South ural state university, Chelyabinsk, Russian federation
#Import
library(fpp2)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v ggplot2 3.3.2 v fma 2.4
## v forecast 8.13 v expsmooth 2.3
##
library(forecast)
library(ggplot2)
library("readxl")
library(moments)
library(forecast)
require(forecast)
require(tseries)
## Loading required package: tseries
require(markovchain)
## Loading required package: markovchain
## Package: markovchain
## Version: 0.8.5-3
## Date: 2020-12-03
## BugReport: https://github.com/spedygiorgio/markovchain/issues
require(data.table)
## Loading required package: data.table
library(Hmisc)
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(ascii)
library(pander)
##
## Attaching package: 'pander'
## The following object is masked from 'package:ascii':
##
## Pandoc
library(ascii)
require(tseries) # need to install tseries tj test Stationarity in time series
library(forecast) # install library forecast
library(tseries)
##Global vriable##
Full_original_data <- read.csv("data.csv") # path of your data ( time series data)
original_data<-Full_original_data$cases #Cumulative #cases
y_lab <- "Forecasting cumulative Covid 19 Infection cases in Italy" # input name of data
Actual_date_interval <- c("2020/03/01","2021/05/08")
Forecast_date_interval <- c("2021/05/09","2021/05/30")
validation_data_days <-45
frequency<-"day"
Number_Neural<-3# Number of Neural For model NNAR Model
NNAR_Model<- TRUE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Italy"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 211633 273778 1107816 2170088 4092747
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.423727
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.9692781
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 1303697
#processing on data (input data)
rows <- NROW(original_data) # calculate number of rows in time series (number of days)
training_data<-original_data[1:(rows-validation_data_days)] # Training data
testing_data<-original_data[(rows-validation_data_days+1):rows] #testing data
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD)) #calculate number of days that you want to forecasting
validation_dates<-tail(AD,validation_data_days) # select validation_dates
validation_data_by_name<-weekdays(validation_dates) # put names of validation dates
forecasting_data_by_name<-weekdays(FD) # put names of Forecasting dates
#NNAR Model
if(NNAR_Model==TRUE){
data_series<-ts(training_data)
model_NNAR<-nnetar(data_series, size = Number_Neural)
saveRDS(model_NNAR, file = "model_NNAR.RDS")
my_model <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
## Series: data_series
## Model: NNAR(1,3)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 1-3-1 network with 10 weights
## options were - linear output units
##
## sigma^2 estimated as 10259590
if(NNAR_Model==FALSE){
data_series<-ts(training_data)
#model_NNAR<-nnetar(data_series, size = Number_Numeral)
model_NNAR <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
# Testing Data Evaluation
forecasting_NNAR <- forecast(model_NNAR, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_NNAR$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Mean_All_NNAR<-round(mean(MAPE_Per_Day),3)
MAPE_NNAR<-paste(round(MAPE_Per_Day,3),"%")
MAPE_NNAR_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
paste(MAPE_Mean_All,"%")
## [1] "3.265 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Italy %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(date_NNAR=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_NNAR=validation_forecast,MAPE_NNAR_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | | date_NNAR | validation_data_by_name | actual_data | forecasting_NNAR | MAPE_NNAR_Model |
## +====+============+=========================+=============+==================+=================+
## | 1 | 2021-03-25 | Thursday | 3440862.00 | 3439795.76 | 0.031 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 3464543.00 | 3459488.18 | 0.146 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 3488619.00 | 3478643.13 | 0.286 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 3512453.00 | 3497214.65 | 0.434 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 3532057.00 | 3515161.75 | 0.478 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 3544957.00 | 3532448.87 | 0.353 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 3561012.00 | 3549046.42 | 0.336 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 3584899.00 | 3564930.94 | 0.557 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 3607083.00 | 3580085.33 | 0.748 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 3629000.00 | 3594498.73 | 0.951 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 3650247.00 | 3608166.40 | 1.153 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 3668264.00 | 3621089.38 | 1.286 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 3678944.00 | 3633274.15 | 1.241 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 3686707.00 | 3644732.05 | 1.139 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 3700393.00 | 3655478.82 | 1.214 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 3717602.00 | 3665533.98 | 1.401 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 3736526.00 | 3674920.20 | 1.649 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 3754077.00 | 3683662.78 | 1.876 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 3769814.00 | 3691789.00 | 2.07 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 3779594.00 | 3699327.63 | 2.124 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 3793033.00 | 3706308.41 | 2.286 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 3809193.00 | 3712761.62 | 2.532 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 3826156.00 | 3718717.63 | 2.808 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 3842079.00 | 3724206.64 | 3.068 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 3857443.00 | 3729258.33 | 3.323 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 3870131.00 | 3733901.61 | 3.52 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 3878994.00 | 3738164.50 | 3.631 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 3891063.00 | 3742073.91 | 3.829 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 3904899.00 | 3745655.56 | 4.078 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 3920945.00 | 3748933.91 | 4.387 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 3935703.00 | 3751932.11 | 4.669 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 3949517.00 | 3754671.96 | 4.933 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 3962674.00 | 3757173.94 | 5.186 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 3971114.00 | 3759457.21 | 5.33 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 3981512.00 | 3761539.65 | 5.525 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 3994894.00 | 3763437.88 | 5.794 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4009208.00 | 3765167.33 | 6.087 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4022653.00 | 3766742.29 | 6.362 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4035617.00 | 3768175.97 | 6.627 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4044762.00 | 3769480.54 | 6.806 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4050708.00 | 3770667.23 | 6.913 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4059821.00 | 3771746.33 | 7.096 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4070400.00 | 3772727.33 | 7.313 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4082198.00 | 3773618.91 | 7.559 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4092747.00 | 3774429.03 | 7.778 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +====+============+=================+=====================+
## | 1 | 2021-05-09 | Sunday | 3775164.97 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 3775833.40 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 3776440.39 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 3776991.51 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 3777491.83 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 3777945.96 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 3778358.12 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 3778732.15 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 3779071.54 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 3779379.48 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 3779658.84 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 3779912.28 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 3780142.17 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 3780350.69 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 3780539.81 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 3780711.34 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 3780866.91 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 3781007.98 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 3781135.91 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 3781251.92 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 3781357.12 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 3781452.50 |
## +----+------------+-----------------+---------------------+
plot(forecasting_NNAR,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph1<-autoplot(forecasting_NNAR,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph1
##bats model
# Data Modeling
data_series<-ts(training_data) # make your data to time series
autoplot(data_series ,xlab=paste ("Time in", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 103.7615 1616.055 875.9063 NaN Inf 0.1142293 0.1476203
# Print Model Parameters
model_bats
## BATS(1, {2,2}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.3435945
## Beta: 0.3646252
## Damping Parameter: 1
## AR coefficients: 1.210798 -0.951168
## MA coefficients: -0.469538 0.498922
##
## Seed States:
## [,1]
## [1,] 163.25953
## [2,] -79.18204
## [3,] 0.00000
## [4,] 0.00000
## [5,] 0.00000
## [6,] 0.00000
##
## Sigma: 1616.055
## AIC: 9358.486
#ploting BATS Model
plot(model_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "))
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
paste(MAPE_Mean_All.bats,"%")
## [1] "3.897 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Italy %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | | date_bats | validation_data_by_name | actual_data | forecasting_bats | MAPE_bats_Model |
## +====+============+=========================+=============+==================+=================+
## | 1 | 2021-03-25 | Thursday | 3440862.00 | 3444039.09 | 0.092 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 3464543.00 | 3468939.03 | 0.127 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 3488619.00 | 3494346.84 | 0.164 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 3512453.00 | 3518776.50 | 0.18 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 3532057.00 | 3541538.78 | 0.268 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 3544957.00 | 3563212.56 | 0.515 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 3561012.00 | 3585154.36 | 0.678 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 3584899.00 | 3608456.02 | 0.657 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 3607083.00 | 3633149.25 | 0.723 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 3629000.00 | 3658233.95 | 0.806 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 3650247.00 | 3682469.02 | 0.883 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 3668264.00 | 3705302.99 | 1.01 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 3678944.00 | 3727248.67 | 1.313 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 3686707.00 | 3749451.49 | 1.702 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 3700393.00 | 3772810.55 | 1.957 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 3717602.00 | 3797325.01 | 2.144 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 3736526.00 | 3822138.65 | 2.291 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 3754077.00 | 3846215.55 | 2.454 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 3769814.00 | 3869115.83 | 2.634 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 3779594.00 | 3891292.23 | 2.955 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 3793033.00 | 3913711.33 | 3.182 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 3809193.00 | 3937112.80 | 3.358 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 3826156.00 | 3961472.88 | 3.537 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 3842079.00 | 3986059.26 | 3.747 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 3857443.00 | 4010007.81 | 3.955 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 3870131.00 | 4032968.86 | 4.208 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 3878994.00 | 4055340.91 | 4.546 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 3891063.00 | 4077939.08 | 4.803 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 3904899.00 | 4101371.28 | 5.031 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 3920945.00 | 4125598.23 | 5.219 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 3935703.00 | 4149994.18 | 5.445 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 3949517.00 | 4173838.78 | 5.68 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 3962674.00 | 4196855.09 | 5.91 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 3971114.00 | 4219392.91 | 6.252 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 3981512.00 | 4242139.24 | 6.546 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 3994894.00 | 4265593.13 | 6.776 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4009208.00 | 4289705.43 | 6.996 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4022653.00 | 4313941.90 | 7.241 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4035617.00 | 4337702.47 | 7.485 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4044762.00 | 4360768.71 | 7.813 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4050708.00 | 4383446.91 | 8.214 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4059821.00 | 4406315.70 | 8.535 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4070400.00 | 4429784.35 | 8.829 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4082198.00 | 4453798.02 | 9.103 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4092747.00 | 4477901.03 | 9.411 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4501593.81 | 4307040.84 | 4204050.72 | 4307040.84 | 4204050.72 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4524704.90 | 4323925.44 | 4217639.22 | 4323925.44 | 4217639.22 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4547501.89 | 4340456.12 | 4230852.72 | 4340456.12 | 4230852.72 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4570471.83 | 4357077.54 | 4244113.42 | 4357077.54 | 4244113.42 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4593949.97 | 4374097.86 | 4257715.18 | 4374097.86 | 4257715.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4617878.90 | 4391467.28 | 4271612.21 | 4391467.28 | 4271612.21 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4641870.28 | 4408832.46 | 4285469.69 | 4408832.46 | 4285469.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4665508.49 | 4425813.06 | 4298925.97 | 4425813.06 | 4298925.97 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4688659.68 | 4442285.26 | 4311862.51 | 4442285.26 | 4311862.51 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4711557.12 | 4458461.98 | 4324481.51 | 4458461.98 | 4324481.51 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4734610.54 | 4474719.68 | 4337141.77 | 4474719.68 | 4337141.77 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4758094.19 | 4491311.82 | 4350085.76 | 4491311.82 | 4350085.76 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4781950.40 | 4508187.29 | 4363265.86 | 4508187.29 | 4363265.86 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4805848.47 | 4525043.26 | 4376393.96 | 4525043.26 | 4376393.96 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4829442.87 | 4541561.77 | 4389166.73 | 4541561.77 | 4389166.73 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4852629.76 | 4557646.43 | 4401491.69 | 4557646.43 | 4401491.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4875612.08 | 4573483.72 | 4413546.63 | 4573483.72 | 4413546.63 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4898734.33 | 4589391.79 | 4425635.74 | 4589391.79 | 4425635.74 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4922220.56 | 4605578.67 | 4437958.58 | 4605578.67 | 4437958.58 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4946014.42 | 4621993.74 | 4450467.55 | 4621993.74 | 4450467.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4969834.54 | 4638377.94 | 4462915.42 | 4638377.94 | 4462915.42 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4993393.86 | 4654465.94 | 4475048.33 | 4654465.94 | 4475048.33 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
plot(forecasting_bats)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph1<-autoplot(forecasting_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph1
## TBATS Model
# Data Modeling
data_series<-ts(training_data)
model_TBATS<-forecast:::fitSpecificTBATS(data_series,use.box.cox=FALSE, use.beta=TRUE, seasonal.periods=c(6),use.damping=FALSE,k.vector=c(2))
accuracy(model_TBATS) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 79.71788 1982.715 1163.536 NaN Inf 0.1517398 0.06066793
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.364111
## Beta: 0.5721247
## Damping Parameter: 1
## Gamma-1 Values: -0.002494483
## Gamma-2 Values: 0.00190877
##
## Seed States:
## [,1]
## [1,] 200.42506
## [2,] -95.37015
## [3,] -86.74606
## [4,] -65.86513
## [5,] -209.78713
## [6,] 52.58304
##
## Sigma: 1982.715
## AIC: 9535.291
plot(model_TBATS,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
# Testing Data Evaluation
forecasting_tbats <- predict(model_TBATS, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_tbats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "2.021 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Italy %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | | date_TBATS | validation_data_by_name | actual_data | forecasting_TBATS | MAPE_TBATS_Model |
## +====+============+=========================+=============+===================+==================+
## | 1 | 2021-03-25 | Thursday | 3440862.00 | 3437595.95 | 0.095 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-26 | Friday | 3464543.00 | 3458405.74 | 0.177 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-27 | Saturday | 3488619.00 | 3478431.58 | 0.292 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-28 | Sunday | 3512453.00 | 3498273.64 | 0.404 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-29 | Monday | 3532057.00 | 3518875.70 | 0.373 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-30 | Tuesday | 3544957.00 | 3539098.82 | 0.165 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-31 | Wednesday | 3561012.00 | 3559345.90 | 0.047 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-04-01 | Thursday | 3584899.00 | 3580155.70 | 0.132 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 9 | 2021-04-02 | Friday | 3607083.00 | 3600181.54 | 0.191 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 10 | 2021-04-03 | Saturday | 3629000.00 | 3620023.60 | 0.247 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 11 | 2021-04-04 | Sunday | 3650247.00 | 3640625.65 | 0.264 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 12 | 2021-04-05 | Monday | 3668264.00 | 3660848.77 | 0.202 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 13 | 2021-04-06 | Tuesday | 3678944.00 | 3681095.86 | 0.058 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 14 | 2021-04-07 | Wednesday | 3686707.00 | 3701905.66 | 0.412 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 15 | 2021-04-08 | Thursday | 3700393.00 | 3721931.50 | 0.582 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 16 | 2021-04-09 | Friday | 3717602.00 | 3741773.56 | 0.65 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 17 | 2021-04-10 | Saturday | 3736526.00 | 3762375.61 | 0.692 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 18 | 2021-04-11 | Sunday | 3754077.00 | 3782598.73 | 0.76 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 19 | 2021-04-12 | Monday | 3769814.00 | 3802845.82 | 0.876 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 20 | 2021-04-13 | Tuesday | 3779594.00 | 3823655.61 | 1.166 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 21 | 2021-04-14 | Wednesday | 3793033.00 | 3843681.45 | 1.335 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 22 | 2021-04-15 | Thursday | 3809193.00 | 3863523.52 | 1.426 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 23 | 2021-04-16 | Friday | 3826156.00 | 3884125.57 | 1.515 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 24 | 2021-04-17 | Saturday | 3842079.00 | 3904348.69 | 1.621 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 25 | 2021-04-18 | Sunday | 3857443.00 | 3924595.78 | 1.741 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 26 | 2021-04-19 | Monday | 3870131.00 | 3945405.57 | 1.945 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 27 | 2021-04-20 | Tuesday | 3878994.00 | 3965431.41 | 2.228 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 28 | 2021-04-21 | Wednesday | 3891063.00 | 3985273.47 | 2.421 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 29 | 2021-04-22 | Thursday | 3904899.00 | 4005875.53 | 2.586 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 30 | 2021-04-23 | Friday | 3920945.00 | 4026098.65 | 2.682 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 31 | 2021-04-24 | Saturday | 3935703.00 | 4046345.74 | 2.811 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 32 | 2021-04-25 | Sunday | 3949517.00 | 4067155.53 | 2.979 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 33 | 2021-04-26 | Monday | 3962674.00 | 4087181.37 | 3.142 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 34 | 2021-04-27 | Tuesday | 3971114.00 | 4107023.43 | 3.422 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 35 | 2021-04-28 | Wednesday | 3981512.00 | 4127625.48 | 3.67 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 36 | 2021-04-29 | Thursday | 3994894.00 | 4147848.61 | 3.829 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 37 | 2021-04-30 | Friday | 4009208.00 | 4168095.69 | 3.963 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 38 | 2021-05-01 | Saturday | 4022653.00 | 4188905.49 | 4.133 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 39 | 2021-05-02 | Sunday | 4035617.00 | 4208931.33 | 4.295 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 40 | 2021-05-03 | Monday | 4044762.00 | 4228773.39 | 4.549 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 41 | 2021-05-04 | Tuesday | 4050708.00 | 4249375.44 | 4.905 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 42 | 2021-05-05 | Wednesday | 4059821.00 | 4269598.56 | 5.167 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 43 | 2021-05-06 | Thursday | 4070400.00 | 4289845.65 | 5.391 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 44 | 2021-05-07 | Friday | 4082198.00 | 4310655.45 | 5.596 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 45 | 2021-05-08 | Saturday | 4092747.00 | 4330681.28 | 5.814 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+======================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4350523.35 | 4328098.08 | 4316226.86 | 4372948.62 | 4384819.84 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4371125.40 | 4348474.97 | 4336484.56 | 4393775.83 | 4405766.24 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4391348.52 | 4368478.07 | 4356371.18 | 4414218.97 | 4426325.86 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4411595.61 | 4388508.96 | 4376287.63 | 4434682.26 | 4446903.59 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4432405.40 | 4409104.30 | 4396769.44 | 4455706.51 | 4468041.37 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4452431.24 | 4428918.47 | 4416471.56 | 4475944.01 | 4488390.92 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4472273.30 | 4448550.76 | 4435992.80 | 4495995.85 | 4508553.81 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4492875.36 | 4468944.89 | 4456276.86 | 4516805.83 | 4529473.85 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4513098.48 | 4488964.60 | 4476188.90 | 4537232.35 | 4550008.06 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4533345.57 | 4509011.61 | 4496129.99 | 4557679.52 | 4570561.14 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4554155.36 | 4529622.71 | 4516635.91 | 4578688.02 | 4591674.82 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4574181.20 | 4549452.23 | 4536361.50 | 4598910.17 | 4612000.90 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4594023.26 | 4569099.52 | 4555905.69 | 4618947.00 | 4632140.83 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4614625.32 | 4589508.33 | 4576212.20 | 4639742.30 | 4653038.43 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4634848.44 | 4609542.25 | 4596145.96 | 4660154.63 | 4673550.91 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4655095.52 | 4629603.07 | 4616108.18 | 4680587.98 | 4694082.87 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4675905.32 | 4650227.71 | 4636634.81 | 4701582.92 | 4715175.83 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4695931.16 | 4670070.47 | 4656380.65 | 4721791.85 | 4735481.67 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4715773.22 | 4689730.74 | 4675944.68 | 4741815.70 | 4755601.76 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4736375.27 | 4710152.27 | 4696270.65 | 4762598.28 | 4776479.90 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4756598.39 | 4730198.53 | 4716223.29 | 4782998.26 | 4796973.50 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4776845.48 | 4750271.39 | 4736203.92 | 4803419.57 | 4817487.05 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
plot(forecasting_tbats)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph2<-autoplot(forecasting_tbats,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph2
## Holt's linear trend
# Data Modeling
data_series<-ts(training_data)
model_holt<-holt(data_series,h=N_forecasting_days+validation_data_days,lambda = "auto")
accuracy(model_holt) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -48.58205 2164.12 1167.205 NaN Inf 0.1522184 0.2449641
# Print Model Parameters
summary(model_holt$model)
## Holt's method
##
## Call:
## holt(y = data_series, h = N_forecasting_days + validation_data_days,
##
## Call:
## lambda = "auto")
##
## Box-Cox transformation: lambda= 0.4606
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.7819
##
## Initial states:
## l = -2.4567
## b = -0.6129
##
## sigma: 1.3921
##
## AIC AICc BIC
## 3029.553 3029.689 3050.066
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -48.58205 2164.12 1167.205 NaN Inf 0.1522184 0.2449641
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
paste(MAPE_Mean_All.Holt,"%")
## [1] "2.37 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Italy %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | | date_holt | validation_data_by_name | actual_data | forecasting_holt | MAPE_holt_Model |
## +====+============+=========================+=============+==================+=================+
## | 1 | 2021-03-25 | Thursday | 3440862.00 | 3439527.01 | 0.039 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 3464543.00 | 3459499.86 | 0.146 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 3488619.00 | 3479535.11 | 0.26 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 3512453.00 | 3499632.79 | 0.365 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 3532057.00 | 3519792.91 | 0.347 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 3544957.00 | 3540015.51 | 0.139 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 3561012.00 | 3560300.61 | 0.02 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 3584899.00 | 3580648.25 | 0.119 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 3607083.00 | 3601058.45 | 0.167 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 3629000.00 | 3621531.24 | 0.206 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 3650247.00 | 3642066.65 | 0.224 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 3668264.00 | 3662664.71 | 0.153 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 3678944.00 | 3683325.44 | 0.119 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 3686707.00 | 3704048.87 | 0.47 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 3700393.00 | 3724835.03 | 0.661 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 3717602.00 | 3745683.95 | 0.755 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 3736526.00 | 3766595.65 | 0.805 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 3754077.00 | 3787570.17 | 0.892 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 3769814.00 | 3808607.52 | 1.029 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 3779594.00 | 3829707.74 | 1.326 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 3793033.00 | 3850870.86 | 1.525 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 3809193.00 | 3872096.90 | 1.651 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 3826156.00 | 3893385.88 | 1.757 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 3842079.00 | 3914737.85 | 1.891 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 3857443.00 | 3936152.82 | 2.04 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 3870131.00 | 3957630.81 | 2.261 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 3878994.00 | 3979171.87 | 2.583 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 3891063.00 | 4000776.01 | 2.82 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 3904899.00 | 4022443.26 | 3.01 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 3920945.00 | 4044173.65 | 3.143 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 3935703.00 | 4065967.21 | 3.31 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 3949517.00 | 4087823.96 | 3.502 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 3962674.00 | 4109743.92 | 3.711 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 3971114.00 | 4131727.13 | 4.045 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 3981512.00 | 4153773.62 | 4.327 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 3994894.00 | 4175883.40 | 4.531 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4009208.00 | 4198056.51 | 4.71 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4022653.00 | 4220292.96 | 4.913 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4035617.00 | 4242592.80 | 5.129 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4044762.00 | 4264956.04 | 5.444 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4050708.00 | 4287382.71 | 5.843 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4059821.00 | 4309872.84 | 6.159 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4070400.00 | 4332426.45 | 6.437 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4082198.00 | 4355043.56 | 6.684 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4092747.00 | 4377724.22 | 6.963 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4400468.43 | 3472343.36 | 3028660.50 | 5448119.71 | 6051796.60 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4423276.23 | 3464373.91 | 3007515.25 | 5509586.75 | 6136986.92 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4446147.65 | 3456120.33 | 2986034.34 | 5571806.30 | 6223437.44 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4469082.70 | 3447586.78 | 2964226.81 | 5634781.64 | 6311156.37 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4492081.42 | 3438777.35 | 2942101.61 | 5698516.14 | 6400152.09 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4515143.83 | 3429696.07 | 2919667.56 | 5763013.22 | 6490433.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4538269.95 | 3420346.89 | 2896933.39 | 5828276.39 | 6582007.94 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4561459.81 | 3410733.73 | 2873907.75 | 5894309.22 | 6674885.37 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4584713.45 | 3400860.45 | 2850599.20 | 5961115.33 | 6769074.20 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4608030.87 | 3390730.83 | 2827016.18 | 6028698.42 | 6864583.33 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4631412.11 | 3380348.64 | 2803167.10 | 6097062.24 | 6961421.79 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4654857.20 | 3369717.57 | 2779060.25 | 6166210.59 | 7059598.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4678366.16 | 3358841.30 | 2754703.87 | 6236147.33 | 7159123.21 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4701939.01 | 3347723.43 | 2730106.11 | 6306876.37 | 7260004.65 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4725575.78 | 3336367.54 | 2705275.08 | 6378401.66 | 7362252.38 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4749276.49 | 3324777.18 | 2680218.80 | 6450727.20 | 7465875.83 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4773041.18 | 3312955.85 | 2654945.24 | 6523857.04 | 7570884.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4796869.86 | 3300907.02 | 2629462.29 | 6597795.26 | 7677288.11 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4820762.56 | 3288634.12 | 2603777.80 | 6672546.01 | 7785096.20 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4844719.31 | 3276140.55 | 2577899.57 | 6748113.44 | 7894318.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4868740.13 | 3263429.70 | 2551835.32 | 6824501.77 | 8004964.99 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4892825.04 | 3250504.89 | 2525592.75 | 6901715.24 | 8117045.37 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3
#Auto arima model
##################
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Forecasting cumulative Covid 19 Infection cases in Italy"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 5.9493, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
## Warning in pp.test(data_series): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = 0.93102, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -2.561, Lag order = 7, p-value = 0.3406
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Forecasting cumulative Covid 19 Infection cases in Italy"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 4.2577, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -9.6341, Truncation lag parameter = 5, p-value
## = 0.5717
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -2.1001, Lag order = 7, p-value = 0.5354
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking Second differences in",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking Second differences in Forecasting cumulative Covid 19 Infection cases in Italy"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
## Warning in kpss.test(diff2_x1): p-value greater than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.078691, Truncation lag parameter = 5, p-value = 0.1
pp.test(diff2_x1) # applay pp test after taking Second differences
## Warning in pp.test(diff2_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff2_x1
## Dickey-Fuller Z(alpha) = -254.11, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
## Warning in adf.test(diff2_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -5.0311, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
####Fitting an ARIMA Model
#1. Using auto arima function
model1 <- auto.arima(data_series,stepwise=FALSE, approximation=FALSE, trace=T, test = c("kpss", "adf", "pp")) #applaying auto arima
##
## ARIMA(0,2,0) : 8066.968
## ARIMA(0,2,1) : 8064.516
## ARIMA(0,2,2) : 8038.38
## ARIMA(0,2,3) : 8020.346
## ARIMA(0,2,4) : 7995.467
## ARIMA(0,2,5) : 7996.653
## ARIMA(1,2,0) : 8065.72
## ARIMA(1,2,1) : 8040.893
## ARIMA(1,2,2) : 8027.737
## ARIMA(1,2,3) : 8021.992
## ARIMA(1,2,4) : 7997.173
## ARIMA(2,2,0) : 8055.067
## ARIMA(2,2,1) : 8006.225
## ARIMA(2,2,2) : 7857.392
## ARIMA(2,2,3) : 7859.238
## ARIMA(3,2,0) : 8020.335
## ARIMA(3,2,1) : 7974.749
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 7951.995
## ARIMA(4,2,1) : 7938.679
## ARIMA(5,2,0) : 7923.852
##
##
##
## Best model: ARIMA(2,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2505 -0.8822 -1.5269 0.8733
## s.e. 0.0255 0.0249 0.0376 0.0286
##
## sigma^2 estimated as 2673854: log likelihood=-3923.63
## AIC=7857.26 AICc=7857.39 BIC=7877.75
#Make changes in the source of auto arima to run the best model
arima.string <- function (object, padding = FALSE)
{
order <- object$arma[c(1, 6, 2, 3, 7, 4, 5)]
m <- order[7]
result <- paste("ARIMA(", order[1], ",", order[2], ",",
order[3], ")", sep = "")
if (m > 1 && sum(order[4:6]) > 0) {
result <- paste(result, "(", order[4], ",", order[5],
",", order[6], ")[", m, "]", sep = "")
}
if (padding && m > 1 && sum(order[4:6]) == 0) {
result <- paste(result, " ", sep = "")
if (m <= 9) {
result <- paste(result, " ", sep = "")
}
else if (m <= 99) {
result <- paste(result, " ", sep = "")
}
else {
result <- paste(result, " ", sep = "")
}
}
if (!is.null(object$xreg)) {
if (NCOL(object$xreg) == 1 && is.element("drift", names(object$coef))) {
result <- paste(result, "with drift ")
}
else {
result <- paste("Regression with", result, "errors")
}
}
else {
if (is.element("constant", names(object$coef)) || is.element("intercept",
names(object$coef))) {
result <- paste(result, "with non-zero mean")
}
else if (order[2] == 0 && order[5] == 0) {
result <- paste(result, "with zero mean ")
}
else {
result <- paste(result, " ")
}
}
if (!padding) {
result <- gsub("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2505 -0.8822 -1.5269 0.8733
## s.e. 0.0255 0.0249 0.0376 0.0286
##
## sigma^2 estimated as 2649820: log likelihood = -3923.63, aic = 7857.26
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting cumulative Covid 19 Infection cases in Italy"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 90.14275 1624.181 883.8675 0.8132793 1.873187 0.1152676
## ACF1
## Training set -0.02067537
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,2,2)
## Q* = 130.18, df = 6, p-value < 2.2e-16
##
## Model df: 4. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
Box.test(x1_model1$residuals^2, lag=20, type="Ljung-Box") # Do test for resdulas by using Box-Ljung test , Ljung-Box test For Modelling
##
## Box-Ljung test
##
## data: x1_model1$residuals^2
## X-squared = 760.36, df = 20, p-value < 2.2e-16
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 423.47, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "3.066 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Italy %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)), type = "rest")
##
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | | date_auto.arima | validation_data_by_name | actual_data | forecasting_auto.arima | MAPE_auto.arima_Model |
## +====+=================+=========================+=============+========================+=======================+
## | 1 | 2021-03-25 | Thursday | 3440862.00 | 3439524.21 | 0.039 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-26 | Friday | 3464543.00 | 3461846.24 | 0.078 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-27 | Saturday | 3488619.00 | 3486155.23 | 0.071 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-28 | Sunday | 3512453.00 | 3510819.40 | 0.047 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-29 | Monday | 3532057.00 | 3534174.88 | 0.06 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-30 | Tuesday | 3544957.00 | 3555580.56 | 0.3 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-31 | Wednesday | 3561012.00 | 3575702.59 | 0.413 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-04-01 | Thursday | 3584899.00 | 3595939.51 | 0.308 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 9 | 2021-04-02 | Friday | 3607083.00 | 3617452.52 | 0.287 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 10 | 2021-04-03 | Saturday | 3629000.00 | 3640459.87 | 0.316 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 11 | 2021-04-04 | Sunday | 3650247.00 | 3664210.10 | 0.383 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 12 | 2021-04-05 | Monday | 3668264.00 | 3687571.00 | 0.526 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 13 | 2021-04-06 | Tuesday | 3678944.00 | 3709789.71 | 0.838 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 14 | 2021-04-07 | Wednesday | 3686707.00 | 3730923.62 | 1.199 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 15 | 2021-04-08 | Thursday | 3700393.00 | 3751708.63 | 1.387 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 16 | 2021-04-09 | Friday | 3717602.00 | 3773014.35 | 1.491 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 17 | 2021-04-10 | Saturday | 3736526.00 | 3795278.98 | 1.572 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 18 | 2021-04-11 | Sunday | 3754077.00 | 3818283.32 | 1.71 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 19 | 2021-04-12 | Monday | 3769814.00 | 3841366.75 | 1.898 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 20 | 2021-04-13 | Tuesday | 3779594.00 | 3863896.48 | 2.23 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 21 | 2021-04-14 | Wednesday | 3793033.00 | 3885664.09 | 2.442 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 22 | 2021-04-15 | Thursday | 3809193.00 | 3906967.15 | 2.567 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 23 | 2021-04-16 | Friday | 3826156.00 | 3928361.62 | 2.671 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 24 | 2021-04-17 | Saturday | 3842079.00 | 3950280.23 | 2.816 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 25 | 2021-04-18 | Sunday | 3857443.00 | 3972773.60 | 2.99 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 26 | 2021-04-19 | Monday | 3870131.00 | 3995523.31 | 3.24 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 27 | 2021-04-20 | Tuesday | 3878994.00 | 4018086.52 | 3.586 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 28 | 2021-04-21 | Wednesday | 3891063.00 | 4040190.39 | 3.833 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 29 | 2021-04-22 | Thursday | 3904899.00 | 4061884.39 | 4.02 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 30 | 2021-04-23 | Friday | 3920945.00 | 4083471.08 | 4.145 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 31 | 2021-04-24 | Saturday | 3935703.00 | 4105285.18 | 4.309 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 32 | 2021-04-25 | Sunday | 3949517.00 | 4127478.28 | 4.506 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 33 | 2021-04-26 | Monday | 3962674.00 | 4149944.72 | 4.726 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 34 | 2021-04-27 | Tuesday | 3971114.00 | 4172418.60 | 5.069 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 35 | 2021-04-28 | Wednesday | 3981512.00 | 4194660.65 | 5.353 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 36 | 2021-04-29 | Thursday | 3994894.00 | 4216606.26 | 5.55 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 37 | 2021-04-30 | Friday | 4009208.00 | 4238385.67 | 5.716 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 38 | 2021-05-01 | Saturday | 4022653.00 | 4260218.79 | 5.906 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 39 | 2021-05-02 | Sunday | 4035617.00 | 4282265.67 | 6.112 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 40 | 2021-05-03 | Monday | 4044762.00 | 4304532.49 | 6.422 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 41 | 2021-05-04 | Tuesday | 4050708.00 | 4326885.74 | 6.818 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 42 | 2021-05-05 | Wednesday | 4059821.00 | 4349153.05 | 7.127 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 43 | 2021-05-06 | Thursday | 4070400.00 | 4371236.66 | 7.391 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 44 | 2021-05-07 | Friday | 4082198.00 | 4393166.35 | 7.618 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 45 | 2021-05-08 | Saturday | 4092747.00 | 4415065.65 | 7.875 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+===========================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4437062.72 | 4226416.93 | 4114907.78 | 4647708.52 | 4759217.67 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4459208.86 | 4241742.12 | 4126622.18 | 4676675.59 | 4791795.53 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4481455.15 | 4257104.14 | 4138339.89 | 4705806.15 | 4824570.40 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4503695.17 | 4272401.09 | 4149961.40 | 4734989.26 | 4857428.95 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4525839.02 | 4287539.39 | 4161391.20 | 4764138.64 | 4890286.84 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4547868.11 | 4302492.51 | 4172598.51 | 4793243.70 | 4923137.70 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4569838.56 | 4317310.24 | 4183629.82 | 4822366.88 | 4956047.29 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4591836.91 | 4332078.62 | 4194570.89 | 4851595.20 | 4989102.93 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4613921.89 | 4346861.63 | 4205488.48 | 4880982.14 | 5022355.30 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4636090.57 | 4361663.71 | 4216390.91 | 4910517.42 | 5055790.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4658287.50 | 4376434.35 | 4227230.31 | 4940140.65 | 5089344.69 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4680445.92 | 4391106.93 | 4237940.13 | 4969784.90 | 5122951.71 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4702531.25 | 4405643.15 | 4248480.09 | 4999419.34 | 5156582.41 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4724559.17 | 4420054.29 | 4258859.14 | 5029064.06 | 5190259.21 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4746579.78 | 4434388.54 | 4269124.48 | 5058771.02 | 5224035.07 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4768641.88 | 4448696.55 | 4279327.72 | 5088587.21 | 5257956.03 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4790762.32 | 4462999.40 | 4289492.18 | 5118525.25 | 5292032.46 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4812919.12 | 4477279.08 | 4299601.98 | 5148559.16 | 5326236.26 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4835069.90 | 4491494.83 | 4309617.18 | 5178644.96 | 5360522.62 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4857181.09 | 4505611.91 | 4319502.42 | 5208750.27 | 5394859.76 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4879248.09 | 4519623.15 | 4329249.21 | 5238873.02 | 5429246.96 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4901294.74 | 4533550.57 | 4338878.57 | 5269038.90 | 5463710.90 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
plot(forecasting_auto_arima)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph4<-autoplot(forecasting_auto_arima,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph4
MAPE_Mean_All.ARIMA
## [1] "3.066 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Italy"
## Ensembling (Average)
weight.model<-0.90# optimization the weights ( weight average)
re_NNAR<-forecasting_NNAR$mean
re_BATS<-forecasting_bats$mean
re_TBATS<-forecasting_tbats$mean
re_holt<-forecasting_holt$mean
re_autoarima<-forecasting_auto_arima$mean
re_bestmodel<-min(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
y1<-if(re_bestmodel >= MAPE_Mean_All.bats_Model) {re_BATS*weight.model
} else {
(re_BATS*(1-weight.model))/4
}
y2<-if(re_bestmodel >= MAPE_Mean_All.TBATS_Model) {re_TBATS*weight.model
} else {
(re_TBATS*(1-weight.model))/4
}
y3<-if(re_bestmodel >= MAPE_Mean_All.Holt_Model) {re_holt*weight.model
} else {
(re_holt*(1-weight.model))/4
}
y4<-if(re_bestmodel >= MAPE_Mean_All.ARIMA_Model) {re_autoarima*weight.model
} else {
(re_autoarima*(1-weight.model))/4
}
y5<-if(re_bestmodel >= MAPE_Mean_All_NNAR) {re_NNAR*weight.model
} else {
(re_NNAR*(1-weight.model))/4
}
Ensembling.Average<-(y1+y2+y3+y4+y5)
# Testing Data Evaluation
validation_forecast<-head(Ensembling.Average,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using Ensembling (Average) for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using Ensembling (Average) for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
MAPE_Mean_EnsemblingAverage<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_Ensembling<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Ensembling<-paste(round(MAPE_Per_Day,3),"%")
MAPE_Ensembling_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in Ensembling Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in Ensembling Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
paste(MAPE_Mean_EnsemblingAverage,"%")
## [1] "1.969 %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in Ensembling Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in Ensembling Model for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(date_Ensembling=validation_dates,validation_data_by_name,actual_data=testing_data,Ensembling=validation_forecast,MAPE_Ensembling)), type = "rest")
##
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | | date_Ensembling | validation_data_by_name | actual_data | Ensembling | MAPE_Ensembling |
## +====+=================+=========================+=============+============+=================+
## | 1 | 2021-03-25 | Thursday | 3440862.00 | 3437908.50 | 0.086 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 2 | 2021-03-26 | Friday | 3464543.00 | 3458809.50 | 0.165 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 3488619.00 | 3479055.43 | 0.274 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 3512453.00 | 3499107.36 | 0.38 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 5 | 2021-03-29 | Monday | 3532057.00 | 3519754.83 | 0.348 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 3544957.00 | 3539970.37 | 0.141 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 3561012.00 | 3560166.41 | 0.024 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 3584899.00 | 3580889.50 | 0.112 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 9 | 2021-04-02 | Friday | 3607083.00 | 3600957.02 | 0.17 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 3629000.00 | 3620889.34 | 0.223 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 3650247.00 | 3641485.89 | 0.24 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 12 | 2021-04-05 | Monday | 3668264.00 | 3661679.60 | 0.179 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 3678944.00 | 3681827.23 | 0.078 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 3686707.00 | 3702443.99 | 0.427 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 3700393.00 | 3722359.17 | 0.594 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 16 | 2021-04-09 | Friday | 3717602.00 | 3742135.13 | 0.66 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 3736526.00 | 3762611.39 | 0.698 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 3754077.00 | 3782732.15 | 0.763 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 19 | 2021-04-12 | Monday | 3769814.00 | 3802833.22 | 0.876 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 3779594.00 | 3823395.66 | 1.159 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 3793033.00 | 3843227.18 | 1.323 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 3809193.00 | 3862894.63 | 1.41 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 23 | 2021-04-16 | Friday | 3826156.00 | 3883261.46 | 1.493 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 3842079.00 | 3903295.92 | 1.593 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 3857443.00 | 3923341.01 | 1.708 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 26 | 2021-04-19 | Monday | 3870131.00 | 3943865.63 | 1.905 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 3878994.00 | 3963657.36 | 2.183 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 3891063.00 | 3983270.61 | 2.37 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 3904899.00 | 4003571.84 | 2.527 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 30 | 2021-04-23 | Friday | 3920945.00 | 4023543.21 | 2.617 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 3935703.00 | 4043540.63 | 2.74 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 3949517.00 | 4064035.30 | 2.9 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 33 | 2021-04-26 | Monday | 3962674.00 | 4083806.17 | 3.057 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 3971114.00 | 4103395.98 | 3.331 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 3981512.00 | 4123665.76 | 3.57 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 3994894.00 | 4143601.76 | 3.722 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4009208.00 | 4163569.00 | 3.85 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4022653.00 | 4184044.84 | 4.012 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4035617.00 | 4203806.62 | 4.168 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4044762.00 | 4223389.49 | 4.416 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4050708.00 | 4243647.46 | 4.763 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4059821.00 | 4263565.91 | 5.019 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4070400.00 | 4283515.46 | 5.236 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4082198.00 | 4303980.57 | 5.433 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4092747.00 | 4323741.15 | 5.644 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_Ensembling=tail(Ensembling.Average,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+
## | | FD | forecating_date | forecasting_by_Ensembling |
## +====+============+=================+===========================+
## | 1 | 2021-05-09 | Sunday | 4343328.26 |
## +----+------------+-----------------+---------------------------+
## | 2 | 2021-05-10 | Monday | 4363588.44 |
## +----+------------+-----------------+---------------------------+
## | 3 | 2021-05-11 | Tuesday | 4383502.30 |
## +----+------------+-----------------+---------------------------+
## | 4 | 2021-05-12 | Wednesday | 4403442.08 |
## +----+------------+-----------------+---------------------------+
## | 5 | 2021-05-13 | Thursday | 4423898.92 |
## +----+------------+-----------------+---------------------------+
## | 6 | 2021-05-14 | Friday | 4443659.04 |
## +----+------------+-----------------+---------------------------+
## | 7 | 2021-05-15 | Saturday | 4463254.40 |
## +----+------------+-----------------+---------------------------+
## | 8 | 2021-05-16 | Sunday | 4483526.26 |
## +----+------------+-----------------+---------------------------+
## | 9 | 2021-05-17 | Monday | 4503447.80 |
## +----+------------+-----------------+---------------------------+
## | 10 | 2021-05-18 | Tuesday | 4523387.46 |
## +----+------------+-----------------+---------------------------+
## | 11 | 2021-05-19 | Wednesday | 4543839.05 |
## +----+------------+-----------------+---------------------------+
## | 12 | 2021-05-20 | Thursday | 4563595.82 |
## +----+------------+-----------------+---------------------------+
## | 13 | 2021-05-21 | Friday | 4583195.69 |
## +----+------------+-----------------+---------------------------+
## | 14 | 2021-05-22 | Saturday | 4603480.22 |
## +----+------------+-----------------+---------------------------+
## | 15 | 2021-05-23 | Sunday | 4623417.05 |
## +----+------------+-----------------+---------------------------+
## | 16 | 2021-05-24 | Monday | 4643367.46 |
## +----+------------+-----------------+---------------------------+
## | 17 | 2021-05-25 | Tuesday | 4663821.85 |
## +----+------------+-----------------+---------------------------+
## | 18 | 2021-05-26 | Wednesday | 4683576.32 |
## +----+------------+-----------------+---------------------------+
## | 19 | 2021-05-27 | Thursday | 4703175.62 |
## +----+------------+-----------------+---------------------------+
## | 20 | 2021-05-28 | Friday | 4723466.91 |
## +----+------------+-----------------+---------------------------+
## | 21 | 2021-05-29 | Saturday | 4743418.05 |
## +----+------------+-----------------+---------------------------+
## | 22 | 2021-05-30 | Sunday | 4763385.09 |
## +----+------------+-----------------+---------------------------+
graph5<-autoplot(Ensembling.Average,xlab = paste ("Time in", frequency ,y_lab,"by using Ensembling models" , sep=" "), ylab=y_lab)
graph5
# Table for MAPE For counry
best_recommended_model <- min(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_EnsemblingAverage)
paste("System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> Forecasting cumulative Covid 19 Infection cases in Italy"
best_recommended_model
## [1] 1.969
x1<-if(best_recommended_model >= MAPE_Mean_All.bats_Model) {paste("BATS Model")}
x2<-if(best_recommended_model >= MAPE_Mean_All.TBATS_Model) {paste("TBATS Model")}
x3<-if(best_recommended_model >= MAPE_Mean_All.Holt_Model) {paste("Holt Model")}
x4<-if(best_recommended_model >= MAPE_Mean_All.ARIMA_Model) {paste("ARIMA Model")}
x5<-if(best_recommended_model >= MAPE_Mean_All_NNAR) {paste("NNAR Model")}
x6<-if(best_recommended_model >= MAPE_Mean_EnsemblingAverage) {paste("Ensembling")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4501593.81 | 4307040.84 | 4204050.72 | 4307040.84 | 4204050.72 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4524704.90 | 4323925.44 | 4217639.22 | 4323925.44 | 4217639.22 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4547501.89 | 4340456.12 | 4230852.72 | 4340456.12 | 4230852.72 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4570471.83 | 4357077.54 | 4244113.42 | 4357077.54 | 4244113.42 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4593949.97 | 4374097.86 | 4257715.18 | 4374097.86 | 4257715.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4617878.90 | 4391467.28 | 4271612.21 | 4391467.28 | 4271612.21 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4641870.28 | 4408832.46 | 4285469.69 | 4408832.46 | 4285469.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4665508.49 | 4425813.06 | 4298925.97 | 4425813.06 | 4298925.97 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4688659.68 | 4442285.26 | 4311862.51 | 4442285.26 | 4311862.51 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4711557.12 | 4458461.98 | 4324481.51 | 4458461.98 | 4324481.51 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4734610.54 | 4474719.68 | 4337141.77 | 4474719.68 | 4337141.77 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4758094.19 | 4491311.82 | 4350085.76 | 4491311.82 | 4350085.76 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4781950.40 | 4508187.29 | 4363265.86 | 4508187.29 | 4363265.86 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4805848.47 | 4525043.26 | 4376393.96 | 4525043.26 | 4376393.96 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4829442.87 | 4541561.77 | 4389166.73 | 4541561.77 | 4389166.73 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4852629.76 | 4557646.43 | 4401491.69 | 4557646.43 | 4401491.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4875612.08 | 4573483.72 | 4413546.63 | 4573483.72 | 4413546.63 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4898734.33 | 4589391.79 | 4425635.74 | 4589391.79 | 4425635.74 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4922220.56 | 4605578.67 | 4437958.58 | 4605578.67 | 4437958.58 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4946014.42 | 4621993.74 | 4450467.55 | 4621993.74 | 4450467.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4969834.54 | 4638377.94 | 4462915.42 | 4638377.94 | 4462915.42 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4993393.86 | 4654465.94 | 4475048.33 | 4654465.94 | 4475048.33 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+======================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4350523.35 | 4328098.08 | 4316226.86 | 4372948.62 | 4384819.84 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4371125.40 | 4348474.97 | 4336484.56 | 4393775.83 | 4405766.24 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4391348.52 | 4368478.07 | 4356371.18 | 4414218.97 | 4426325.86 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4411595.61 | 4388508.96 | 4376287.63 | 4434682.26 | 4446903.59 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4432405.40 | 4409104.30 | 4396769.44 | 4455706.51 | 4468041.37 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4452431.24 | 4428918.47 | 4416471.56 | 4475944.01 | 4488390.92 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4472273.30 | 4448550.76 | 4435992.80 | 4495995.85 | 4508553.81 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4492875.36 | 4468944.89 | 4456276.86 | 4516805.83 | 4529473.85 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4513098.48 | 4488964.60 | 4476188.90 | 4537232.35 | 4550008.06 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4533345.57 | 4509011.61 | 4496129.99 | 4557679.52 | 4570561.14 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4554155.36 | 4529622.71 | 4516635.91 | 4578688.02 | 4591674.82 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4574181.20 | 4549452.23 | 4536361.50 | 4598910.17 | 4612000.90 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4594023.26 | 4569099.52 | 4555905.69 | 4618947.00 | 4632140.83 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4614625.32 | 4589508.33 | 4576212.20 | 4639742.30 | 4653038.43 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4634848.44 | 4609542.25 | 4596145.96 | 4660154.63 | 4673550.91 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4655095.52 | 4629603.07 | 4616108.18 | 4680587.98 | 4694082.87 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4675905.32 | 4650227.71 | 4636634.81 | 4701582.92 | 4715175.83 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4695931.16 | 4670070.47 | 4656380.65 | 4721791.85 | 4735481.67 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4715773.22 | 4689730.74 | 4675944.68 | 4741815.70 | 4755601.76 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4736375.27 | 4710152.27 | 4696270.65 | 4762598.28 | 4776479.90 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4756598.39 | 4730198.53 | 4716223.29 | 4782998.26 | 4796973.50 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4776845.48 | 4750271.39 | 4736203.92 | 4803419.57 | 4817487.05 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4400468.43 | 3472343.36 | 3028660.50 | 5448119.71 | 6051796.60 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4423276.23 | 3464373.91 | 3007515.25 | 5509586.75 | 6136986.92 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4446147.65 | 3456120.33 | 2986034.34 | 5571806.30 | 6223437.44 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4469082.70 | 3447586.78 | 2964226.81 | 5634781.64 | 6311156.37 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4492081.42 | 3438777.35 | 2942101.61 | 5698516.14 | 6400152.09 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4515143.83 | 3429696.07 | 2919667.56 | 5763013.22 | 6490433.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4538269.95 | 3420346.89 | 2896933.39 | 5828276.39 | 6582007.94 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4561459.81 | 3410733.73 | 2873907.75 | 5894309.22 | 6674885.37 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4584713.45 | 3400860.45 | 2850599.20 | 5961115.33 | 6769074.20 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4608030.87 | 3390730.83 | 2827016.18 | 6028698.42 | 6864583.33 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4631412.11 | 3380348.64 | 2803167.10 | 6097062.24 | 6961421.79 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4654857.20 | 3369717.57 | 2779060.25 | 6166210.59 | 7059598.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4678366.16 | 3358841.30 | 2754703.87 | 6236147.33 | 7159123.21 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4701939.01 | 3347723.43 | 2730106.11 | 6306876.37 | 7260004.65 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4725575.78 | 3336367.54 | 2705275.08 | 6378401.66 | 7362252.38 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4749276.49 | 3324777.18 | 2680218.80 | 6450727.20 | 7465875.83 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4773041.18 | 3312955.85 | 2654945.24 | 6523857.04 | 7570884.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4796869.86 | 3300907.02 | 2629462.29 | 6597795.26 | 7677288.11 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4820762.56 | 3288634.12 | 2603777.80 | 6672546.01 | 7785096.20 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4844719.31 | 3276140.55 | 2577899.57 | 6748113.44 | 7894318.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4868740.13 | 3263429.70 | 2551835.32 | 6824501.77 | 8004964.99 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4892825.04 | 3250504.89 | 2525592.75 | 6901715.24 | 8117045.37 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+===========================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4437062.72 | 4226416.93 | 4114907.78 | 4647708.52 | 4759217.67 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4459208.86 | 4241742.12 | 4126622.18 | 4676675.59 | 4791795.53 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4481455.15 | 4257104.14 | 4138339.89 | 4705806.15 | 4824570.40 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4503695.17 | 4272401.09 | 4149961.40 | 4734989.26 | 4857428.95 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4525839.02 | 4287539.39 | 4161391.20 | 4764138.64 | 4890286.84 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4547868.11 | 4302492.51 | 4172598.51 | 4793243.70 | 4923137.70 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4569838.56 | 4317310.24 | 4183629.82 | 4822366.88 | 4956047.29 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4591836.91 | 4332078.62 | 4194570.89 | 4851595.20 | 4989102.93 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4613921.89 | 4346861.63 | 4205488.48 | 4880982.14 | 5022355.30 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4636090.57 | 4361663.71 | 4216390.91 | 4910517.42 | 5055790.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4658287.50 | 4376434.35 | 4227230.31 | 4940140.65 | 5089344.69 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4680445.92 | 4391106.93 | 4237940.13 | 4969784.90 | 5122951.71 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4702531.25 | 4405643.15 | 4248480.09 | 4999419.34 | 5156582.41 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4724559.17 | 4420054.29 | 4258859.14 | 5029064.06 | 5190259.21 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4746579.78 | 4434388.54 | 4269124.48 | 5058771.02 | 5224035.07 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4768641.88 | 4448696.55 | 4279327.72 | 5088587.21 | 5257956.03 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4790762.32 | 4462999.40 | 4289492.18 | 5118525.25 | 5292032.46 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4812919.12 | 4477279.08 | 4299601.98 | 5148559.16 | 5326236.26 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4835069.90 | 4491494.83 | 4309617.18 | 5178644.96 | 5360522.62 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4857181.09 | 4505611.91 | 4319502.42 | 5208750.27 | 5394859.76 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4879248.09 | 4519623.15 | 4329249.21 | 5238873.02 | 5429246.96 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4901294.74 | 4533550.57 | 4338878.57 | 5269038.90 | 5463710.90 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +====+============+=================+=====================+
## | 1 | 2021-05-09 | Sunday | 3775164.97 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 3775833.40 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 3776440.39 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 3776991.51 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 3777491.83 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 3777945.96 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 3778358.12 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 3778732.15 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 3779071.54 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 3779379.48 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 3779658.84 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 3779912.28 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 3780142.17 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 3780350.69 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 3780539.81 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 3780711.34 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 3780866.91 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 3781007.98 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 3781135.91 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 3781251.92 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 3781357.12 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 3781452.50 |
## +----+------------+-----------------+---------------------+
paste("Forecasting by using Ensembling Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Ensembling Model ==> Forecasting cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting.Ensembling=tail(Ensembling.Average,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+------------------------+
## | | FD | forecating_date | forecasting.Ensembling |
## +====+============+=================+========================+
## | 1 | 2021-05-09 | Sunday | 4343328.26 |
## +----+------------+-----------------+------------------------+
## | 2 | 2021-05-10 | Monday | 4363588.44 |
## +----+------------+-----------------+------------------------+
## | 3 | 2021-05-11 | Tuesday | 4383502.30 |
## +----+------------+-----------------+------------------------+
## | 4 | 2021-05-12 | Wednesday | 4403442.08 |
## +----+------------+-----------------+------------------------+
## | 5 | 2021-05-13 | Thursday | 4423898.92 |
## +----+------------+-----------------+------------------------+
## | 6 | 2021-05-14 | Friday | 4443659.04 |
## +----+------------+-----------------+------------------------+
## | 7 | 2021-05-15 | Saturday | 4463254.40 |
## +----+------------+-----------------+------------------------+
## | 8 | 2021-05-16 | Sunday | 4483526.26 |
## +----+------------+-----------------+------------------------+
## | 9 | 2021-05-17 | Monday | 4503447.80 |
## +----+------------+-----------------+------------------------+
## | 10 | 2021-05-18 | Tuesday | 4523387.46 |
## +----+------------+-----------------+------------------------+
## | 11 | 2021-05-19 | Wednesday | 4543839.05 |
## +----+------------+-----------------+------------------------+
## | 12 | 2021-05-20 | Thursday | 4563595.82 |
## +----+------------+-----------------+------------------------+
## | 13 | 2021-05-21 | Friday | 4583195.69 |
## +----+------------+-----------------+------------------------+
## | 14 | 2021-05-22 | Saturday | 4603480.22 |
## +----+------------+-----------------+------------------------+
## | 15 | 2021-05-23 | Sunday | 4623417.05 |
## +----+------------+-----------------+------------------------+
## | 16 | 2021-05-24 | Monday | 4643367.46 |
## +----+------------+-----------------+------------------------+
## | 17 | 2021-05-25 | Tuesday | 4663821.85 |
## +----+------------+-----------------+------------------------+
## | 18 | 2021-05-26 | Wednesday | 4683576.32 |
## +----+------------+-----------------+------------------------+
## | 19 | 2021-05-27 | Thursday | 4703175.62 |
## +----+------------+-----------------+------------------------+
## | 20 | 2021-05-28 | Friday | 4723466.91 |
## +----+------------+-----------------+------------------------+
## | 21 | 2021-05-29 | Saturday | 4743418.05 |
## +----+------------+-----------------+------------------------+
## | 22 | 2021-05-30 | Sunday | 4763385.09 |
## +----+------------+-----------------+------------------------+
result<-c(x1,x2,x3,x4,x5,x6)
table.error<-data.frame(country.name,NNAR.model=MAPE_Mean_All_NNAR, BATS.Model=MAPE_Mean_All.bats_Model,TBATS.Model=MAPE_Mean_All.TBATS_Model,Holt.Model=MAPE_Mean_All.Holt_Model,ARIMA.Model=MAPE_Mean_All.ARIMA_Model,Ensemblingt=MAPE_Mean_EnsemblingAverage,Best.Model=result)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Ensemblingt | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+=============+============+======+
## | 1 | Italy | 3.265 | 3.897 | 2.021 | 2.37 | 3.066 | 1.969 | Ensembling | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_EnsemblingAverage)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model","Ensembling.weight")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and Ensembling Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and Ensembling Model ==>Forecasting cumulative Covid 19 Infection cases in Italy
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Forecasting cumulative Covid 19 Infection cases in Italy