South ural state university, Chelyabinsk, Russian federation
# Imports
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
#population in France = 65351079
#WHO COVID-19 global table data January 11th 2021 at 11.53.00 AM.csv
Full_original_data<-read.csv("F:/Phd/COVID 19 in 2021/WHO_data.csv")
View(Full_original_data)
y_lab<- "Covid 19 Infection cases in France " # input name of data
Actual_date_interval <- c("2020/01/03","2021/01/10")
Forecast_date_interval <- c("2021/01/11","2021/01/17")
validation_data_days <-7
frequency <-"days"
Population <-65351079 # population in The United Kingdom
# Data Preparation & calculate some of statistics measures
Covid_data<-Full_original_data[Full_original_data$Country == "France", ]
original_data<-Covid_data$Cumulative_cases
View(original_data)
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 68220 159739 579272 640047 2721692
sd(original_data) # calculate standard deviation
## [1] 828412.2
skewness(original_data) # calculate Cofficient of skewness
## [1] 1.463495
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 3.540325
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
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))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
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 95.50453 5053.442 2328.272 NaN Inf 0.3276473 -0.005556488
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.289331
## Beta: 0.3378169
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 94.22191
## [2,] 17.07528
##
## Sigma: 5053.442
## AIC: 8434.691
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> Covid 19 Infection cases in France "
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Covid 19 Infection cases in France "
paste(MAPE_Mean_All,"%")
## [1] "0.737 % MAPE 7 days Covid 19 Infection cases in France %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Covid 19 Infection cases in France "
data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)
## date_bats validation_data_by_name actual_data forecasting_bats
## 1 2021-01-04 Monday 2611616 2606845
## 2 2021-01-05 Tuesday 2615185 2618703
## 3 2021-01-06 Wednesday 2635551 2630561
## 4 2021-01-07 Thursday 2660740 2642418
## 5 2021-01-08 Friday 2682250 2654276
## 6 2021-01-09 Saturday 2701658 2666133
## 7 2021-01-10 Sunday 2721692 2677991
## MAPE_bats_Model
## 1 0.183 %
## 2 0.135 %
## 3 0.189 %
## 4 0.689 %
## 5 1.043 %
## 6 1.315 %
## 7 1.606 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days))
## FD forecating_date forecasting_by_bats
## 1 2021-01-11 Monday 2689849
## 2 2021-01-12 Tuesday 2701706
## 3 2021-01-13 Wednesday 2713564
## 4 2021-01-14 Thursday 2725422
## 5 2021-01-15 Friday 2737279
## 6 2021-01-16 Saturday 2749137
## 7 2021-01-17 Sunday 2760994
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph1
## Error of forecasting
Error_bats<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_bats<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_bats<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_bats<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_bats<-sqrt(sum((Error_bats^2))/validation_data_days) # Root mean square forecast error
MSE_bats<-(sum((Error_bats^2))/validation_data_days) # Root mean square forecast error
MAD_bats<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_bats<-c(Error_bats)
REOF_Abats<-c(paste(round(REOF_A_bats,3),"%"))
REOF_Fbats<-c(paste(round(REOF_F_bats,3),"%"))
data.frame(correlation_bats,MSE_bats,RMSE_bats,MAPE_Mean_All,MAD_bats) # analysis of Error by using Bats Model shows result of correlation ,MSE ,MPER
## correlation_bats MSE_bats RMSE_bats
## 1 0.9920089 621434175 24928.58
## MAPE_Mean_All MAD_bats
## 1 0.737 % MAPE 7 days Covid 19 Infection cases in France 18823.46
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_bats,REOF_Abats,REOF_Fbats) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_bats REOF_Abats REOF_Fbats
## 1 2021-01-04 Monday 4770.577 0.183 % 0.183 %
## 2 2021-01-05 Tuesday 3518.033 0.135 % 0.134 %
## 3 2021-01-06 Wednesday 4990.357 0.189 % 0.19 %
## 4 2021-01-07 Thursday 18321.746 0.689 % 0.693 %
## 5 2021-01-08 Friday 27974.136 1.043 % 1.054 %
## 6 2021-01-09 Saturday 35524.526 1.315 % 1.332 %
## 7 2021-01-10 Sunday 43700.915 1.606 % 1.632 %
## 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 96.41653 5002.77 2448.114 NaN Inf 0.3445122 -0.009355887
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.297666
## Beta: 0.340283
## Damping Parameter: 1
## Gamma-1 Values: -0.002418955
## Gamma-2 Values: 0.002956272
##
## Seed States:
## [,1]
## [1,] 195.27949
## [2,] -20.89611
## [3,] -151.22193
## [4,] -10.81590
## [5,] -660.19708
## [6,] -213.01129
##
## Sigma: 5002.77
## AIC: 8439.294
plot(model_TBATS,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
# Testing Data Evaluation
forecasting_tbats <- predict(model_TBATS, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_tbats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using TBATS Model for ==> Covid 19 Infection cases in France "
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in TBATS Model for ==> Covid 19 Infection cases in France "
paste(MAPE_Mean_All,"%")
## [1] "0.711 % MAPE 7 days Covid 19 Infection cases in France %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in TBATS Model for ==> Covid 19 Infection cases in France "
data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)
## date_TBATS validation_data_by_name actual_data forecasting_TBATS
## 1 2021-01-04 Monday 2611616 2606385
## 2 2021-01-05 Tuesday 2615185 2619338
## 3 2021-01-06 Wednesday 2635551 2631660
## 4 2021-01-07 Thursday 2660740 2643525
## 5 2021-01-08 Friday 2682250 2656212
## 6 2021-01-09 Saturday 2701658 2667455
## 7 2021-01-10 Sunday 2721692 2678505
## MAPE_TBATS_Model
## 1 0.2 %
## 2 0.159 %
## 3 0.148 %
## 4 0.647 %
## 5 0.971 %
## 6 1.266 %
## 7 1.587 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days))
## FD forecating_date forecasting_by_TBATS
## 1 2021-01-11 Monday 2691458
## 2 2021-01-12 Tuesday 2703780
## 3 2021-01-13 Wednesday 2715644
## 4 2021-01-14 Thursday 2728332
## 5 2021-01-15 Friday 2739574
## 6 2021-01-16 Saturday 2750624
## 7 2021-01-17 Sunday 2763578
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph2
## Error of forecasting TBATS Model
Error_tbats<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_tbats1<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_tbats<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_tbats<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_tbats<-sqrt(sum((Error_tbats^2))/validation_data_days) # Root mean square forecast error
MSE_tbats<-(sum((Error_tbats^2))/validation_data_days) # Root mean square forecast error
MAD_tbats<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_tbats<-c(Error_tbats)
REOF_A_tbats<-c(paste(round(REOF_A_tbats1,3),"%"))
REOF_F_tbats<-c(paste(round(REOF_F_tbats,3),"%"))
data.frame(correlation_tbats,MSE_tbats,RMSE_tbats,MAPE_Mean_All,MAD_tbats) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_tbats MSE_tbats RMSE_tbats
## 1 0.9900834 581302842 24110.22
## MAPE_Mean_All MAD_tbats
## 1 0.711 % MAPE 7 days Covid 19 Infection cases in France 17944.74
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_tbats,REOF_A_tbats,REOF_F_tbats) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_tbats REOF_A_tbats REOF_F_tbats
## 1 2021-01-04 Monday 5231.302 0.2 % 0.201 %
## 2 2021-01-05 Tuesday 4152.959 0.159 % 0.159 %
## 3 2021-01-06 Wednesday 3890.765 0.148 % 0.148 %
## 4 2021-01-07 Thursday 17215.406 0.647 % 0.651 %
## 5 2021-01-08 Friday 26037.752 0.971 % 0.98 %
## 6 2021-01-09 Saturday 34203.453 1.266 % 1.282 %
## 7 2021-01-10 Sunday 43187.467 1.587 % 1.612 %
## 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 -252.3653 5403.496 2460.661 NaN Inf 0.3462779 0.2550632
# Print Model Parameters
summary(model_holt$model)
## Holt's method
##
## Call:
## holt(y = data_series, h = N_forecasting_days + validation_data_days,
##
## Call:
## lambda = "auto")
##
## Box-Cox transformation: lambda= 0.3406
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.3248
##
## Initial states:
## l = -3.0438
## b = 0.0957
##
## sigma: 0.7122
##
## AIC AICc BIC
## 1924.132 1924.299 1943.659
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -252.3653 5403.496 2460.661 NaN Inf 0.3462779 0.2550632
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$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 7 days by using holt Model for ==> 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_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 7 days in holt Model for ==> Covid 19 Infection cases in France "
paste(MAPE_Mean_All,"%")
## [1] "0.504 % MAPE 7 days 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 7 days in holt Model for ==> Covid 19 Infection cases in France "
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2021-01-04 Monday 2611616 2612120
## 2 2021-01-05 Tuesday 2615185 2625154
## 3 2021-01-06 Wednesday 2635551 2638231
## 4 2021-01-07 Thursday 2660740 2651351
## 5 2021-01-08 Friday 2682250 2664514
## 6 2021-01-09 Saturday 2701658 2677720
## 7 2021-01-10 Sunday 2721692 2690969
## MAPE_holt_Model
## 1 0.019 %
## 2 0.381 %
## 3 0.102 %
## 4 0.353 %
## 5 0.661 %
## 6 0.886 %
## 7 1.129 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2021-01-11 Monday 2704261
## 2 2021-01-12 Tuesday 2717597
## 3 2021-01-13 Wednesday 2730976
## 4 2021-01-14 Thursday 2744398
## 5 2021-01-15 Friday 2757863
## 6 2021-01-16 Saturday 2771372
## 7 2021-01-17 Sunday 2784925
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph3
## Error of forecasting by using Holt's linear model
Error_Holt<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_Holt1<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_Holt<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_Holt<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_Holt<-sqrt(sum((Error_Holt^2))/validation_data_days) # Root mean square forecast error
MSE_Holt<-(sum((Error_Holt^2))/validation_data_days) # Root mean square forecast error
MAD_Holt<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_Holt<-c(Error_Holt)
REOF_A_Holt<-c(paste(round(REOF_A_Holt1,3),"%"))
REOF_F_Holt<-c(paste(round(REOF_F_Holt,3),"%"))
REOF_A_Holt11<-mean(abs(((testing_data-validation_forecast)/testing_data)*100))
data.frame(correlation_Holt,MSE_Holt,RMSE_Holt,MAPE_Mean_All,MAD_Holt) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_Holt MSE_Holt RMSE_Holt
## 1 0.9922116 289490676 17014.43
## MAPE_Mean_All MAD_Holt
## 1 0.504 % MAPE 7 days Covid 19 Infection cases in France 9804.497
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_Holt,REOF_A_Holt,REOF_F_Holt) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_Holt REOF_A_Holt REOF_F_Holt
## 1 2021-01-04 Monday 503.950 0.019 % 0.019 %
## 2 2021-01-05 Tuesday 9969.235 0.381 % 0.38 %
## 3 2021-01-06 Wednesday 2680.335 0.102 % 0.102 %
## 4 2021-01-07 Thursday 9388.683 0.353 % 0.354 %
## 5 2021-01-08 Friday 17735.751 0.661 % 0.666 %
## 6 2021-01-09 Saturday 23937.801 0.886 % 0.894 %
## 7 2021-01-10 Sunday 30722.766 1.129 % 1.142 %
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> 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 = 4.253, 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) = 1.1659, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -2.3947, Lag order = 7, p-value = 0.4104
## 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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main = "1nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub, cex.main,
## cex.lab, cex.sub, font.main, font.lab
##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 ==> 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 = 3.023, 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) = -45.141, 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 = -1.8077, Lag order = 7, p-value = 0.6581
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab ,main = "2nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub, cex.main,
## cex.lab, cex.sub, font.main, font.lab
##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 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 = 0.049254, 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) = -319.01, 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 = -7.6004, 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) : 7340.466
## ARIMA(0,2,1) : 7301.808
## ARIMA(0,2,2) : 7269.693
## ARIMA(0,2,3) : 7271.583
## ARIMA(0,2,4) : 7273.378
## ARIMA(0,2,5) : 7252.943
## ARIMA(1,2,0) : 7327.788
## ARIMA(1,2,1) : 7276.775
## ARIMA(1,2,2) : 7271.582
## ARIMA(1,2,3) : 7272.55
## ARIMA(1,2,4) : 7273.879
## ARIMA(2,2,0) : 7306.726
## ARIMA(2,2,1) : 7269.251
## ARIMA(2,2,2) : 7272.886
## ARIMA(2,2,3) : 7274.432
## ARIMA(3,2,0) : 7297.035
## ARIMA(3,2,1) : 7267.362
## ARIMA(3,2,2) : 7246.132
## ARIMA(4,2,0) : 7263.527
## ARIMA(4,2,1) : 7254.384
## ARIMA(5,2,0) : 7259.495
##
##
##
## Best model: ARIMA(3,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(3,2,2)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.9506 -0.5996 -0.2395 -1.3615 0.8860
## s.e. 0.0629 0.0671 0.0575 0.0412 0.0357
##
## sigma^2 estimated as 23903096: log likelihood=-3616.95
## AIC=7245.9 AICc=7246.13 BIC=7269.3
#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)
}
source("stringthearima.R")
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] 3 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, 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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, 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
library(forecast) # install library forecast
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 ar3 ma1 ma2
## 0.9506 -0.5996 -0.2395 -1.3615 0.8860
## s.e. 0.0629 0.0671 0.0575 0.0412 0.0357
##
## sigma^2 estimated as 23575657: log likelihood = -3616.95, aic = 7245.9
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Covid 19 Infection cases in France "
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 55.0802 4842.229 2142.61 0.7576608 2.40337 0.30152 -0.04451188
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,2,2)
## Q* = 54.127, df = 5, p-value = 1.973e-10
##
## Model df: 5. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Covid 19 Infection cases in France "
Box.test(x1_model1$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$residuals^2
## X-squared = 446.04, df = 20, p-value < 2.2e-16
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 4202.3, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$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 7 days by using bats Model for ==> 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_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 7 days in bats Model for ==> Covid 19 Infection cases in France "
paste(MAPE_Mean_All,"%")
## [1] "0.55 % MAPE 7 days 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 7 days in bats Model for ==> Covid 19 Infection cases in France "
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2021-01-04 Monday 2611616 2605784
## 2 2021-01-05 Tuesday 2615185 2616028
## 3 2021-01-06 Wednesday 2635551 2631547
## 4 2021-01-07 Thursday 2660740 2649165
## 5 2021-01-08 Friday 2682250 2664756
## 6 2021-01-09 Saturday 2701658 2675899
## 7 2021-01-10 Sunday 2721692 2683526
## MAPE_auto.arima_Model
## 1 0.223 %
## 2 0.032 %
## 3 0.152 %
## 4 0.435 %
## 5 0.652 %
## 6 0.953 %
## 7 1.402 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2021-01-11 Monday 2690964
## 2 2021-01-12 Tuesday 2701395
## 3 2021-01-13 Wednesday 2715626
## 4 2021-01-14 Thursday 2731721
## 5 2021-01-15 Friday 2746592
## 6 2021-01-16 Saturday 2758272
## 7 2021-01-17 Sunday 2767206
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph4
## Error of forecasting
Error_auto.arima<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_auto.arima<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_auto.arima<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_auto.arima<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_auto.arima<-sqrt(sum((Error_auto.arima^2))/validation_data_days) # Root mean square forecast error
MSE_auto.arima<-(sum((Error_auto.arima^2))/validation_data_days) # Root mean square forecast error
MAD_auto.arima<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_auto.arima<-c(Error_auto.arima)
REOF_auto.arima1<-c(paste(round(REOF_A_auto.arima,3),"%"))
REOF_auto.arima2<-c(paste(round(REOF_F_auto.arima,3),"%"))
data.frame(correlation_auto.arima,MSE_auto.arima,RMSE_auto.arima,MAPE_Mean_All,MAD_auto.arima) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_auto.arima MSE_auto.arima RMSE_auto.arima
## 1 0.9908258 372993126 19313.03
## MAPE_Mean_All MAD_auto.arima
## 1 0.55 % MAPE 7 days Covid 19 Infection cases in France 14569.65
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_auto.arima,REOF_A_auto.arima=REOF_auto.arima1,REOF_F_auto.arima=REOF_auto.arima2) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_auto.arima REOF_A_auto.arima
## 1 2021-01-04 Monday 5832.195 0.223 %
## 2 2021-01-05 Tuesday 843.062 0.032 %
## 3 2021-01-06 Wednesday 4004.023 0.152 %
## 4 2021-01-07 Thursday 11575.277 0.435 %
## 5 2021-01-08 Friday 17494.181 0.652 %
## 6 2021-01-09 Saturday 25759.150 0.953 %
## 7 2021-01-10 Sunday 38165.786 1.402 %
## REOF_F_auto.arima
## 1 0.224 %
## 2 0.032 %
## 3 0.152 %
## 4 0.437 %
## 5 0.657 %
## 6 0.963 %
## 7 1.422 %
# SIR Model
#install.packages("dplyr")
library(deSolve)
first<-rows-13
secondr<-rows-7
vector_SIR<-original_data[first:secondr]
Infected <- c(vector_SIR)
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.01574447 0.00957691
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR<-data.frame(out)
validation_forecast<-result_SIR$I
## Error of forecasting
Error_SIR<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_SIR<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_SIR<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_SIR<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_SIR<-sqrt(sum((Error_SIR^2))/validation_data_days) # Root mean square forecast error
MSE_SIR<-(sum((Error_SIR^2))/validation_data_days) # Root mean square forecast error
MAD_SIR<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_SIR<-c(Error_SIR)
REOF_A_SIR<-c(paste(round(REOF_A_SIR,3),"%"))
REOF_A_SIR1<-mean(abs(((testing_data-validation_forecast)/testing_data)*100))
REOF_F_SIR<-c(paste(round(REOF_F_SIR,3),"%"))
MAPE_Mean_All<-paste(round(mean(abs(((testing_data-validation_forecast)/testing_data)*100)),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
data.frame(correlation_SIR,MSE_SIR,RMSE_SIR,MAPE_Mean_All,MAD_SIR) # analysis of Error by using SIR's linear model shows result of correlation ,MSE ,MPER
## correlation_SIR MSE_SIR RMSE_SIR
## 1 0.9922474 10662297408 103258.4
## MAPE_Mean_All MAD_SIR
## 1 3.848 % MAPE 7 days Covid 19 Infection cases in France 102556.1
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_SIR,REOF_A_SIR,REOF_F_SIR,validation_forecast,testing_data) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_SIR REOF_A_SIR REOF_F_SIR
## 1 2021-01-04 Monday 95268.00 3.648 % 3.786 %
## 2 2021-01-05 Tuesday 84815.43 3.243 % 3.352 %
## 3 2021-01-06 Wednesday 91105.20 3.457 % 3.581 %
## 4 2021-01-07 Thursday 102163.37 3.84 % 3.993 %
## 5 2021-01-08 Friday 109488.03 4.082 % 4.256 %
## 6 2021-01-09 Saturday 114656.27 4.244 % 4.432 %
## 7 2021-01-10 Sunday 120396.15 4.424 % 4.628 %
## validation_forecast testing_data
## 1 2516348 2611616
## 2 2530370 2615185
## 3 2544446 2635551
## 4 2558577 2660740
## 5 2572762 2682250
## 6 2587002 2701658
## 7 2601296 2721692
## forecasting by SIR model
Infected <- c(tail(original_data,validation_data_days))
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.011226678 0.004171974
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)
## FD forecating_date forecasting_by_SIR
## 1 2021-01-11 Monday 2611616
## 2 2021-01-12 Tuesday 2628919
## 3 2021-01-13 Wednesday 2646324
## 4 2021-01-14 Thursday 2663831
## 5 2021-01-15 Friday 2681441
## 6 2021-01-16 Saturday 2699154
## 7 2021-01-17 Sunday 2716970
# Choose Best model by least error
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> Covid 19 Infection cases in France "
M1<-mean(REOF_A_bats)
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using TBATS Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using TBATS Model For ==> Covid 19 Infection cases in France "
M2<-mean(REOF_A_tbats1)
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using Holt's Linear << Exponential Smoothing >> For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using Holt's Linear << Exponential Smoothing >> For ==> Covid 19 Infection cases in France "
M3<-REOF_A_Holt11
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using auto arima Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using auto arima Model For ==> Covid 19 Infection cases in France "
M4<-mean(REOF_A_auto.arima)
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using SIR Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using SIR Model For ==> Covid 19 Infection cases in France "
M5<-REOF_A_SIR1
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using autoarima Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using autoarima Model For ==> Covid 19 Infection cases in France "
data.frame(validation_dates,forecating_date=forecasting_data_by_name,MAPE_bats_error=REOF_A_bats,MAPE_TBATS_error=REOF_A_tbats1,MAPE_Holt_error=REOF_A_Holt1,MAPE_autoarima_error = REOF_A_auto.arima)
## validation_dates forecating_date MAPE_bats_error MAPE_TBATS_error
## 1 2021-01-04 Monday 0.1826676 0.2003090
## 2 2021-01-05 Tuesday 0.1345233 0.1588017
## 3 2021-01-06 Wednesday 0.1893478 0.1476262
## 4 2021-01-07 Thursday 0.6885959 0.6470157
## 5 2021-01-08 Friday 1.0429354 0.9707429
## 6 2021-01-09 Saturday 1.3149157 1.2660171
## 7 2021-01-10 Sunday 1.6056525 1.5867874
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.01929648 0.22331749
## 2 0.38120573 0.03223718
## 3 0.10169922 0.15192355
## 4 0.35285986 0.43503976
## 5 0.66122664 0.65222038
## 6 0.88604115 0.95345710
## 7 1.12881125 1.40228159
recommend_Model<-c(M1,M2,M3,M4,M5)
best_recommended_model<-min(recommend_Model)
paste ("lodaing ..... ... . .Select Minimum MAPE from Models for select best Model ==> ", y_lab , sep=" ")
## [1] "lodaing ..... ... . .Select Minimum MAPE from Models for select best Model ==> Covid 19 Infection cases in France "
best_recommended_model
## [1] 0.5044486
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> Covid 19 Infection cases in France "
if(best_recommended_model >= M1) {paste("System Recommend Bats Model That's better For forecasting==> ",y_lab, sep=" ")}
if(best_recommended_model >= M2) {paste("System Recommend That's better TBATS For forecasting ==> ",y_lab, sep=" ")}
if(best_recommended_model >= M3) {paste("System Recommend Holt's Linear Model < Exponential Smoothing Model > That's better For forecasting ==> ",y_lab, sep=" ")}
## [1] "System Recommend Holt's Linear Model < Exponential Smoothing Model > That's better For forecasting ==> Covid 19 Infection cases in France "
if(best_recommended_model >= M4) {paste("System Recommend auto arima Model That's better For forecasting ==> ",y_lab, sep=" ")}
if(best_recommended_model >= M5) {paste("System Recommend SIR Model That's better For forecasting ==> ",y_lab, sep=" ")}
message("System finished Forecasting by using autoarima and Holt's ,TBATS, and SIR Model ==>",y_lab, sep=" ")
## System finished Forecasting by using autoarima and Holt's ,TBATS, and SIR Model ==>Covid 19 Infection cases in France
message(" Thank you for using our System For Modelling ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling ==> Covid 19 Infection cases in France