Jawaharlal Nehru Krishi Vishwavidyalaya, India
#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
##Global vriable##
Full_original_data <- read_excel("F:/Phd/vaccination/Vaccine data.xlsx", sheet = "England_vaccine") # path of your data ( time series data)
original_data<-Full_original_data$cum_vaccine
y_lab <- "Covid 19 vaccination cases in England" # input name of data
Actual_date_interval <- c("2020/12/14","2021/03/10")
Forecast_date_interval <- c("2021/03/11","2021/03/17")
validation_data_days <-7
frequency<-"days"
country.name <- "England"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 74179 1317380 5963830 7591661 13327317 19933433
# calculate standard deviation
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.4542546
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 1.755602
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 6485606
#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
##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 training data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE
## Training set 4522.336 24345.38 13229.49 -0.3022656 3.709728 0.05862319
## ACF1
## Training set -0.05448596
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 1
## Alpha: 0.9112004
## Beta: 0.8168303
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 174476.79
## [2,] 12239.83
## attr(,"lambda")
## [1] 0.9999999
##
## Sigma: 24345.35
## AIC: 1976.578
#ploting BATS Model
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 vaccination cases in England"
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 7 days in bats Model for ==> Covid 19 vaccination cases in England"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.388 % MAPE 7 days Covid 19 vaccination cases in England %"
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 vaccination cases in England"
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 2021-03-04 Thursday 18194890 18211909
## 2 2021-03-05 Friday 18481094 18519667
## 3 2021-03-06 Saturday 18769920 18827426
## 4 2021-03-07 Sunday 19055646 19135184
## 5 2021-03-08 Monday 19346275 19442943
## 6 2021-03-09 Tuesday 19639663 19750701
## 7 2021-03-10 Wednesday 19933433 20058460
## MAPE_bats_Model
## 1 0.094 %
## 2 0.209 %
## 3 0.306 %
## 4 0.417 %
## 5 0.5 %
## 6 0.565 %
## 7 0.627 %
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 2021-03-11 Thursday 20366218
## 2 2021-03-12 Friday 20673977
## 3 2021-03-13 Saturday 20981735
## 4 2021-03-14 Sunday 21289493
## 5 2021-03-15 Monday 21597252
## 6 2021-03-16 Tuesday 21905010
## 7 2021-03-17 Wednesday 22212769
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.bats_Model,MAD_bats) # analysis of Error by using Bats Model shows result of correlation ,MSE ,MPER
## correlation_bats MSE_bats RMSE_bats MAPE_Mean_All.bats_Model MAD_bats
## 1 0.9999861 6959512255 83423.69 0.388 75052.7
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 2021-03-04 Thursday 17018.93 0.094 % 0.093 %
## 2 2021-03-05 Friday 38573.38 0.209 % 0.208 %
## 3 2021-03-06 Saturday 57505.82 0.306 % 0.305 %
## 4 2021-03-07 Sunday 79538.27 0.417 % 0.416 %
## 5 2021-03-08 Monday 96667.72 0.5 % 0.497 %
## 6 2021-03-09 Tuesday 111038.17 0.565 % 0.562 %
## 7 2021-03-10 Wednesday 125026.62 0.627 % 0.623 %
## 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
## Training set 3747.694 25234.83 14759.43 -1.587306 4.155822 0.06540274
## ACF1
## Training set -0.02629988
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.9017306
## Beta: 0.7336273
## Damping Parameter: 1
## Gamma-1 Values: 0.002167977
## Gamma-2 Values: -0.001746456
##
## Seed States:
## [,1]
## [1,] 143088.4275
## [2,] 92635.2779
## [3,] 1774.7409
## [4,] -1362.1766
## [5,] -3809.2027
## [6,] 102.8208
##
## Sigma: 25234.83
## AIC: 1992.319
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 vaccination cases in England"
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 7 days in TBATS Model for ==> Covid 19 vaccination cases in England"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.496 % MAPE 7 days Covid 19 vaccination cases in England %"
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 vaccination cases in England"
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 2021-03-04 Thursday 18194890 18215364
## 2 2021-03-05 Friday 18481094 18528409
## 3 2021-03-06 Saturday 18769920 18846701
## 4 2021-03-07 Sunday 19055646 19161018
## 5 2021-03-08 Monday 19346275 19469496
## 6 2021-03-09 Tuesday 19639663 19779898
## 7 2021-03-10 Wednesday 19933433 20090893
## MAPE_TBATS_Model
## 1 0.113 %
## 2 0.256 %
## 3 0.409 %
## 4 0.553 %
## 5 0.637 %
## 6 0.714 %
## 7 0.79 %
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 2021-03-11 Thursday 20403938
## 2 2021-03-12 Friday 20722230
## 3 2021-03-13 Saturday 21036547
## 4 2021-03-14 Sunday 21345025
## 5 2021-03-15 Monday 21655427
## 6 2021-03-16 Tuesday 21966422
## 7 2021-03-17 Wednesday 22279467
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.TBATS_Model,MAD_tbats) # analysis of Error by using TBATS model shows result of correlation ,MSE ,MPER
## correlation_tbats MSE_tbats RMSE_tbats MAPE_Mean_All.TBATS_Model MAD_tbats
## 1 0.9999546 11328499304 106435.4 0.496 95836.96
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 2021-03-04 Thursday 20474.23 0.113 % 0.112 %
## 2 2021-03-05 Friday 47315.07 0.256 % 0.255 %
## 3 2021-03-06 Saturday 76781.17 0.409 % 0.407 %
## 4 2021-03-07 Sunday 105372.49 0.553 % 0.55 %
## 5 2021-03-08 Monday 123220.64 0.637 % 0.633 %
## 6 2021-03-09 Tuesday 140234.95 0.714 % 0.709 %
## 7 2021-03-10 Wednesday 157460.18 0.79 % 0.784 %
## 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
## Training set -1931.5 10180.71 8446.923 -0.5699167 0.8149895 0.03743044
## ACF1
## Training set 0.6569311
# 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= 0.5838
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.9999
##
## Initial states:
## l = 542.8926
## b = 793.8615
##
## sigma: 30.249
##
## AIC AICc BIC
## 901.9726 902.7834 913.8827
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -1931.5 10180.71 8446.923 -0.5699167 0.8149895 0.03743044
## ACF1
## Training set 0.6569311
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> Covid 19 vaccination cases in England"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> Covid 19 vaccination cases in England"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.446 % MAPE 7 days Covid 19 vaccination cases in England %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> Covid 19 vaccination cases in England"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2021-03-04 Thursday 18194890 18208901
## 2 2021-03-05 Friday 18481094 18517864
## 3 2021-03-06 Saturday 18769920 18828988
## 4 2021-03-07 Sunday 19055646 19142266
## 5 2021-03-08 Monday 19346275 19457693
## 6 2021-03-09 Tuesday 19639663 19775262
## 7 2021-03-10 Wednesday 19933433 20094969
## MAPE_holt_Model
## 1 0.077 %
## 2 0.199 %
## 3 0.315 %
## 4 0.455 %
## 5 0.576 %
## 6 0.69 %
## 7 0.81 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2021-03-11 Thursday 20416806
## 2 2021-03-12 Friday 20740769
## 3 2021-03-13 Saturday 21066852
## 4 2021-03-14 Sunday 21395049
## 5 2021-03-15 Monday 21725355
## 6 2021-03-16 Tuesday 22057764
## 7 2021-03-17 Wednesday 22392272
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.Holt_Model,MAD_Holt) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_Holt MSE_Holt RMSE_Holt MAPE_Mean_All.Holt_Model MAD_Holt
## 1 0.9999982 9919318864 99595.78 0.446 86431.66
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 2021-03-04 Thursday 14010.92 0.077 % 0.077 %
## 2 2021-03-05 Friday 36770.12 0.199 % 0.199 %
## 3 2021-03-06 Saturday 59067.84 0.315 % 0.314 %
## 4 2021-03-07 Sunday 86620.06 0.455 % 0.453 %
## 5 2021-03-08 Monday 111417.83 0.576 % 0.573 %
## 6 2021-03-09 Tuesday 135599.27 0.69 % 0.686 %
## 7 2021-03-10 Wednesday 161535.58 0.81 % 0.804 %
#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 vaccination cases in England"
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 = 2.0197, Truncation lag parameter = 3, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -1.6581, Truncation lag parameter = 3, p-value
## = 0.9756
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -4.014, Lag order = 4, p-value = 0.01331
## 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", ylab=y_lab,main = "1nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub
##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 vaccination cases in England"
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 = 1.7751, Truncation lag parameter = 3, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -1.1942, Truncation lag parameter = 3, p-value
## = 0.9826
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.483, Lag order = 4, p-value = 0.9803
## 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", ylab=y_lab ,main = "2nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub
##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 vaccination cases in England"
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 = 0.33363, Truncation lag parameter = 3, p-value = 0.1
pp.test(diff2_x1) # applay pp test after taking Second differences
##
## Phillips-Perron Unit Root Test
##
## data: diff2_x1
## Dickey-Fuller Z(alpha) = -23.91, Truncation lag parameter = 3, p-value
## = 0.02138
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -2.8579, Lag order = 4, p-value = 0.225
## 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) : 1664.114
## ARIMA(0,2,1) : 1620.83
## ARIMA(0,2,2) : 1611.25
## ARIMA(0,2,3) : 1610.347
## ARIMA(0,2,4) : 1611.768
## ARIMA(0,2,5) : 1613.91
## ARIMA(1,2,0) : 1609.102
## ARIMA(1,2,1) : 1607.286
## ARIMA(1,2,2) : 1609.495
## ARIMA(1,2,3) : 1610.997
## ARIMA(1,2,4) : 1612.741
## ARIMA(2,2,0) : 1607.566
## ARIMA(2,2,1) : 1609.497
## ARIMA(2,2,2) : Inf
## ARIMA(2,2,3) : 1613.989
## ARIMA(3,2,0) : 1609.458
## ARIMA(3,2,1) : 1610.023
## ARIMA(3,2,2) : 1612.847
## ARIMA(4,2,0) : 1611.721
## ARIMA(4,2,1) : 1614.089
## ARIMA(5,2,0) : 1613.843
##
##
##
## Best model: ARIMA(1,2,1)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,1)
##
## Coefficients:
## ar1 ma1
## 0.5943 0.3038
## s.e. 0.1206 0.1391
##
## sigma^2 estimated as 48747711: log likelihood=-800.48
## AIC=1606.96 AICc=1607.29 BIC=1614.03
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 1
strtoi(bestmodel[3])
## [1] 1
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1
## 0.5943 0.3038
## s.e. 0.1206 0.1391
##
## sigma^2 estimated as 47497699: log likelihood = -800.48, aic = 1606.96
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Covid 19 vaccination cases in England"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 762.0841 6805.169 5108.247 0.03485609 0.1456201 0.02263592
## ACF1
## Training set -0.0004192353
x1_model1$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(1,2,1)
## Q* = 11.909, df = 8, p-value = 0.1553
##
## Model df: 2. 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 vaccination cases in England"
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 = 32.506, df = 20, p-value = 0.03819
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 0.24177, df = 2, p-value = 0.8861
#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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> Covid 19 vaccination cases in England"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Covid 19 vaccination cases in England"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.196 % MAPE 7 days Covid 19 vaccination cases in England %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Covid 19 vaccination cases in England"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2021-03-04 Thursday 18194890 18192590
## 2 2021-03-05 Friday 18481094 18474678
## 3 2021-03-06 Saturday 18769920 18751774
## 4 2021-03-07 Sunday 19055646 19025903
## 5 2021-03-08 Monday 19346275 19298269
## 6 2021-03-09 Tuesday 19639663 19569587
## 7 2021-03-10 Wednesday 19933433 19840282
## MAPE_auto.arima_Model
## 1 0.013 %
## 2 0.035 %
## 3 0.097 %
## 4 0.156 %
## 5 0.248 %
## 6 0.357 %
## 7 0.467 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2021-03-11 Thursday 20110608
## 2 2021-03-12 Friday 20380713
## 3 2021-03-13 Saturday 20650688
## 4 2021-03-14 Sunday 20920585
## 5 2021-03-15 Monday 21190436
## 6 2021-03-16 Tuesday 21460260
## 7 2021-03-17 Wednesday 21730067
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
MAPE_Mean_All.ARIMA
## [1] "0.196 % MAPE 7 days Covid 19 vaccination cases in England"
## 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.ARIMA_Model,MAD_auto.arima) # analysis of Error by using Auto ARIMAA model shows result of correlation ,MSE ,MPER
## correlation_auto.arima MSE_auto.arima RMSE_auto.arima
## 1 0.99993 2450400138 49501.52
## MAPE_Mean_All.ARIMA_Model MAD_auto.arima
## 1 0.196 38262.78
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 2021-03-04 Thursday 2299.971 0.013 %
## 2 2021-03-05 Friday 6416.134 0.035 %
## 3 2021-03-06 Saturday 18146.398 0.097 %
## 4 2021-03-07 Sunday 29743.390 0.156 %
## 5 2021-03-08 Monday 48006.461 0.248 %
## 6 2021-03-09 Tuesday 70076.303 0.357 %
## 7 2021-03-10 Wednesday 93150.818 0.467 %
## REOF_F_auto.arima
## 1 0.013 %
## 2 0.035 %
## 3 0.097 %
## 4 0.156 %
## 5 0.249 %
## 6 0.358 %
## 7 0.47 %
# Table for MAPE For counry
best_recommended_model <- min(MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
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 ==> Covid 19 vaccination cases in England"
best_recommended_model
## [1] 0.196
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")}
result<-c(x1,x2,x3,x4)
table.error<-data.frame(country.name,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,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+-------------+------------+-------------+-------------+------+
## | | country.name | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Best.Model | Freq |
## +===+==============+============+=============+============+=============+=============+======+
## | 1 | England | 0.388 | 0.496 | 0.446 | 0.196 | ARIMA Model | 1.00 |
## +---+--------------+------------+-------------+------------+-------------+-------------+------+
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 vaccination cases in England
message(" Thank you for using our System For Modelling ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling ==> Covid 19 vaccination cases in England