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 The United Kingdom = 68078368
#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 The United Kingdom " # 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 <-68078368 # population in The United Kingdom
# Data Preparation & calculate some of statistics measures
Covid_data<-Full_original_data[Full_original_data$Country == "The United Kingdom", ]
original_data<-Covid_data$Cumulative_cases
View(original_data)
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 54165 288032 528772 557434 3017413
sd(original_data) # calculate standard deviation
## [1] 684530.8
skewness(original_data) # calculate Cofficient of skewness
## [1] 1.742938
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 5.188567
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 114.5686 1969.839 895.0024 NaN Inf 0.1259988 -0.02881263
# Print Model Parameters
model_bats
## BATS(1, {1,1}, 0.996, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.4573979
## Beta: 0.04588305
## Damping Parameter: 0.995972
## AR coefficients: 0.990099
## MA coefficients: 0.312657
##
## Seed States:
## [,1]
## [1,] 26.28688
## [2,] 31.23649
## [3,] 0.00000
## [4,] 0.00000
##
## Sigma: 1969.839
## AIC: 7753.177
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$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> Covid 19 Infection cases in The United Kingdom "
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Covid 19 Infection cases in The United Kingdom "
paste(MAPE_Mean_All,"%")
## [1] "0.454 % MAPE 7 days Covid 19 Infection cases in The United Kingdom %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Covid 19 Infection cases in The United Kingdom "
data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)
## date_bats validation_data_by_name actual_data forecasting_bats
## 1 2021-01-04 Monday 2654783 2658925
## 2 2021-01-05 Tuesday 2713567 2719205
## 3 2021-01-06 Wednesday 2774483 2781163
## 4 2021-01-07 Thursday 2836805 2844773
## 5 2021-01-08 Friday 2889423 2910011
## 6 2021-01-09 Saturday 2957476 2976851
## 7 2021-01-10 Sunday 3017413 3045268
## MAPE_bats_Model
## 1 0.156 %
## 2 0.208 %
## 3 0.241 %
## 4 0.281 %
## 5 0.713 %
## 6 0.655 %
## 7 0.923 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days))
## FD forecating_date forecasting_by_bats
## 1 2021-01-11 Monday 3115238
## 2 2021-01-12 Tuesday 3186736
## 3 2021-01-13 Wednesday 3259738
## 4 2021-01-14 Thursday 3334220
## 5 2021-01-15 Friday 3410159
## 6 2021-01-16 Saturday 3487531
## 7 2021-01-17 Sunday 3566314
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 0.9997066 247465805 15731.05
## MAPE_Mean_All MAD_bats
## 1 0.454 % MAPE 7 days Covid 19 Infection cases in The United Kingdom 13178.14
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 4142.274 0.156 % 0.156 %
## 2 2021-01-05 Tuesday 5637.682 0.208 % 0.207 %
## 3 2021-01-06 Wednesday 6679.628 0.241 % 0.24 %
## 4 2021-01-07 Thursday 7968.328 0.281 % 0.28 %
## 5 2021-01-08 Friday 20588.288 0.713 % 0.707 %
## 6 2021-01-09 Saturday 19375.306 0.655 % 0.651 %
## 7 2021-01-10 Sunday 27855.466 0.923 % 0.915 %
## 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 217.574 2035.066 1017.958 NaN Inf 0.1433086 -0.009596333
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.110404
## Beta: 0.7066523
## Damping Parameter: 1
## Gamma-1 Values: 0.0008801099
## Gamma-2 Values: -0.001787153
##
## Seed States:
## [,1]
## [1,] 56.85541
## [2,] 24.62076
## [3,] 49.91159
## [4,] 110.65960
## [5,] -239.39399
## [6,] -118.06086
##
## Sigma: 2035.066
## AIC: 7779.088
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$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using TBATS Model for ==> Covid 19 Infection cases in The United Kingdom "
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in TBATS Model for ==> Covid 19 Infection cases in The United Kingdom "
paste(MAPE_Mean_All,"%")
## [1] "0.319 % MAPE 7 days Covid 19 Infection cases in The United Kingdom %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in TBATS Model for ==> Covid 19 Infection cases in The United Kingdom "
data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)
## date_TBATS validation_data_by_name actual_data forecasting_TBATS
## 1 2021-01-04 Monday 2654783 2656498
## 2 2021-01-05 Tuesday 2713567 2712970
## 3 2021-01-06 Wednesday 2774483 2769479
## 4 2021-01-07 Thursday 2836805 2826048
## 5 2021-01-08 Friday 2889423 2882806
## 6 2021-01-09 Saturday 2957476 2939118
## 7 2021-01-10 Sunday 3017413 2995202
## MAPE_TBATS_Model
## 1 0.065 %
## 2 0.022 %
## 3 0.18 %
## 4 0.379 %
## 5 0.229 %
## 6 0.621 %
## 7 0.736 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days))
## FD forecating_date forecasting_by_TBATS
## 1 2021-01-11 Monday 3051673
## 2 2021-01-12 Tuesday 3108183
## 3 2021-01-13 Wednesday 3164751
## 4 2021-01-14 Thursday 3221510
## 5 2021-01-15 Friday 3277821
## 6 2021-01-16 Saturday 3333905
## 7 2021-01-17 Sunday 3390377
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 0.9997615 145457920 12060.59
## MAPE_Mean_All
## 1 0.319 % MAPE 7 days Covid 19 Infection cases in The United Kingdom
## MAD_tbats
## 1 8832.75
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 1715.1683 0.065 % 0.065 %
## 2 2021-01-05 Tuesday 597.0167 0.022 % 0.022 %
## 3 2021-01-06 Wednesday 5003.6576 0.18 % 0.181 %
## 4 2021-01-07 Thursday 10757.4204 0.379 % 0.381 %
## 5 2021-01-08 Friday 6616.8130 0.229 % 0.23 %
## 6 2021-01-09 Saturday 18358.1364 0.621 % 0.625 %
## 7 2021-01-10 Sunday 22211.3742 0.736 % 0.742 %
## 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 85.94693 2017.146 915.629 Inf Inf 0.1289026 0.05307677
# Print Model Parameters
summary(model_holt$model)
## Holt's method
##
## Call:
## holt(y = data_series, h = N_forecasting_days + validation_data_days,
##
## Call:
## lambda = "auto")
##
## Box-Cox transformation: lambda= 0.3892
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.7276
##
## Initial states:
## l = -2.3039
## b = -0.3774
##
## sigma: 0.6143
##
## AIC AICc BIC
## 1815.571 1815.738 1835.098
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 85.94693 2017.146 915.629 Inf Inf 0.1289026 0.05307677
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$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 The United Kingdom "
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 The United Kingdom "
paste(MAPE_Mean_All,"%")
## [1] "0.08 % MAPE 7 days Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom "
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 2654783 2657423
## 2 2021-01-05 Tuesday 2713567 2715828
## 3 2021-01-06 Wednesday 2774483 2775010
## 4 2021-01-07 Thursday 2836805 2834972
## 5 2021-01-08 Friday 2889423 2895720
## 6 2021-01-09 Saturday 2957476 2957256
## 7 2021-01-10 Sunday 3017413 3019584
## MAPE_holt_Model
## 1 0.099 %
## 2 0.083 %
## 3 0.019 %
## 4 0.065 %
## 5 0.218 %
## 6 0.007 %
## 7 0.072 %
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 3082708
## 2 2021-01-12 Tuesday 3146631
## 3 2021-01-13 Wednesday 3211358
## 4 2021-01-14 Thursday 3276891
## 5 2021-01-15 Friday 3343234
## 6 2021-01-16 Saturday 3410392
## 7 2021-01-17 Sunday 3478367
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 0.9998037 8590000 2930.87
## MAPE_Mean_All MAD_Holt
## 1 0.08 % MAPE 7 days Covid 19 Infection cases in The United Kingdom 1691.778
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 2640.4472 0.099 % 0.099 %
## 2 2021-01-05 Tuesday 2260.8162 0.083 % 0.083 %
## 3 2021-01-06 Wednesday 526.5172 0.019 % 0.019 %
## 4 2021-01-07 Thursday 1832.7289 0.065 % 0.065 %
## 5 2021-01-08 Friday 6296.7852 0.218 % 0.217 %
## 6 2021-01-09 Saturday 220.2462 0.007 % 0.007 %
## 7 2021-01-10 Sunday 2170.8579 0.072 % 0.072 %
#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 The United Kingdom "
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 = 4.4287, 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) = 6.0668, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = 1.7351, Lag order = 7, p-value = 0.99
## 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 The United Kingdom "
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 = 3.6524, 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 greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = 5.6508, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = 2.1134, Lag order = 7, p-value = 0.99
## 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 The United Kingdom "
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.72221, Truncation lag parameter = 5, p-value = 0.01153
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) = -362.72, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -3.7891, Lag order = 7, p-value = 0.01982
## 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) : 6609.382
## ARIMA(0,2,1) : 6600.259
## ARIMA(0,2,2) : 6598.279
## ARIMA(0,2,3) : 6600.295
## ARIMA(0,2,4) : 6601.255
## ARIMA(0,2,5) : 6599.026
## ARIMA(1,2,0) : 6602.73
## ARIMA(1,2,1) : 6599.1
## ARIMA(1,2,2) : 6596.312
## ARIMA(1,2,3) : 6597.503
## ARIMA(1,2,4) : 6598.946
## ARIMA(2,2,0) : 6599.441
## ARIMA(2,2,1) : 6600.478
## ARIMA(2,2,2) : 6597.233
## ARIMA(2,2,3) : 6599.298
## ARIMA(3,2,0) : 6601.374
## ARIMA(3,2,1) : 6602.533
## ARIMA(3,2,2) : 6599.296
## ARIMA(4,2,0) : 6598.948
## ARIMA(4,2,1) : 6600.821
## ARIMA(5,2,0) : 6600.422
##
##
##
## Best model: ARIMA(1,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,2)
##
## Coefficients:
## ar1 ma1 ma2
## -0.8252 0.6543 -0.2412
## s.e. 0.0890 0.0998 0.0565
##
## sigma^2 estimated as 4072343: log likelihood=-3294.1
## AIC=6596.2 AICc=6596.31 BIC=6611.8
#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] 1 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 ma1 ma2
## -0.8252 0.6543 -0.2412
## s.e. 0.0890 0.0998 0.0565
##
## sigma^2 estimated as 4038872: log likelihood = -3294.1, aic = 6596.2
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Covid 19 Infection cases in The United Kingdom "
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 200.204 2004.211 937.5939 0.6121025 2.243849 0.1319949
## ACF1
## Training set 0.0004357398
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,2,2)
## Q* = 28.793, df = 7, p-value = 0.0001578
##
## Model df: 3. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Covid 19 Infection cases in The United Kingdom "
Box.test(x1_model1$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$residuals^2
## X-squared = 215.91, df = 20, p-value < 2.2e-16
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 2433.8, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$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 The United Kingdom "
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 The United Kingdom "
paste(MAPE_Mean_All,"%")
## [1] "0.272 % MAPE 7 days Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom "
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 2654783 2657059
## 2 2021-01-05 Tuesday 2713567 2713630
## 3 2021-01-06 Wednesday 2774483 2770774
## 4 2021-01-07 Thursday 2836805 2827446
## 5 2021-01-08 Friday 2889423 2884507
## 6 2021-01-09 Saturday 2957476 2941247
## 7 2021-01-10 Sunday 3017413 2998252
## MAPE_auto.arima_Model
## 1 0.086 %
## 2 0.002 %
## 3 0.134 %
## 4 0.33 %
## 5 0.17 %
## 6 0.549 %
## 7 0.635 %
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 3055038
## 2 2021-01-12 Tuesday 3112005
## 3 2021-01-13 Wednesday 3168823
## 4 2021-01-14 Thursday 3225764
## 5 2021-01-15 Friday 3282603
## 6 2021-01-16 Saturday 3339527
## 7 2021-01-17 Sunday 3396380
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 0.9997772 108743630 10428.02
## MAPE_Mean_All
## 1 0.272 % MAPE 7 days Covid 19 Infection cases in The United Kingdom
## MAD_auto.arima
## 1 7290.617
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 2275.81442 0.086 %
## 2 2021-01-05 Tuesday 62.98577 0.002 %
## 3 2021-01-06 Wednesday 3708.65629 0.134 %
## 4 2021-01-07 Thursday 9359.26480 0.33 %
## 5 2021-01-08 Friday 4915.60377 0.17 %
## 6 2021-01-09 Saturday 16228.97470 0.549 %
## 7 2021-01-10 Sunday 19160.62010 0.635 %
## REOF_F_auto.arima
## 1 0.086 %
## 2 0.002 %
## 3 0.134 %
## 4 0.331 %
## 5 0.17 %
## 6 0.552 %
## 7 0.639 %
# 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.02177408 0.00000000
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR<-data.frame(out)
validation_forecast<-result_SIR$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 0.9997617 156756415019 395924.8
## MAPE_Mean_All
## 1 13.949 % MAPE 7 days Covid 19 Infection cases in The United Kingdom
## MAD_SIR
## 1 395490.2
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 366434.0 13.803 % 16.013 %
## 2 2021-01-05 Tuesday 376573.1 13.877 % 16.114 %
## 3 2021-01-06 Wednesday 387847.9 13.979 % 16.251 %
## 4 2021-01-07 Thursday 399513.6 14.083 % 16.392 %
## 5 2021-01-08 Friday 400441.7 13.859 % 16.089 %
## 6 2021-01-09 Saturday 415750.7 14.058 % 16.357 %
## 7 2021-01-10 Sunday 421870.2 13.981 % 16.254 %
## validation_forecast testing_data
## 1 2288349 2654783
## 2 2336994 2713567
## 3 2386635 2774483
## 4 2437291 2836805
## 5 2488981 2889423
## 6 2541725 2957476
## 7 2595543 3017413
## 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$message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.10232895 0.07586272
# 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 2654783
## 2 2021-01-12 Tuesday 2714591
## 3 2021-01-13 Wednesday 2774637
## 4 2021-01-14 Thursday 2834859
## 5 2021-01-15 Friday 2895188
## 6 2021-01-16 Saturday 2955558
## 7 2021-01-17 Sunday 3015896
# 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 The United Kingdom "
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 The United Kingdom "
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 The United Kingdom "
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 The United Kingdom "
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 The United Kingdom "
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 The United Kingdom "
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 0.1560306 0.06460672
## 2 2021-01-05 Tuesday 0.2077591 0.02200118
## 3 2021-01-06 Wednesday 0.2407522 0.18034558
## 4 2021-01-07 Thursday 0.2808909 0.37920902
## 5 2021-01-08 Friday 0.7125398 0.22900119
## 6 2021-01-09 Saturday 0.6551298 0.62073661
## 7 2021-01-10 Sunday 0.9231572 0.73610653
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.099460000 0.085725064
## 2 0.083315289 0.002321143
## 3 0.018977129 0.133670175
## 4 0.064605388 0.329922740
## 5 0.217925352 0.170124062
## 6 0.007447101 0.548744088
## 7 0.071944340 0.635001576
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 The United Kingdom "
best_recommended_model
## [1] 0.08052494
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> Covid 19 Infection cases in The United Kingdom "
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 The United Kingdom "
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 The United Kingdom
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 The United Kingdom