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 France" # 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 <- "France"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 130108 287695 1414088 2620276 5655548
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.618052
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.9819582
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 1710849
#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 37204516
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 France"
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 France"
paste(MAPE_Mean_All,"%")
## [1] "9.37 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in France %"
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 France"
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 | 4306105.00 | 4296621.06 | 0.22 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4351506.00 | 4319803.54 | 0.729 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4393375.00 | 4342215.27 | 1.164 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4435187.00 | 4363814.37 | 1.609 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4472201.00 | 4384565.69 | 1.96 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4481295.00 | 4404441.20 | 1.715 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4510870.00 | 4423420.14 | 1.939 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4569698.00 | 4441489.02 | 2.806 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4620357.00 | 4458641.49 | 3.5 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4665877.00 | 4474878.01 | 4.094 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4679794.00 | 4490205.47 | 4.051 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4746588.00 | 4504636.60 | 5.097 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4758923.00 | 4518189.46 | 5.059 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4807569.00 | 4530886.67 | 5.755 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4838354.00 | 4542754.85 | 6.109 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4861992.00 | 4553823.84 | 6.338 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4901955.00 | 4564126.08 | 6.892 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4945238.00 | 4573695.96 | 7.513 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4980133.00 | 4582569.23 | 7.983 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4987689.00 | 4590782.42 | 7.958 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 5026645.00 | 4598372.39 | 8.52 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 5069999.00 | 4605375.89 | 9.164 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 5107935.00 | 4611829.21 | 9.712 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 5144295.00 | 4617767.84 | 10.235 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 5178513.00 | 4623226.24 | 10.723 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 5207857.00 | 4628237.67 | 11.13 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 5214493.00 | 4632833.98 | 11.155 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 5257046.00 | 4637045.56 | 11.794 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 5291414.00 | 4640901.24 | 12.294 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 5325448.00 | 4644428.26 | 12.788 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 5357640.00 | 4647652.24 | 13.252 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 5388524.00 | 4650597.22 | 13.694 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 5412989.00 | 4653285.68 | 14.035 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 5417903.00 | 4655738.56 | 14.068 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 5447883.00 | 4657975.34 | 14.499 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 5479327.00 | 4660014.09 | 14.953 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 5505700.00 | 4661871.52 | 15.326 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 5529820.00 | 4663563.10 | 15.665 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 5553806.00 | 4665103.07 | 16.002 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 5563694.00 | 4666504.56 | 16.126 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 5567300.00 | 4667779.63 | 16.157 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 5590416.00 | 4668939.38 | 16.483 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 5616180.00 | 4669993.96 | 16.848 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 5637744.00 | 4670952.69 | 17.149 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 5655548.00 | 4671824.11 | 17.394 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 4672616.02 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 4673335.54 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 4673989.20 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 4674582.93 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 4675122.17 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 4675611.85 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 4676056.49 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 4676460.18 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 4676826.67 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 4677159.36 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 4677461.34 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 4677735.43 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 4677984.19 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 4678209.95 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 4678414.83 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 4678600.74 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 4678769.45 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 4678922.52 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 4679061.42 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 4679187.44 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 4679301.78 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 4679405.52 |
## +----+------------+-----------------+---------------------+
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 233.5392 5645.514 2977.452 NaN Inf 0.3106847 -0.01656129
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.288904
## Beta: 0.2815286
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 94.11346
## [2,] 17.07223
##
## Sigma: 5645.514
## AIC: 10458.77
#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 France"
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 France"
paste(MAPE_Mean_All.bats,"%")
## [1] "2.291 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in France %"
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 France"
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 | 4306105.00 | 4298968.33 | 0.166 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4351506.00 | 4328374.75 | 0.532 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4393375.00 | 4357781.16 | 0.81 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4435187.00 | 4387187.58 | 1.082 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4472201.00 | 4416593.99 | 1.243 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4481295.00 | 4446000.41 | 0.788 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4510870.00 | 4475406.82 | 0.786 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4569698.00 | 4504813.24 | 1.42 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4620357.00 | 4534219.66 | 1.864 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4665877.00 | 4563626.07 | 2.191 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4679794.00 | 4593032.49 | 1.854 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4746588.00 | 4622438.90 | 2.616 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4758923.00 | 4651845.32 | 2.25 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4807569.00 | 4681251.73 | 2.627 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4838354.00 | 4710658.15 | 2.639 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4861992.00 | 4740064.56 | 2.508 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4901955.00 | 4769470.98 | 2.703 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4945238.00 | 4798877.39 | 2.96 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4980133.00 | 4828283.81 | 3.049 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4987689.00 | 4857690.22 | 2.606 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 5026645.00 | 4887096.64 | 2.776 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 5069999.00 | 4916503.06 | 3.028 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 5107935.00 | 4945909.47 | 3.172 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 5144295.00 | 4975315.89 | 3.285 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 5178513.00 | 5004722.30 | 3.356 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 5207857.00 | 5034128.72 | 3.336 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 5214493.00 | 5063535.13 | 2.895 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 5257046.00 | 5092941.55 | 3.122 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 5291414.00 | 5122347.96 | 3.195 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 5325448.00 | 5151754.38 | 3.262 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 5357640.00 | 5181160.79 | 3.294 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 5388524.00 | 5210567.21 | 3.303 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 5412989.00 | 5239973.62 | 3.196 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 5417903.00 | 5269380.04 | 2.741 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 5447883.00 | 5298786.45 | 2.737 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 5479327.00 | 5328192.87 | 2.758 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 5505700.00 | 5357599.29 | 2.69 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 5529820.00 | 5387005.70 | 2.583 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 5553806.00 | 5416412.12 | 2.474 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 5563694.00 | 5445818.53 | 2.119 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 5567300.00 | 5475224.95 | 1.654 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 5590416.00 | 5504631.36 | 1.534 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 5616180.00 | 5534037.78 | 1.463 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 5637744.00 | 5563444.19 | 1.318 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 5655548.00 | 5592850.61 | 1.109 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 5622257.02 | 5205680.75 | 4985158.59 | 5205680.75 | 4985158.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 5651663.44 | 5222537.44 | 4995371.86 | 5222537.44 | 4995371.86 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 5681069.85 | 5239270.94 | 5005396.73 | 5239270.94 | 5005396.73 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 5710476.27 | 5255882.43 | 5015234.98 | 5255882.43 | 5015234.98 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 5739882.69 | 5272373.04 | 5024888.38 | 5272373.04 | 5024888.38 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 5769289.10 | 5288743.89 | 5034358.62 | 5288743.89 | 5034358.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 5798695.52 | 5304996.06 | 5043647.36 | 5304996.06 | 5043647.36 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 5828101.93 | 5321130.62 | 5052756.22 | 5321130.62 | 5052756.22 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 5857508.35 | 5337148.57 | 5061686.75 | 5337148.57 | 5061686.75 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 5886914.76 | 5353050.94 | 5070440.50 | 5353050.94 | 5070440.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 5916321.18 | 5368838.68 | 5079018.95 | 5368838.68 | 5079018.95 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 5945727.59 | 5384512.76 | 5087423.57 | 5384512.76 | 5087423.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 5975134.01 | 5400074.09 | 5095655.76 | 5400074.09 | 5095655.76 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 6004540.42 | 5415523.60 | 5103716.93 | 5415523.60 | 5103716.93 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 6033946.84 | 5430862.15 | 5111608.41 | 5430862.15 | 5111608.41 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 6063353.25 | 5446090.63 | 5119331.53 | 5446090.63 | 5119331.53 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 6092759.67 | 5461209.86 | 5126887.59 | 5461209.86 | 5126887.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 6122166.09 | 5476220.68 | 5134277.85 | 5476220.68 | 5134277.85 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 6151572.50 | 5491123.90 | 5141503.53 | 5491123.90 | 5141503.53 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 6180978.92 | 5505920.30 | 5148565.86 | 5505920.30 | 5148565.86 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 6210385.33 | 5520610.66 | 5155466.00 | 5520610.66 | 5155466.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 6239791.75 | 5535195.73 | 5162205.13 | 5535195.73 | 5162205.13 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
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 232.1378 5614.593 3089.737 NaN Inf 0.3224012 -0.01652168
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.290922
## Beta: 0.2829251
## Damping Parameter: 1
## Gamma-1 Values: -0.000896665
## Gamma-2 Values: 0.002517207
##
## Seed States:
## [,1]
## [1,] 160.074320
## [2,] -9.155408
## [3,] -118.783393
## [4,] -151.336371
## [5,] -344.857365
## [6,] -193.177994
##
## Sigma: 5614.593
## AIC: 10465.86
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 France"
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 France"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "2.32 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in France %"
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 France"
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 | 4306105.00 | 4298314.77 | 0.181 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-26 | Friday | 4351506.00 | 4328381.67 | 0.531 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-27 | Saturday | 4393375.00 | 4358141.53 | 0.802 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-28 | Sunday | 4435187.00 | 4386226.89 | 1.104 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-29 | Monday | 4472201.00 | 4415711.52 | 1.263 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-30 | Tuesday | 4481295.00 | 4445605.48 | 0.796 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-31 | Wednesday | 4510870.00 | 4474407.22 | 0.808 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-04-01 | Thursday | 4569698.00 | 4504474.12 | 1.427 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 9 | 2021-04-02 | Friday | 4620357.00 | 4534233.98 | 1.864 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 10 | 2021-04-03 | Saturday | 4665877.00 | 4562319.34 | 2.219 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 11 | 2021-04-04 | Sunday | 4679794.00 | 4591803.97 | 1.88 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 12 | 2021-04-05 | Monday | 4746588.00 | 4621697.93 | 2.631 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 13 | 2021-04-06 | Tuesday | 4758923.00 | 4650499.67 | 2.278 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 14 | 2021-04-07 | Wednesday | 4807569.00 | 4680566.57 | 2.642 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 15 | 2021-04-08 | Thursday | 4838354.00 | 4710326.43 | 2.646 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 16 | 2021-04-09 | Friday | 4861992.00 | 4738411.79 | 2.542 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 17 | 2021-04-10 | Saturday | 4901955.00 | 4767896.42 | 2.735 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 18 | 2021-04-11 | Sunday | 4945238.00 | 4797790.38 | 2.982 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 19 | 2021-04-12 | Monday | 4980133.00 | 4826592.12 | 3.083 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 20 | 2021-04-13 | Tuesday | 4987689.00 | 4856659.02 | 2.627 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 21 | 2021-04-14 | Wednesday | 5026645.00 | 4886418.88 | 2.79 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 22 | 2021-04-15 | Thursday | 5069999.00 | 4914504.24 | 3.067 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 23 | 2021-04-16 | Friday | 5107935.00 | 4943988.87 | 3.21 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 24 | 2021-04-17 | Saturday | 5144295.00 | 4973882.83 | 3.313 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 25 | 2021-04-18 | Sunday | 5178513.00 | 5002684.57 | 3.395 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 26 | 2021-04-19 | Monday | 5207857.00 | 5032751.47 | 3.362 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 27 | 2021-04-20 | Tuesday | 5214493.00 | 5062511.33 | 2.915 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 28 | 2021-04-21 | Wednesday | 5257046.00 | 5090596.69 | 3.166 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 29 | 2021-04-22 | Thursday | 5291414.00 | 5120081.32 | 3.238 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 30 | 2021-04-23 | Friday | 5325448.00 | 5149975.28 | 3.295 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 31 | 2021-04-24 | Saturday | 5357640.00 | 5178777.02 | 3.338 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 32 | 2021-04-25 | Sunday | 5388524.00 | 5208843.92 | 3.334 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 33 | 2021-04-26 | Monday | 5412989.00 | 5238603.78 | 3.222 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 34 | 2021-04-27 | Tuesday | 5417903.00 | 5266689.14 | 2.791 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 35 | 2021-04-28 | Wednesday | 5447883.00 | 5296173.77 | 2.785 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 36 | 2021-04-29 | Thursday | 5479327.00 | 5326067.73 | 2.797 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 37 | 2021-04-30 | Friday | 5505700.00 | 5354869.47 | 2.74 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 38 | 2021-05-01 | Saturday | 5529820.00 | 5384936.37 | 2.62 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 39 | 2021-05-02 | Sunday | 5553806.00 | 5414696.23 | 2.505 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 40 | 2021-05-03 | Monday | 5563694.00 | 5442781.59 | 2.173 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 41 | 2021-05-04 | Tuesday | 5567300.00 | 5472266.22 | 1.707 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 42 | 2021-05-05 | Wednesday | 5590416.00 | 5502160.18 | 1.579 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 43 | 2021-05-06 | Thursday | 5616180.00 | 5530961.92 | 1.517 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 44 | 2021-05-07 | Friday | 5637744.00 | 5561028.82 | 1.361 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 45 | 2021-05-08 | Saturday | 5655548.00 | 5590788.68 | 1.145 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
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 | 5618874.04 | 5557131.93 | 5524447.64 | 5680616.14 | 5713300.43 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 5648358.67 | 5585961.68 | 5552930.71 | 5710755.65 | 5743786.62 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 5678252.63 | 5615215.06 | 5581844.98 | 5741290.21 | 5774660.29 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 5707054.37 | 5643384.46 | 5609679.65 | 5770724.28 | 5804429.09 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 5737121.27 | 5672820.63 | 5638781.92 | 5801421.92 | 5835460.62 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 5766881.13 | 5701957.91 | 5667589.63 | 5831804.35 | 5866172.63 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 5794966.49 | 5729426.60 | 5694731.88 | 5860506.37 | 5895201.09 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 5824451.12 | 5758299.19 | 5723280.48 | 5890603.04 | 5925621.75 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 5854345.08 | 5787593.78 | 5752257.78 | 5921096.38 | 5956432.39 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 5883146.82 | 5815803.18 | 5780153.61 | 5950490.46 | 5986140.03 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 5913213.72 | 5845278.55 | 5809315.84 | 5981148.89 | 6017111.60 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 5942973.58 | 5874453.90 | 5838181.77 | 6011493.26 | 6047765.38 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 5971058.94 | 5901959.69 | 5865380.76 | 6040158.18 | 6076737.11 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 6000543.57 | 5930868.52 | 5893984.78 | 6070218.61 | 6107102.35 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 6030437.53 | 5960198.07 | 5923015.55 | 6100676.99 | 6137859.52 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 6059239.27 | 5988441.51 | 5950963.44 | 6130037.03 | 6167515.10 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 6089306.17 | 6017950.35 | 5980176.86 | 6160661.99 | 6198435.48 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 6119066.03 | 6047158.29 | 6009092.64 | 6190973.76 | 6229039.42 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 6147151.38 | 6074695.94 | 6036340.35 | 6219606.83 | 6257962.42 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 6176636.02 | 6103635.97 | 6064992.07 | 6249636.06 | 6288279.96 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 6206529.98 | 6132995.70 | 6094069.00 | 6280064.27 | 6318990.96 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 6235331.72 | 6161268.60 | 6122061.95 | 6309394.84 | 6348601.49 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -105.5575 5961.603 3088.36 NaN Inf 0.3222575 0.1966511
# 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= 0.3856
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.3264
##
## Initial states:
## l = -3.2597
## b = -0.2384
##
## sigma: 1.1205
##
## AIC AICc BIC
## 2835.533 2835.669 2856.045
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -105.5575 5961.603 3088.36 NaN Inf 0.3222575 0.1966511
# 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 France"
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 France"
paste(MAPE_Mean_All.Holt,"%")
## [1] "1.229 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in France %"
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 France"
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 | 4306105.00 | 4303684.84 | 0.056 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4351506.00 | 4334790.13 | 0.384 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4393375.00 | 4366033.16 | 0.622 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4435187.00 | 4397414.17 | 0.852 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4472201.00 | 4428933.37 | 0.967 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4481295.00 | 4460591.00 | 0.462 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4510870.00 | 4492387.27 | 0.41 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4569698.00 | 4524322.41 | 0.993 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4620357.00 | 4556396.66 | 1.384 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4665877.00 | 4588610.23 | 1.656 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4679794.00 | 4620963.35 | 1.257 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4746588.00 | 4653456.24 | 1.962 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4758923.00 | 4686089.13 | 1.53 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4807569.00 | 4718862.24 | 1.845 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4838354.00 | 4751775.79 | 1.789 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4861992.00 | 4784830.02 | 1.587 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4901955.00 | 4818025.13 | 1.712 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4945238.00 | 4851361.36 | 1.898 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4980133.00 | 4884838.93 | 1.913 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4987689.00 | 4918458.06 | 1.388 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 5026645.00 | 4952218.98 | 1.481 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 5069999.00 | 4986121.89 | 1.654 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 5107935.00 | 5020167.04 | 1.718 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 5144295.00 | 5054354.63 | 1.748 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 5178513.00 | 5088684.89 | 1.735 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 5207857.00 | 5123158.05 | 1.626 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 5214493.00 | 5157774.31 | 1.088 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 5257046.00 | 5192533.91 | 1.227 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 5291414.00 | 5227437.06 | 1.209 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 5325448.00 | 5262483.98 | 1.182 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 5357640.00 | 5297674.90 | 1.119 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 5388524.00 | 5333010.03 | 1.03 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 5412989.00 | 5368489.59 | 0.822 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 5417903.00 | 5404113.81 | 0.255 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 5447883.00 | 5439882.89 | 0.147 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 5479327.00 | 5475797.06 | 0.064 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 5505700.00 | 5511856.55 | 0.112 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 5529820.00 | 5548061.55 | 0.33 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 5553806.00 | 5584412.31 | 0.551 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 5563694.00 | 5620909.02 | 1.028 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 5567300.00 | 5657551.92 | 1.621 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 5590416.00 | 5694341.21 | 1.859 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 5616180.00 | 5731277.12 | 2.049 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 5637744.00 | 5768359.86 | 2.317 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 5655548.00 | 5805589.65 | 2.653 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 5842966.71 | 4616723.83 | 4038013.60 | 7251200.18 | 8073503.07 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 2 | 2021-05-10 | Monday | 5880491.25 | 4613779.02 | 4018096.16 | 7340953.90 | 8195964.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 5918163.48 | 4610477.39 | 3997737.63 | 7431866.94 | 8320347.38 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 5955983.63 | 4606822.95 | 3976947.60 | 7523947.30 | 8446669.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 5 | 2021-05-13 | Thursday | 5993951.91 | 4602819.67 | 3955735.56 | 7617203.06 | 8574949.11 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 6 | 2021-05-14 | Friday | 6032068.54 | 4598471.45 | 3934110.88 | 7711642.44 | 8705204.26 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 7 | 2021-05-15 | Saturday | 6070333.72 | 4593782.14 | 3912082.86 | 7807273.74 | 8837453.49 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 8 | 2021-05-16 | Sunday | 6108747.68 | 4588755.55 | 3889660.69 | 7904105.37 | 8971715.47 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 9 | 2021-05-17 | Monday | 6147310.63 | 4583395.43 | 3866853.49 | 8002145.82 | 9108009.07 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 6186022.79 | 4577705.48 | 3843670.29 | 8101403.70 | 9246353.34 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 6224884.37 | 4571689.39 | 3820120.04 | 8201887.69 | 9386767.53 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 12 | 2021-05-20 | Thursday | 6263895.58 | 4565350.76 | 3796211.60 | 8303606.57 | 9529271.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 13 | 2021-05-21 | Friday | 6303056.64 | 4558693.21 | 3771953.79 | 8406569.19 | 9673883.60 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 14 | 2021-05-22 | Saturday | 6342367.76 | 4551720.26 | 3747355.32 | 8510784.51 | 9820624.87 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 15 | 2021-05-23 | Sunday | 6381829.16 | 4544435.46 | 3722424.85 | 8616261.55 | 9969514.87 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 16 | 2021-05-24 | Monday | 6421441.04 | 4536842.28 | 3697170.99 | 8723009.42 | 10120573.75 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 6461203.63 | 4528944.18 | 3671602.26 | 8831037.32 | 10273821.80 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 6501117.13 | 4520744.60 | 3645727.12 | 8940354.50 | 10429279.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 19 | 2021-05-27 | Thursday | 6541181.76 | 4512246.92 | 3619553.99 | 9050970.30 | 10586967.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 20 | 2021-05-28 | Friday | 6581397.73 | 4503454.52 | 3593091.21 | 9162894.14 | 10746906.61 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 21 | 2021-05-29 | Saturday | 6621765.26 | 4494370.76 | 3566347.06 | 9276135.50 | 10909117.78 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 22 | 2021-05-30 | Sunday | 6662284.55 | 4484998.94 | 3539329.79 | 9390703.95 | 11073622.15 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
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 France"
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 = 6.2506, 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) = 0.55251, 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 = -1.1108, Lag order = 7, p-value = 0.9205
## 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 France"
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 = 4.4963, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -91.204, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -1.9997, Lag order = 7, p-value = 0.5779
## 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 France"
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 = 0.020907, 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) = -392.27, 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 = -8.9684, 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) : 9072.473
## ARIMA(0,2,1) : 8996.876
## ARIMA(0,2,2) : 8959.9
## ARIMA(0,2,3) : 8960.289
## ARIMA(0,2,4) : 8955.005
## ARIMA(0,2,5) : 8934.262
## ARIMA(1,2,0) : 9051.528
## ARIMA(1,2,1) : 8970.142
## ARIMA(1,2,2) : 8960.529
## ARIMA(1,2,3) : 8959.941
## ARIMA(1,2,4) : 8926.156
## ARIMA(2,2,0) : 9012.95
## ARIMA(2,2,1) : 8957.784
## ARIMA(2,2,2) : Inf
## ARIMA(2,2,3) : 8922.909
## ARIMA(3,2,0) : 9002.024
## ARIMA(3,2,1) : 8957.501
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 8980.252
## ARIMA(4,2,1) : 8943.549
## ARIMA(5,2,0) : 8950.501
##
##
##
## Best model: ARIMA(2,2,3)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,3)
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## 1.1076 -0.3667 -1.6487 0.6203 0.1407
## s.e. 0.1229 0.1167 0.1307 0.2338 0.1112
##
## sigma^2 estimated as 29297132: log likelihood=-4455.36
## AIC=8922.72 AICc=8922.91 BIC=8947.31
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 3
strtoi(bestmodel[3])
## [1] 3
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## 1.1076 -0.3667 -1.6487 0.6203 0.1407
## s.e. 0.1229 0.1167 0.1307 0.2338 0.1112
##
## sigma^2 estimated as 28967951: log likelihood = -4455.36, aic = 8922.72
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting cumulative Covid 19 Infection cases in France"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 183.0749 5370.134 2783.803 0.8889177 2.064387 0.2904783
## ACF1
## Training set -0.004684419
x1_model1$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(2,2,3)
## Q* = 68.002, df = 5, p-value = 2.668e-13
##
## Model df: 5. 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 France"
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 = 518.7, 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 = 1441.9, 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 France"
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 France"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.909 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in France %"
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 France"
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 | 4306105.00 | 4302788.93 | 0.077 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-26 | Friday | 4351506.00 | 4338307.41 | 0.303 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-27 | Saturday | 4393375.00 | 4375811.31 | 0.4 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-28 | Sunday | 4435187.00 | 4413517.41 | 0.489 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-29 | Monday | 4472201.00 | 4450719.43 | 0.48 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-30 | Tuesday | 4481295.00 | 4487289.00 | 0.134 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-31 | Wednesday | 4510870.00 | 4523342.94 | 0.277 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-04-01 | Thursday | 4569698.00 | 4559057.67 | 0.233 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 9 | 2021-04-02 | Friday | 4620357.00 | 4594585.78 | 0.558 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 10 | 2021-04-03 | Saturday | 4665877.00 | 4630031.59 | 0.768 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 11 | 2021-04-04 | Sunday | 4679794.00 | 4665454.65 | 0.306 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 12 | 2021-04-05 | Monday | 4746588.00 | 4700882.72 | 0.963 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 13 | 2021-04-06 | Tuesday | 4758923.00 | 4736324.66 | 0.475 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 14 | 2021-04-07 | Wednesday | 4807569.00 | 4771780.14 | 0.744 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 15 | 2021-04-08 | Thursday | 4838354.00 | 4807245.52 | 0.643 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 16 | 2021-04-09 | Friday | 4861992.00 | 4842716.91 | 0.396 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 17 | 2021-04-10 | Saturday | 4901955.00 | 4878191.31 | 0.485 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 18 | 2021-04-11 | Sunday | 4945238.00 | 4913666.86 | 0.638 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 19 | 2021-04-12 | Monday | 4980133.00 | 4949142.56 | 0.622 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 20 | 2021-04-13 | Tuesday | 4987689.00 | 4984618.02 | 0.062 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 21 | 2021-04-14 | Wednesday | 5026645.00 | 5020093.16 | 0.13 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 22 | 2021-04-15 | Thursday | 5069999.00 | 5055568.02 | 0.285 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 23 | 2021-04-16 | Friday | 5107935.00 | 5091042.69 | 0.331 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 24 | 2021-04-17 | Saturday | 5144295.00 | 5126517.27 | 0.346 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 25 | 2021-04-18 | Sunday | 5178513.00 | 5161991.80 | 0.319 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 26 | 2021-04-19 | Monday | 5207857.00 | 5197466.31 | 0.2 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 27 | 2021-04-20 | Tuesday | 5214493.00 | 5232940.83 | 0.354 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 28 | 2021-04-21 | Wednesday | 5257046.00 | 5268415.35 | 0.216 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 29 | 2021-04-22 | Thursday | 5291414.00 | 5303889.88 | 0.236 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 30 | 2021-04-23 | Friday | 5325448.00 | 5339364.42 | 0.261 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 31 | 2021-04-24 | Saturday | 5357640.00 | 5374838.96 | 0.321 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 32 | 2021-04-25 | Sunday | 5388524.00 | 5410313.50 | 0.404 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 33 | 2021-04-26 | Monday | 5412989.00 | 5445788.04 | 0.606 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 34 | 2021-04-27 | Tuesday | 5417903.00 | 5481262.58 | 1.169 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 35 | 2021-04-28 | Wednesday | 5447883.00 | 5516737.12 | 1.264 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 36 | 2021-04-29 | Thursday | 5479327.00 | 5552211.66 | 1.33 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 37 | 2021-04-30 | Friday | 5505700.00 | 5587686.20 | 1.489 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 38 | 2021-05-01 | Saturday | 5529820.00 | 5623160.75 | 1.688 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 39 | 2021-05-02 | Sunday | 5553806.00 | 5658635.29 | 1.888 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 40 | 2021-05-03 | Monday | 5563694.00 | 5694109.83 | 2.344 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 41 | 2021-05-04 | Tuesday | 5567300.00 | 5729584.37 | 2.915 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 42 | 2021-05-05 | Wednesday | 5590416.00 | 5765058.91 | 3.124 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 43 | 2021-05-06 | Thursday | 5616180.00 | 5800533.45 | 3.283 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 44 | 2021-05-07 | Friday | 5637744.00 | 5836007.99 | 3.517 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 45 | 2021-05-08 | Saturday | 5655548.00 | 5871482.53 | 3.818 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 5906957.07 | 5386724.44 | 5111329.92 | 6427189.71 | 6702584.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 5942431.61 | 5404756.47 | 5120128.45 | 6480106.76 | 6764734.78 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 5977906.16 | 5422596.88 | 5128633.91 | 6533215.43 | 6827178.40 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 6013380.70 | 5440247.75 | 5136849.50 | 6586513.64 | 6889911.89 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 6048855.24 | 5457711.11 | 5144778.31 | 6639999.37 | 6952932.16 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 6084329.78 | 5474988.90 | 5152423.33 | 6693670.65 | 7016236.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 6119804.32 | 5492083.03 | 5159787.45 | 6747525.61 | 7079821.19 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 6155278.86 | 5508995.33 | 5166873.50 | 6801562.39 | 7143684.22 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 6190753.40 | 5525727.58 | 5173684.18 | 6855779.22 | 7207822.62 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 6226227.94 | 5542281.52 | 5180222.16 | 6910174.36 | 7272233.73 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 6261702.48 | 5558658.82 | 5186489.99 | 6964746.14 | 7336914.98 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 6297177.02 | 5574861.12 | 5192490.18 | 7019492.93 | 7401863.87 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 6332651.56 | 5590890.00 | 5198225.15 | 7074413.13 | 7467077.98 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 6368126.11 | 5606747.02 | 5203697.27 | 7129505.19 | 7532554.94 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 6403600.65 | 5622433.66 | 5208908.84 | 7184767.63 | 7598292.45 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 6439075.19 | 5637951.41 | 5213862.10 | 7240198.96 | 7664288.27 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 6474549.73 | 5653301.68 | 5218559.23 | 7295797.77 | 7730540.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 6510024.27 | 5668485.87 | 5223002.35 | 7351562.67 | 7797046.19 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 6545498.81 | 5683505.33 | 5227193.55 | 7407492.29 | 7863804.07 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 6580973.35 | 5698361.39 | 5231134.84 | 7463585.31 | 7930811.86 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 6616447.89 | 5713055.34 | 5234828.21 | 7519840.45 | 7998067.57 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 6651922.43 | 5727588.44 | 5238275.58 | 7576256.43 | 8065569.29 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.909 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in France"
## 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 France"
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 France"
paste(MAPE_Mean_EnsemblingAverage,"%")
## [1] "0.825 %"
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 France"
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 | 4306105.00 | 4302449.76 | 0.085 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4351506.00 | 4337260.42 | 0.327 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4393375.00 | 4373834.46 | 0.445 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4435187.00 | 4410531.74 | 0.556 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4472201.00 | 4446792.60 | 0.568 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4481295.00 | 4482476.06 | 0.026 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4510870.00 | 4517649.18 | 0.15 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4569698.00 | 4552529.37 | 0.376 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4620357.00 | 4587214.50 | 0.717 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4665877.00 | 4621764.27 | 0.945 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4679794.00 | 4656309.32 | 0.502 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4746588.00 | 4690850.19 | 1.174 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4758923.00 | 4725357.79 | 0.705 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4807569.00 | 4759891.31 | 0.992 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4838354.00 | 4794408.85 | 0.908 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4861992.00 | 4828873.47 | 0.681 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4901955.00 | 4863360.14 | 0.787 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4945238.00 | 4897843.30 | 0.958 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4980133.00 | 4932285.41 | 0.961 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4987689.00 | 4966745.96 | 0.42 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 5026645.00 | 5001186.51 | 0.506 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 5069999.00 | 5035573.84 | 0.679 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 23 | 2021-04-16 | Friday | 5107935.00 | 5069985.79 | 0.743 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 5144295.00 | 5104398.57 | 0.776 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 5178513.00 | 5138775.57 | 0.767 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 26 | 2021-04-19 | Monday | 5207857.00 | 5173176.58 | 0.666 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 5214493.00 | 5207563.11 | 0.133 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 5257046.00 | 5241901.76 | 0.288 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 5291414.00 | 5276270.08 | 0.286 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 30 | 2021-04-23 | Friday | 5325448.00 | 5310644.02 | 0.278 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 5357640.00 | 5344986.69 | 0.236 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 5388524.00 | 5379357.61 | 0.17 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 33 | 2021-04-26 | Monday | 5412989.00 | 5413718.05 | 0.013 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 5417903.00 | 5448034.36 | 0.556 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 5447883.00 | 5482383.87 | 0.633 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 5479327.00 | 5516742.29 | 0.683 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 37 | 2021-04-30 | Friday | 5505700.00 | 5551072.51 | 0.824 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 5529820.00 | 5585433.84 | 1.006 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 5553806.00 | 5619787.35 | 1.188 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 40 | 2021-05-03 | Monday | 5563694.00 | 5654099.19 | 1.625 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 5567300.00 | 5688446.50 | 2.176 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 5590416.00 | 5722804.82 | 2.368 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 5616180.00 | 5757136.88 | 2.51 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 44 | 2021-05-07 | Friday | 5637744.00 | 5791501.83 | 2.727 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 5655548.00 | 5825860.61 | 3.011 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
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 | 5860179.21 |
## +----+------------+-----------------+---------------------------+
## | 2 | 2021-05-10 | Monday | 5894534.68 |
## +----+------------+-----------------+---------------------------+
## | 3 | 2021-05-11 | Tuesday | 5928902.42 |
## +----+------------+-----------------+---------------------------+
## | 4 | 2021-05-12 | Wednesday | 5963245.06 |
## +----+------------+-----------------+---------------------------+
## | 5 | 2021-05-13 | Thursday | 5997621.66 |
## +----+------------+-----------------+---------------------------+
## | 6 | 2021-05-14 | Friday | 6031993.07 |
## +----+------------+-----------------+---------------------------+
## | 7 | 2021-05-15 | Saturday | 6066325.19 |
## +----+------------+-----------------+---------------------------+
## | 8 | 2021-05-16 | Sunday | 6100695.00 |
## +----+------------+-----------------+---------------------------+
## | 9 | 2021-05-17 | Monday | 6135077.83 |
## +----+------------+-----------------+---------------------------+
## | 10 | 2021-05-18 | Tuesday | 6169436.24 |
## +----+------------+-----------------+---------------------------+
## | 11 | 2021-05-19 | Wednesday | 6203829.25 |
## +----+------------+-----------------+---------------------------+
## | 12 | 2021-05-20 | Thursday | 6238217.63 |
## +----+------------+-----------------+---------------------------+
## | 13 | 2021-05-21 | Friday | 6272567.25 |
## +----+------------+-----------------+---------------------------+
## | 14 | 2021-05-22 | Saturday | 6306955.04 |
## +----+------------+-----------------+---------------------------+
## | 15 | 2021-05-23 | Sunday | 6341356.29 |
## +----+------------+-----------------+---------------------------+
## | 16 | 2021-05-24 | Monday | 6375733.53 |
## +----+------------+-----------------+---------------------------+
## | 17 | 2021-05-25 | Tuesday | 6410145.73 |
## +----+------------+-----------------+---------------------------+
## | 18 | 2021-05-26 | Wednesday | 6444553.64 |
## +----+------------+-----------------+---------------------------+
## | 19 | 2021-05-27 | Thursday | 6478923.11 |
## +----+------------+-----------------+---------------------------+
## | 20 | 2021-05-28 | Friday | 6513331.02 |
## +----+------------+-----------------+---------------------------+
## | 21 | 2021-05-29 | Saturday | 6547752.66 |
## +----+------------+-----------------+---------------------------+
## | 22 | 2021-05-30 | Sunday | 6582150.53 |
## +----+------------+-----------------+---------------------------+
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 France"
best_recommended_model
## [1] 0.825
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 France"
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 | 5622257.02 | 5205680.75 | 4985158.59 | 5205680.75 | 4985158.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 5651663.44 | 5222537.44 | 4995371.86 | 5222537.44 | 4995371.86 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 5681069.85 | 5239270.94 | 5005396.73 | 5239270.94 | 5005396.73 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 5710476.27 | 5255882.43 | 5015234.98 | 5255882.43 | 5015234.98 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 5739882.69 | 5272373.04 | 5024888.38 | 5272373.04 | 5024888.38 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 5769289.10 | 5288743.89 | 5034358.62 | 5288743.89 | 5034358.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 5798695.52 | 5304996.06 | 5043647.36 | 5304996.06 | 5043647.36 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 5828101.93 | 5321130.62 | 5052756.22 | 5321130.62 | 5052756.22 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 5857508.35 | 5337148.57 | 5061686.75 | 5337148.57 | 5061686.75 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 5886914.76 | 5353050.94 | 5070440.50 | 5353050.94 | 5070440.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 5916321.18 | 5368838.68 | 5079018.95 | 5368838.68 | 5079018.95 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 5945727.59 | 5384512.76 | 5087423.57 | 5384512.76 | 5087423.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 5975134.01 | 5400074.09 | 5095655.76 | 5400074.09 | 5095655.76 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 6004540.42 | 5415523.60 | 5103716.93 | 5415523.60 | 5103716.93 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 6033946.84 | 5430862.15 | 5111608.41 | 5430862.15 | 5111608.41 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 6063353.25 | 5446090.63 | 5119331.53 | 5446090.63 | 5119331.53 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 6092759.67 | 5461209.86 | 5126887.59 | 5461209.86 | 5126887.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 6122166.09 | 5476220.68 | 5134277.85 | 5476220.68 | 5134277.85 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 6151572.50 | 5491123.90 | 5141503.53 | 5491123.90 | 5141503.53 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 6180978.92 | 5505920.30 | 5148565.86 | 5505920.30 | 5148565.86 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 6210385.33 | 5520610.66 | 5155466.00 | 5520610.66 | 5155466.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 6239791.75 | 5535195.73 | 5162205.13 | 5535195.73 | 5162205.13 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting cumulative Covid 19 Infection cases in France"
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 | 5618874.04 | 5557131.93 | 5524447.64 | 5680616.14 | 5713300.43 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 5648358.67 | 5585961.68 | 5552930.71 | 5710755.65 | 5743786.62 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 5678252.63 | 5615215.06 | 5581844.98 | 5741290.21 | 5774660.29 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 5707054.37 | 5643384.46 | 5609679.65 | 5770724.28 | 5804429.09 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 5737121.27 | 5672820.63 | 5638781.92 | 5801421.92 | 5835460.62 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 5766881.13 | 5701957.91 | 5667589.63 | 5831804.35 | 5866172.63 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 5794966.49 | 5729426.60 | 5694731.88 | 5860506.37 | 5895201.09 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 5824451.12 | 5758299.19 | 5723280.48 | 5890603.04 | 5925621.75 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 5854345.08 | 5787593.78 | 5752257.78 | 5921096.38 | 5956432.39 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 5883146.82 | 5815803.18 | 5780153.61 | 5950490.46 | 5986140.03 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 5913213.72 | 5845278.55 | 5809315.84 | 5981148.89 | 6017111.60 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 5942973.58 | 5874453.90 | 5838181.77 | 6011493.26 | 6047765.38 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 5971058.94 | 5901959.69 | 5865380.76 | 6040158.18 | 6076737.11 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 6000543.57 | 5930868.52 | 5893984.78 | 6070218.61 | 6107102.35 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 6030437.53 | 5960198.07 | 5923015.55 | 6100676.99 | 6137859.52 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 6059239.27 | 5988441.51 | 5950963.44 | 6130037.03 | 6167515.10 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 6089306.17 | 6017950.35 | 5980176.86 | 6160661.99 | 6198435.48 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 6119066.03 | 6047158.29 | 6009092.64 | 6190973.76 | 6229039.42 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 6147151.38 | 6074695.94 | 6036340.35 | 6219606.83 | 6257962.42 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 6176636.02 | 6103635.97 | 6064992.07 | 6249636.06 | 6288279.96 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 6206529.98 | 6132995.70 | 6094069.00 | 6280064.27 | 6318990.96 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 6235331.72 | 6161268.60 | 6122061.95 | 6309394.84 | 6348601.49 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
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 France"
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 | 5842966.71 | 4616723.83 | 4038013.60 | 7251200.18 | 8073503.07 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 2 | 2021-05-10 | Monday | 5880491.25 | 4613779.02 | 4018096.16 | 7340953.90 | 8195964.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 5918163.48 | 4610477.39 | 3997737.63 | 7431866.94 | 8320347.38 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 5955983.63 | 4606822.95 | 3976947.60 | 7523947.30 | 8446669.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 5 | 2021-05-13 | Thursday | 5993951.91 | 4602819.67 | 3955735.56 | 7617203.06 | 8574949.11 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 6 | 2021-05-14 | Friday | 6032068.54 | 4598471.45 | 3934110.88 | 7711642.44 | 8705204.26 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 7 | 2021-05-15 | Saturday | 6070333.72 | 4593782.14 | 3912082.86 | 7807273.74 | 8837453.49 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 8 | 2021-05-16 | Sunday | 6108747.68 | 4588755.55 | 3889660.69 | 7904105.37 | 8971715.47 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 9 | 2021-05-17 | Monday | 6147310.63 | 4583395.43 | 3866853.49 | 8002145.82 | 9108009.07 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 6186022.79 | 4577705.48 | 3843670.29 | 8101403.70 | 9246353.34 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 6224884.37 | 4571689.39 | 3820120.04 | 8201887.69 | 9386767.53 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 12 | 2021-05-20 | Thursday | 6263895.58 | 4565350.76 | 3796211.60 | 8303606.57 | 9529271.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 13 | 2021-05-21 | Friday | 6303056.64 | 4558693.21 | 3771953.79 | 8406569.19 | 9673883.60 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 14 | 2021-05-22 | Saturday | 6342367.76 | 4551720.26 | 3747355.32 | 8510784.51 | 9820624.87 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 15 | 2021-05-23 | Sunday | 6381829.16 | 4544435.46 | 3722424.85 | 8616261.55 | 9969514.87 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 16 | 2021-05-24 | Monday | 6421441.04 | 4536842.28 | 3697170.99 | 8723009.42 | 10120573.75 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 6461203.63 | 4528944.18 | 3671602.26 | 8831037.32 | 10273821.80 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 6501117.13 | 4520744.60 | 3645727.12 | 8940354.50 | 10429279.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 19 | 2021-05-27 | Thursday | 6541181.76 | 4512246.92 | 3619553.99 | 9050970.30 | 10586967.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 20 | 2021-05-28 | Friday | 6581397.73 | 4503454.52 | 3593091.21 | 9162894.14 | 10746906.61 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 21 | 2021-05-29 | Saturday | 6621765.26 | 4494370.76 | 3566347.06 | 9276135.50 | 10909117.78 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
## | 22 | 2021-05-30 | Sunday | 6662284.55 | 4484998.94 | 3539329.79 | 9390703.95 | 11073622.15 |
## +----+------------+-----------------+---------------------+------------+------------+------------+-------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting cumulative Covid 19 Infection cases in France"
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 | 5906957.07 | 5386724.44 | 5111329.92 | 6427189.71 | 6702584.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 5942431.61 | 5404756.47 | 5120128.45 | 6480106.76 | 6764734.78 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 5977906.16 | 5422596.88 | 5128633.91 | 6533215.43 | 6827178.40 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 6013380.70 | 5440247.75 | 5136849.50 | 6586513.64 | 6889911.89 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 6048855.24 | 5457711.11 | 5144778.31 | 6639999.37 | 6952932.16 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 6084329.78 | 5474988.90 | 5152423.33 | 6693670.65 | 7016236.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 6119804.32 | 5492083.03 | 5159787.45 | 6747525.61 | 7079821.19 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 6155278.86 | 5508995.33 | 5166873.50 | 6801562.39 | 7143684.22 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 6190753.40 | 5525727.58 | 5173684.18 | 6855779.22 | 7207822.62 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 6226227.94 | 5542281.52 | 5180222.16 | 6910174.36 | 7272233.73 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 6261702.48 | 5558658.82 | 5186489.99 | 6964746.14 | 7336914.98 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 6297177.02 | 5574861.12 | 5192490.18 | 7019492.93 | 7401863.87 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 6332651.56 | 5590890.00 | 5198225.15 | 7074413.13 | 7467077.98 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 6368126.11 | 5606747.02 | 5203697.27 | 7129505.19 | 7532554.94 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 6403600.65 | 5622433.66 | 5208908.84 | 7184767.63 | 7598292.45 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 6439075.19 | 5637951.41 | 5213862.10 | 7240198.96 | 7664288.27 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 6474549.73 | 5653301.68 | 5218559.23 | 7295797.77 | 7730540.23 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 6510024.27 | 5668485.87 | 5223002.35 | 7351562.67 | 7797046.19 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 6545498.81 | 5683505.33 | 5227193.55 | 7407492.29 | 7863804.07 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 6580973.35 | 5698361.39 | 5231134.84 | 7463585.31 | 7930811.86 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 6616447.89 | 5713055.34 | 5234828.21 | 7519840.45 | 7998067.57 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 6651922.43 | 5727588.44 | 5238275.58 | 7576256.43 | 8065569.29 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting cumulative Covid 19 Infection cases in France"
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 | 4672616.02 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 4673335.54 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 4673989.20 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 4674582.93 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 4675122.17 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 4675611.85 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 4676056.49 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 4676460.18 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 4676826.67 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 4677159.36 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 4677461.34 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 4677735.43 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 4677984.19 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 4678209.95 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 4678414.83 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 4678600.74 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 4678769.45 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 4678922.52 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 4679061.42 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 4679187.44 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 4679301.78 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 4679405.52 |
## +----+------------+-----------------+---------------------+
paste("Forecasting by using Ensembling Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Ensembling Model ==> Forecasting cumulative Covid 19 Infection cases in France"
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 | 5860179.21 |
## +----+------------+-----------------+------------------------+
## | 2 | 2021-05-10 | Monday | 5894534.68 |
## +----+------------+-----------------+------------------------+
## | 3 | 2021-05-11 | Tuesday | 5928902.42 |
## +----+------------+-----------------+------------------------+
## | 4 | 2021-05-12 | Wednesday | 5963245.06 |
## +----+------------+-----------------+------------------------+
## | 5 | 2021-05-13 | Thursday | 5997621.66 |
## +----+------------+-----------------+------------------------+
## | 6 | 2021-05-14 | Friday | 6031993.07 |
## +----+------------+-----------------+------------------------+
## | 7 | 2021-05-15 | Saturday | 6066325.19 |
## +----+------------+-----------------+------------------------+
## | 8 | 2021-05-16 | Sunday | 6100695.00 |
## +----+------------+-----------------+------------------------+
## | 9 | 2021-05-17 | Monday | 6135077.83 |
## +----+------------+-----------------+------------------------+
## | 10 | 2021-05-18 | Tuesday | 6169436.24 |
## +----+------------+-----------------+------------------------+
## | 11 | 2021-05-19 | Wednesday | 6203829.25 |
## +----+------------+-----------------+------------------------+
## | 12 | 2021-05-20 | Thursday | 6238217.63 |
## +----+------------+-----------------+------------------------+
## | 13 | 2021-05-21 | Friday | 6272567.25 |
## +----+------------+-----------------+------------------------+
## | 14 | 2021-05-22 | Saturday | 6306955.04 |
## +----+------------+-----------------+------------------------+
## | 15 | 2021-05-23 | Sunday | 6341356.29 |
## +----+------------+-----------------+------------------------+
## | 16 | 2021-05-24 | Monday | 6375733.53 |
## +----+------------+-----------------+------------------------+
## | 17 | 2021-05-25 | Tuesday | 6410145.73 |
## +----+------------+-----------------+------------------------+
## | 18 | 2021-05-26 | Wednesday | 6444553.64 |
## +----+------------+-----------------+------------------------+
## | 19 | 2021-05-27 | Thursday | 6478923.11 |
## +----+------------+-----------------+------------------------+
## | 20 | 2021-05-28 | Friday | 6513331.02 |
## +----+------------+-----------------+------------------------+
## | 21 | 2021-05-29 | Saturday | 6547752.66 |
## +----+------------+-----------------+------------------------+
## | 22 | 2021-05-30 | Sunday | 6582150.53 |
## +----+------------+-----------------+------------------------+
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 | France | 9.37 | 2.291 | 2.32 | 1.229 | 0.909 | 0.825 | 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 France
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 France