190015
## [71] 4.159238 4.219873 4.489050 4.522208 4.942143
## [76] 4.754054 4.956331 4.860297 4.942143 4.942143
## [81] 4.844668 4.860297 5.130439 4.949262 4.682581
## [86] 4.357098 4.248865 4.394845 4.644833 4.500225
## [91] 4.443056 4.007663 3.970615 4.174745 3.496758
## [96] 3.637858 4.077878 3.689159 3.611185 3.367528
## [101] 3.401435 3.401435 3.332432 3.135696 3.178261
## [106] 3.367528 3.258314 3.135696 2.995916 2.944617
## [111] 2.995916 3.258314 3.367528 3.434229 3.332432
## [116] 3.258314 3.465982 3.555607 3.496758 3.401435
## [121] 3.951564 4.077878 4.205055 4.174745 4.304445
## [126] 4.248865 4.111221 3.970615 4.331118 4.111221
## [131] 4.043387 3.784483 3.526616 3.850452 4.094688
## [136] 4.094688 3.970615 3.583782 3.434229 3.401435
## [141] 3.465982 3.332432 3.496758 3.496758 3.555607
## [146] 3.091238 2.565084 2.565084 3.044713 2.833378
## [151] 2.398013 2.079530 2.079530 1.791825 1.791825
## [156] 1.945988 2.485033 2.833378 2.302694 2.302694
## [161] 2.890543 2.944617 2.485033 3.091238 2.485033
## [166] 3.044713 2.890543 2.772746 2.772746 3.091238
## [171] 2.833378 3.219088 3.135696 2.485033 3.219088
## [176] 3.332432 3.296060 2.890543 3.135696 3.135696
## [181] 3.367528 3.637858 3.583782 3.761490 3.828942
## [186] 3.434229 3.219088 3.689159 3.434229 3.637858
## [191] 3.401435 3.091238 3.434229 3.258314 3.555607
## [196] 3.583782 3.663837 3.219088 3.434229 3.611185
## [201] 3.496758 3.219088 3.178261 2.890543 3.135696
## [206] 2.565084 2.890543 2.639200 2.833378 3.091238
## [211] 2.565084 3.178261 3.434229 3.526616 3.434229
## [216] 3.434229 3.637858 3.892131 3.737956 3.892131
## [221] 4.007663 4.382421 4.431220 4.277041 4.489050
## [226] 4.745394 5.187938 5.308846 5.606447 5.711096
## [231] 5.979619 6.055191 6.134170 5.943524 5.808834
## [236] 5.867174 6.016900 5.897867 5.884032 5.663618
## [241] 5.398760 5.004460 4.718956 5.037473 4.511277
## [246] 4.277041 4.025684 3.828942 3.611185 3.258314
## [251] 2.833378 2.833378 2.995916 2.398013 1.945988
## [256] 2.772746 2.639200 2.772746 1.609491 0.693157
## [261] 1.791825 1.609491 1.386334 1.098637 1.386334
## [266] 2.772746 2.079530 1.945988 2.302694 2.639200
## [271] 1.945988 2.197324 2.398013 3.135696 2.833378
## [276] 2.944617 3.178261 2.833378 3.332432 3.689159
## [281] 3.496758 3.434229 3.496758 3.367528 3.401435
## [286] 3.583782 3.871508 3.689159 3.332432 3.583782
## [291] 2.944617 3.526616 3.135696 2.833378 2.833378
## [296] 3.135696 2.639200 2.995916 2.565084 3.135696
## [301] 2.995916 2.772746 2.772746 3.135696 2.639200
## [306] 2.708201 1.386334 1.609491 1.609491 2.398013
## [311] 2.398013 1.945988 1.386334 1.791825 1.609491
## [316] 0.693157 1.386334 0.693157 1.386334 1.791825
## [321] 1.791825 1.386334 1.791825 2.398013 2.772746
## [326] 2.197324 2.485033 2.565084 3.296060 3.044713
## [331] 2.944617 2.833378 3.178261 3.296060 3.401435
## [336] 3.367528 3.219088 3.555607 3.496758 3.401435
## [341] 3.367528 3.434229 3.367528 3.091238 3.296060
## [346] 3.178261 3.258314 3.367528 3.091238 3.496758
## [351] 3.178261 3.401435 2.995916 2.833378 3.178261
## [356] 3.332432 2.890543 2.565084 2.197324 2.639200
## [361] 2.398013 2.398013 2.944617 2.302694 2.079530
## [366] 2.079530 2.197324 1.098637 1.945988 2.639200
## [371] 1.386334 2.197324 2.639200 1.945988 2.197324
## [376] 1.098637 1.098637 2.639200 2.485033 2.302694
## [381] 3.044713 3.258314 3.850452 3.737956 3.434229
## [386] 3.526616 3.496758 3.951564 4.025684 4.248865
## [391] 4.718956 4.248865 3.850452 3.871508 3.892131
## [396] 4.190015 4.025684 4.111221 4.205055 4.159238
## [401] 4.219873 3.892131 3.912337 4.025684 4.317870
## [406] 4.143487 4.127484 3.713855 3.912337 3.526616
## [411] 3.434229 3.637858 3.401435 3.465982 3.258314
## [416] 3.401435 3.583782 3.555607 3.828942 3.871508
## [421] 3.784483 3.932143 4.077878 4.263053 4.625412
## [426] 4.852513 4.844668 5.011150 5.252839 5.545808
## [431] 5.796747 5.572791 5.394224 5.318700 5.199051
## [436] 4.595553 3.989310 4.382421 4.625412 4.844668
## [441] 4.290837 4.219873 4.159238 4.007663 4.205055
## [446] 4.431220 4.443056 4.205055 4.290837 4.489050
## [451] 4.219873 4.077878 4.025684 4.344192 4.317870
## [456] 3.850452 3.912337 3.737956 3.332432 3.611185
## [461] 3.611185 3.296060 2.485033 2.708201 3.091238
## [466] 2.079530 2.708201 2.833378 2.302694 2.197324
## [471] 2.398013 2.995916 2.565084 2.398013 2.772746
## [476] 2.398013 1.945988 2.833378 2.639200 2.565084
## [481] 2.708201 3.401435 3.219088 3.689159 3.784483
## [486] 3.219088 3.044713 3.871508 4.025684 4.094688
## [491] 3.806960 4.007663 3.465982 3.828942 4.111221
## [496] 3.737956 3.611185 3.761490 3.526616 3.689159
## [501] 3.219088 2.772746 2.833378 2.833378 2.772746
## [506] 3.135696 2.890543 2.890543 2.197324 1.945988
## [511] 1.945988 1.386334 1.098637 0.693157 2.079530
## [516] 1.098637 0.000000 0.000000 0.693157 1.098637
## [521] 1.098637 0.693157 -24376.811309 -24376.811309 0.693157
## [526] 0.693157 -24376.811309 1.791825 1.098637 1.791825
## [531] 0.693157 1.098637 0.693157 1.386334 1.609491
## [536] 0.693157 2.197324 0.693157 1.386334 2.079530
## [541] 1.791825 1.098637 2.398013 2.639200 2.708201
## [546] 2.995916 2.197324 2.995916 3.332432 3.637858
## [551] 3.401435 3.401435 3.135696 2.772746 3.091238
## [556] 3.332432 2.639200 2.833378 2.995916 2.833378
## [561] 2.302694 2.565084 2.995916 2.197324 2.890543
## [566] 2.197324 2.079530 2.944617 2.398013 1.386334
## [571] 1.791825 1.791825 2.079530 2.565084 2.079530
## [576] 2.079530 1.609491 2.772746 2.485033 2.398013
## [581] 2.890543 2.302694 3.091238 2.639200 2.772746
## [586] 2.890543 3.296060 3.637858 3.555607 3.713855
## [591] 3.932143 4.174745 4.007663 3.989310 4.127484
## [596] 4.159238 4.025684 4.174745 4.263053 4.317870
## [601] 4.263053 4.277041 3.850452 3.296060 3.555607
## [606] 3.219088 2.944617 3.611185 3.637858 3.526616
## [611] 3.258314 2.944617 2.890543 3.091238 2.772746
## [616] 2.890543 1.791825 2.485033 1.791825 1.791825
## [621] 1.098637 1.945988 1.791825 0.000000 1.098637
## [626] 0.693157 0.693157 0.000000 2.302694 1.098637
## [631] 1.098637 0.000000 0.000000 0.693157 1.791825
## [636] 1.098637 1.098637 1.609491 1.386334 1.945988
## [641] 1.791825 1.609491 1.945988 1.791825 1.386334
## [646] 1.386334 1.945988 2.197324 1.609491 1.609491
## [651] 2.302694 1.791825 2.565084 1.791825 1.609491
## [656] 1.609491 2.197324 1.098637 1.791825 2.398013
## [661] 1.945988 1.945988 2.708201 2.197324 1.791825
## [666] 1.791825 1.791825 1.945988 2.302694 2.079530
## [671] 1.945988 2.485033 1.098637 0.693157 1.945988
## [676] 1.609491 1.609491 1.945988 1.945988 1.945988
## [681] 1.945988 2.302694 2.565084 2.302694 2.639200
## [686] 2.398013 2.995916 3.219088 2.833378 2.890543
## [691] 3.219088 3.044713 3.434229 3.465982 3.258314
## [696] 3.555607 3.332432 3.611185 3.713855 3.526616
## [701] 3.401435 3.663837 3.663837 3.663837 3.526616
## [706] 3.401435 3.611185 3.367528 3.258314 2.708201
## [711] 3.091238 2.708201 2.995916 2.639200 2.302694
## [716] 3.044713 2.639200 2.639200 2.197324 2.398013
## [721] 1.609491 1.791825 1.945988 2.398013 1.386334
## [726] 1.098637 0.693157 1.791825 2.302694 1.945988
## [731] 1.609491 1.098637 2.485033 2.565084 2.302694
## [736] 2.565084 2.565084 2.079530 3.044713 2.890543
## [741] 2.079530 1.945988 2.995916 2.639200 2.639200
## [746] 1.945988 2.639200 2.302694 2.565084 3.296060
## [751] 2.565084 2.890543 2.772746 2.772746 2.995916
## [756] 2.833378 1.386334 2.708201 2.079530 1.791825
## [761] 2.485033 2.708201 2.398013 2.302694 2.708201
## [766] 2.833378 1.945988 1.945988 2.079530 2.197324
## [771] 2.485033 2.485033 1.609491 1.386334 2.398013
## [776] 1.386334 1.609491 1.945988 0.000000 0.000000
## [781] 1.386334 0.693157 1.791825 1.098637 1.386334
## [786] 2.302694 2.485033 3.044713 3.258314 3.044713
## [791] 3.401435 3.806960 4.025684 4.317870 4.419241
## [796] 4.407118 4.836762 4.779592 4.920477 4.875685
## [801] 4.718956 4.407118 4.290837 3.761490 4.007663
## [806] 4.007663 3.970615 3.828942 3.761490 3.367528
## [811] 3.091238 3.258314 2.565084 2.833378 2.079530
## [816] 2.565084 2.302694 2.833378 2.944617 2.197324
## [821] 2.197324 2.197324 1.098637 1.945988 1.945988
## [826] -24376.811309 0.693157 1.098637 1.098637 0.000000
## [831] 1.098637 1.098637 1.098637 1.945988 1.098637
## [836] 1.609491 2.398013 1.609491 1.609491 1.791825
## [841] 1.791825 1.386334 1.386334 2.079530 2.639200
## [846] 2.485033 2.772746 2.302694 2.772746 2.890543
## [851] 2.708201 3.135696 2.833378 3.496758 2.708201
## [856] 2.565084 2.398013 2.639200 2.833378 2.944617
## [861] 2.995916 2.485033 3.044713 1.945988 2.944617
## [866] 2.302694 2.565084 2.302694 2.079530 3.044713
## [871] 2.398013 2.197324 2.639200 2.639200 2.708201
## [876] 2.890543 2.772746 2.485033 2.995916 2.079530
## [881] 1.098637 2.565084 1.386334 0.000000 2.302694
## [886] 2.079530 2.565084 2.302694 3.044713 2.890543
## [891] 3.044713 3.526616 3.219088 3.526616 3.496758
## [896] 3.689159 3.737956 3.583782 4.277041 4.317870
## [901] 4.331118 4.522208 4.263053 4.718956 4.663885
## [906] 4.615557 5.136339 4.905768 4.663885 4.219873
## [911] 3.871508 3.871508 3.258314 3.496758 3.367528
## [916] 2.833378 2.485033 2.565084 2.833378 2.708201
## [921] 2.639200 2.708201 2.302694 2.197324 0.693157
## [926] 1.791825 2.079530 1.609491 0.000000 0.693157
## [931] 1.098637 1.386334 1.098637 0.000000 1.098637
## [936] 1.609491
## attr(,"lambda")
## [1] 4.102259e-05
#San Juan ANN
san.juan_Neural_nets <- nnetar(transformed_san.juan)
san.juan_Neural_nets
## Series: transformed_san.juan
## Model: NNAR(7,1,4)[52]
## Call: nnetar(y = transformed_san.juan)
##
## Average of 20 networks, each of which is
## a 8-4-1 network with 41 weights
## options were - linear output units
##
## sigma^2 estimated as 1699311
summary(san.juan_Neural_nets)
## Length Class Mode
## x 936 ts numeric
## m 1 -none- numeric
## p 1 -none- numeric
## P 1 -none- numeric
## scalex 2 -none- list
## size 1 -none- numeric
## subset 936 -none- numeric
## model 20 nnetarmodels list
## nnetargs 0 -none- list
## fitted 936 ts numeric
## residuals 936 ts numeric
## lags 8 -none- numeric
## series 1 -none- character
## method 1 -none- character
## call 2 -none- call
#Forecasting the dengue cases in San Juan City
forecast_San_Juan <- forecast(san.juan_Neural_nets, h = 12)
forecast_San_Juan
## Point Forecast
## 2008.000 -130.3336
## 2008.019 -1580.9993
## 2008.038 -6708.5229
## 2008.058 -7223.5498
## 2008.077 -3535.4338
## 2008.096 -5109.8738
## 2008.115 -10535.4935
## 2008.135 -6090.3269
## 2008.154 -6415.0276
## 2008.173 -5538.9186
## 2008.192 -8073.9457
## 2008.212 -7038.2443
autoplot(forecast_San_Juan)+
ggtitle("Total Dengue Cases in the Next Six Weeks In San Juan City")+
ylab("Dengue Fever Cases")+
xlab("Time") +
theme_gray()
#Checking the RMSE
accuracy_San.juan <- accuracy(forecast_San_Juan, h = 12)
print(accuracy_San.juan)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 1.22496 1303.576 153.5642 Inf Inf 0.6927443 0.000144969
#ANN in Iquitos
iquitos_Neural_nets <- nnetar(iquitos.ts)
iquitos_Neural_nets
## Series: iquitos.ts
## Model: NNAR(5,1,4)[52]
## Call: nnetar(y = iquitos.ts)
##
## Average of 20 networks, each of which is
## a 6-4-1 network with 33 weights
## options were - linear output units
##
## sigma^2 estimated as 23.3
summary(san.juan_Neural_nets)
## Length Class Mode
## x 936 ts numeric
## m 1 -none- numeric
## p 1 -none- numeric
## P 1 -none- numeric
## scalex 2 -none- list
## size 1 -none- numeric
## subset 936 -none- numeric
## model 20 nnetarmodels list
## nnetargs 0 -none- list
## fitted 936 ts numeric
## residuals 936 ts numeric
## lags 8 -none- numeric
## series 1 -none- character
## method 1 -none- character
## call 2 -none- call
#RMSE
forecast_iquitos_city <- forecast(iquitos_Neural_nets, h = 12)
forecast_iquitos_city
## Point Forecast
## 2000.000 3.880639
## 2000.019 4.719079
## 2000.038 4.705055
## 2000.058 4.682420
## 2000.077 4.611933
## 2000.096 4.495722
## 2000.115 4.408870
## 2000.135 4.267140
## 2000.154 4.251814
## 2000.173 4.382139
## 2000.192 4.427632
## 2000.212 4.466648
autoplot(forecast_iquitos_city)+
ggtitle("Total Dengue Cases in the Next Six Weeks In Iquitos City")+
ylab("Dengue Fever Cases")+
xlab("Time") +
theme_gray()
#RMSE
accuracy_model.equitos <- accuracy(forecast_iquitos_city, h = 12)
print(accuracy_model.equitos)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.09081555 4.826704 3.256718 -Inf Inf 0.344985 -0.02161592