South ural state university, Chelyabinsk, Russian federation
# Imports
library(fpp2)
## Warning: package 'fpp2' was built under R version 4.0.3
## 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
## Warning: package 'ggplot2' was built under R version 4.0.3
## Warning: package 'forecast' was built under R version 4.0.3
##
library(forecast)
library(ggplot2)
library("readxl")
## Warning: package 'readxl' was built under R version 4.0.3
library(moments)
## Warning: package 'moments' was built under R version 4.0.3
library(forecast)
require(forecast)
require(tseries)
## Loading required package: tseries
## Warning: package 'tseries' was built under R version 4.0.3
require(markovchain)
## Loading required package: markovchain
## Warning: package 'markovchain' was built under R version 4.0.3
## 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
#usa population =332002416
# Russia population =145966453
#population in japan = 126279505
#population in china =1442182072
#population in cheleabinsk =1130319
#population in moscow =12537954
#population in MO =7690863
#Новгородская обл =1250615
# when you use data from russian websites use ==> unlist for define time series
Full_original_data<-read_excel("F:/Phd/ALL Russia Analysis/Data Russia till 29_11_2020 Covid four country.xlsx",sheet = "japan")
y_lab<- "COVID 19 Infection cases in japan" # input name of data
Actual_date_interval <- c("2020/01/22","2020/11/28")
Forecast_date_interval <- c("2020/11/29","2020/12/5")
validation_data_days <-7
frequency<-"days"
Population <-126279505 # Population size in City for applaying SIR model
# Data Preparation & calculate some of statistics measures
original_data<-Full_original_data$infection
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2 5466 18109 39418 74720 145457
sd(original_data) # calculate standard deviation
## [1] 40030.8
skewness(original_data) # calculate Cofficient of skewness
## [1] 0.8215421
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 2.38523
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
autoplot(data_series ,xlab=paste ("Time in ", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE
## Training set 6.257124 153.0738 93.56592 -0.09642161 1.962456 0.2173474
## ACF1
## Training set 0.1131572
# Print Model Parameters
model_bats
## BATS(0.476, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 0.475859
## Alpha: 1.205209
## Beta: 0.4948307
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 0.5375066
## [2,] 0.5511111
## attr(,"lambda")
## [1] 0.4758594
##
## Sigma: 0.6622323
## AIC: 4425.615
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$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 japan"
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 japan"
paste(MAPE_Mean_All,"%")
## [1] "1.591 % MAPE 7 days COVID 19 Infection cases in japan %"
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 japan"
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 2020-11-22 воскресенье 133034 133337.3
## 2 2020-11-23 понедельник 134554 135764.6
## 3 2020-11-24 вторник 135786 138214.9
## 4 2020-11-25 среда 137735 140688.1
## 5 2020-11-26 четверг 140225 143184.3
## 6 2020-11-27 пятница 142778 145703.6
## 7 2020-11-28 суббота 145457 148245.9
## MAPE_bats_Model
## 1 0.228 %
## 2 0.9 %
## 3 1.789 %
## 4 2.144 %
## 5 2.11 %
## 6 2.049 %
## 7 1.917 %
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 2020-11-29 воскресенье 150811.2
## 2 2020-11-30 понедельник 153399.7
## 3 2020-12-01 вторник 156011.2
## 4 2020-12-02 среда 158645.8
## 5 2020-12-03 четверг 161303.6
## 6 2020-12-04 пятница 163984.5
## 7 2020-12-05 суббота 166688.6
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="blue", 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
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,RMSE_bats,MAPE_Mean_All,MAD_bats) # analysis of Error by using Bats Model shows result of correlation ,MSE ,MPER
## correlation_bats RMSE_bats
## 1 0.991704 2428.18
## MAPE_Mean_All MAD_bats
## 1 1.591 % MAPE 7 days COVID 19 Infection cases in japan 2224.247
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 2020-11-22 воскресенье 303.3351 0.228 % 0.227 %
## 2 2020-11-23 понедельник 1210.6228 0.9 % 0.892 %
## 3 2020-11-24 вторник 2428.8720 1.789 % 1.757 %
## 4 2020-11-25 среда 2953.1026 2.144 % 2.099 %
## 5 2020-11-26 четверг 2959.3342 2.11 % 2.067 %
## 6 2020-11-27 пятница 2925.5864 2.049 % 2.008 %
## 7 2020-11-28 суббота 2788.8786 1.917 % 1.881 %
## 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 14.20245 152.2489 103.7137 1.381866 52.02524 0.2409201 0.01467517
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.25016
## Beta: 0.5521927
## Damping Parameter: 1
## Gamma-1 Values: -5.974693e-05
## Gamma-2 Values: -0.0008001738
##
## Seed States:
## [,1]
## [1,] 17.012499
## [2,] -9.522773
## [3,] -41.481418
## [4,] -2.078669
## [5,] 9.316310
## [6,] 18.685001
##
## Sigma: 152.2489
## AIC: 4830.26
plot(model_TBATS,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", 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 japan"
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 japan"
paste(MAPE_Mean_All,"%")
## [1] "1.39 % MAPE 7 days COVID 19 Infection cases in japan %"
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 japan"
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 2020-11-22 воскресенье 133034 133268.6
## 2 2020-11-23 понедельник 134554 135645.4
## 3 2020-11-24 вторник 135786 138075.0
## 4 2020-11-25 среда 137735 140471.8
## 5 2020-11-26 четверг 140225 142878.2
## 6 2020-11-27 пятница 142778 145252.0
## 7 2020-11-28 суббота 145457 147563.2
## MAPE_TBATS_Model
## 1 0.176 %
## 2 0.811 %
## 3 1.686 %
## 4 1.987 %
## 5 1.892 %
## 6 1.733 %
## 7 1.448 %
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 2020-11-29 воскресенье 149940.0
## 2 2020-11-30 понедельник 152369.6
## 3 2020-12-01 вторник 154766.4
## 4 2020-12-02 среда 157172.8
## 5 2020-12-03 четверг 159546.6
## 6 2020-12-04 пятница 161857.9
## 7 2020-12-05 суббота 164234.6
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="blue", 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
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,RMSE_tbats,MAPE_Mean_All,MAD_tbats) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_tbats RMSE_tbats
## 1 0.9899965 2123.741
## MAPE_Mean_All MAD_tbats
## 1 1.39 % MAPE 7 days COVID 19 Infection cases in japan 1940.743
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 2020-11-22 воскресенье 234.6215 0.176 % 0.176 %
## 2 2020-11-23 понедельник 1091.3842 0.811 % 0.805 %
## 3 2020-11-24 вторник 2288.9757 1.686 % 1.658 %
## 4 2020-11-25 среда 2736.7894 1.987 % 1.948 %
## 5 2020-11-26 четверг 2653.2261 1.892 % 1.857 %
## 6 2020-11-27 пятница 2473.9598 1.733 % 1.703 %
## 7 2020-11-28 суббота 2106.2416 1.448 % 1.427 %
## 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 4.063926 159.52 97.49796 -0.1217473 1.890622 0.2264813 0.1820318
# 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= 0.3879
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.6434
##
## Initial states:
## l = 0.6835
## b = 0.4857
##
## sigma: 0.32
##
## AIC AICc BIC
## 1055.616 1055.817 1074.218
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 4.063926 159.52 97.49796 -0.1217473 1.890622 0.2264813 0.1820318
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> COVID 19 Infection cases in japan"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> COVID 19 Infection cases in japan"
paste(MAPE_Mean_All,"%")
## [1] "2.003 % MAPE 7 days COVID 19 Infection cases in japan %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> COVID 19 Infection cases in japan"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2020-11-22 воскресенье 133034 133421.1
## 2 2020-11-23 понедельник 134554 136001.3
## 3 2020-11-24 вторник 135786 138611.9
## 4 2020-11-25 среда 137735 141253.0
## 5 2020-11-26 четверг 140225 143924.6
## 6 2020-11-27 пятница 142778 146626.9
## 7 2020-11-28 суббота 145457 149360.0
## MAPE_holt_Model
## 1 0.291 %
## 2 1.076 %
## 3 2.081 %
## 4 2.554 %
## 5 2.638 %
## 6 2.696 %
## 7 2.683 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2020-11-29 воскресенье 152124.1
## 2 2020-11-30 понедельник 154919.3
## 3 2020-12-01 вторник 157745.7
## 4 2020-12-02 среда 160603.5
## 5 2020-12-03 четверг 163492.7
## 6 2020-12-04 пятница 166413.5
## 7 2020-12-05 суббота 169366.0
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="blue", 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
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,RMSE_Holt,MAPE_Mean_All,MAD_Holt) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_Holt RMSE_Holt
## 1 0.9919451 3078.523
## MAPE_Mean_All MAD_Holt
## 1 2.003 % MAPE 7 days COVID 19 Infection cases in japan 2804.259
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 2020-11-22 воскресенье 387.0687 0.291 % 0.29 %
## 2 2020-11-23 понедельник 1447.3428 1.076 % 1.064 %
## 3 2020-11-24 вторник 2825.9327 2.081 % 2.039 %
## 4 2020-11-25 среда 3517.9679 2.554 % 2.491 %
## 5 2020-11-26 четверг 3699.5774 2.638 % 2.57 %
## 6 2020-11-27 пятница 3848.8900 2.696 % 2.625 %
## 7 2020-11-28 суббота 3903.0339 2.683 % 2.613 %
#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 japan"
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 = 4.7144, 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) = 1.1288, 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 = 0.38599, Lag order = 6, 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="blue", 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 japan"
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 = 2.7537, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -8.6767, Truncation lag parameter = 5, p-value
## = 0.6239
## 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 = 1.4832, Lag order = 6, 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="blue", 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 japan"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.35466, Truncation lag parameter = 5, p-value = 0.0967
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) = -242.98, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
## Warning in adf.test(diff2_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -5.8101, Lag order = 6, 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) : 3931.73
## ARIMA(0,2,1) : 3930.157
## ARIMA(0,2,2) : 3913.677
## ARIMA(0,2,3) : 3912.983
## ARIMA(0,2,4) : 3915.042
## ARIMA(0,2,5) : 3891.724
## ARIMA(1,2,0) : 3931.486
## ARIMA(1,2,1) : 3917.119
## ARIMA(1,2,2) : 3913.703
## ARIMA(1,2,3) : 3915.05
## ARIMA(1,2,4) : 3908.353
## ARIMA(2,2,0) : 3924.854
## ARIMA(2,2,1) : 3911.222
## ARIMA(2,2,2) : 3866.172
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 3920.241
## ARIMA(3,2,1) : 3908.787
## ARIMA(3,2,2) : 3875.8
## ARIMA(4,2,0) : 3907.718
## ARIMA(4,2,1) : 3899.487
## ARIMA(5,2,0) : 3885.529
##
##
##
## Best model: ARIMA(2,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2144 -0.8476 -1.4263 0.8209
## s.e. 0.0421 0.0571 0.0528 0.0442
##
## sigma^2 estimated as 19861: log likelihood=-1927.99
## AIC=3865.97 AICc=3866.17 BIC=3884.54
#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("[ ]*$", "", result)
}
return(result)
}
source("stringthearima.R")
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2144 -0.8476 -1.4263 0.8209
## s.e. 0.0421 0.0571 0.0528 0.0442
##
## sigma^2 estimated as 19599: log likelihood = -1927.99, aic = 3865.97
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> COVID 19 Infection cases in japan"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 13.34289 139.5351 85.20884 0.3907726 1.676204 0.1979345 -0.1159147
x1_model1$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="blue", 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(2,2,2)
## Q* = 53.692, df = 6, p-value = 8.511e-10
##
## Model df: 4. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> COVID 19 Infection cases in japan"
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 = 366.35, 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 = 254.98, 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='blue')
#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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> COVID 19 Infection cases in japan"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> COVID 19 Infection cases in japan"
paste(MAPE_Mean_All,"%")
## [1] "1.42 % MAPE 7 days COVID 19 Infection cases in japan %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> COVID 19 Infection cases in japan"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2020-11-22 воскресенье 133034 133146.2
## 2 2020-11-23 понедельник 134554 135323.2
## 3 2020-11-24 вторник 135786 137644.2
## 4 2020-11-25 среда 137735 140223.4
## 5 2020-11-26 четверг 140225 142994.2
## 6 2020-11-27 пятница 142778 145778.6
## 7 2020-11-28 суббота 145457 148417.4
## MAPE_auto.arima_Model
## 1 0.084 %
## 2 0.572 %
## 3 1.368 %
## 4 1.807 %
## 5 1.975 %
## 6 2.102 %
## 7 2.035 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2020-11-29 воскресенье 150867.6
## 2 2020-11-30 понедельник 153212.3
## 3 2020-12-01 вторник 155588.8
## 4 2020-12-02 среда 158093.2
## 5 2020-12-03 четверг 160726.0
## 6 2020-12-04 пятница 163406.4
## 7 2020-12-05 суббота 166035.7
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="blue", 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
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,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 RMSE_auto.arima
## 1 0.9953669 2257.854
## MAPE_Mean_All MAD_auto.arima
## 1 1.42 % MAPE 7 days COVID 19 Infection cases in japan 1994.03
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 2020-11-22 воскресенье 112.2287 0.084 %
## 2 2020-11-23 понедельник 769.1802 0.572 %
## 3 2020-11-24 вторник 1858.1867 1.368 %
## 4 2020-11-25 среда 2488.4318 1.807 %
## 5 2020-11-26 четверг 2769.1840 1.975 %
## 6 2020-11-27 пятница 3000.6254 2.102 %
## 7 2020-11-28 суббота 2960.3734 2.035 %
## REOF_F_auto.arima
## 1 0.084 %
## 2 0.568 %
## 3 1.35 %
## 4 1.775 %
## 5 1.937 %
## 6 2.058 %
## 7 1.995 %
# 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$message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.01536525 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
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,RMSE_SIR,MAPE_Mean_All,MAD_SIR) # analysis of Error by using SIR's linear model shows result of correlation ,MSE ,MPER
## correlation_SIR RMSE_SIR
## 1 0.9923446 14263.99
## MAPE_Mean_All MAD_SIR
## 1 10.289 % MAPE 7 days COVID 19 Infection cases in japan 14250.37
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 2020-11-22 воскресенье 14423.00 10.842 % 12.16 %
## 2 2020-11-23 понедельник 14108.15 10.485 % 11.713 %
## 3 2020-11-24 вторник 13476.95 9.925 % 11.019 %
## 4 2020-11-25 среда 13533.96 9.826 % 10.897 %
## 5 2020-11-26 четверг 14102.78 10.057 % 11.182 %
## 6 2020-11-27 пятница 14704.90 10.299 % 11.482 %
## 7 2020-11-28 суббота 15402.87 10.589 % 11.843 %
## validation_forecast testing_data
## 1 118611.0 133034
## 2 120445.8 134554
## 3 122309.0 135786
## 4 124201.0 137735
## 5 126122.2 140225
## 6 128073.1 142778
## 7 130054.1 145457
## 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.01386158 0.00000000
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)
## FD forecating_date forecasting_by_SIR
## 1 2020-11-29 воскресенье 133034.0
## 2 2020-11-30 понедельник 134888.9
## 3 2020-12-01 вторник 136769.7
## 4 2020-12-02 среда 138676.7
## 5 2020-12-03 четверг 140610.2
## 6 2020-12-04 пятница 142570.6
## 7 2020-12-05 суббота 144558.4
# 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 japan"
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 japan"
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 japan"
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 japan"
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 japan"
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 japan"
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 2020-11-22 воскресенье 0.2280132 0.1763620
## 2 2020-11-23 понедельник 0.8997301 0.8111124
## 3 2020-11-24 вторник 1.7887499 1.6857229
## 4 2020-11-25 среда 2.1440466 1.9869963
## 5 2020-11-26 четверг 2.1104184 1.8921206
## 6 2020-11-27 пятница 2.0490457 1.7327318
## 7 2020-11-28 суббота 1.9173217 1.4480167
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.2909547 0.08436094
## 2 1.0756594 0.57165167
## 3 2.0811664 1.36846709
## 4 2.5541568 1.80668077
## 5 2.6383151 1.97481476
## 6 2.6957164 2.10160206
## 7 2.6832905 2.03522238
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 japan"
best_recommended_model
## [1] 1.390438
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> COVID 19 Infection cases in japan"
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=" ")}
## [1] "System Recommend That's better TBATS For forecasting ==> COVID 19 Infection cases in japan"
if(best_recommended_model >= M3) {paste("System Recommend Holt's Linear Model < Exponential Smoothing Model > That's better For forecasting ==> ",y_lab, sep=" ")}
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 japan
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 japan
## Markov Chain For COVID 19 infection cases
require(markovchain)
require(data.table)
xx9<-original_data[rows]
xx8<-original_data[rows-1]
xx7<-original_data[rows-2]
xx6<-original_data[rows-3]
xx5<-original_data[rows-4]
xx4<-original_data[rows-5]
xx3<-original_data[rows-6]
xx2<-original_data[rows-7]
xx1<-original_data[rows-8]
infection_vector1<-c(xx1,xx2,xx3)
infection_vector2<-c(xx4,xx5,xx6)
infection_vector3<-c(xx7,xx8,xx9)
sum_vector1<-sum(infection_vector1)
sum_vector2<-sum(infection_vector2)
sum_vector3<-sum(infection_vector3)
proba_vector1<-c(infection_vector1/sum_vector1)
proba_vector2<-c(infection_vector2/sum_vector2)
proba_vector3<-c(infection_vector3/sum_vector3)
CovidStates = c("Low Infections", "Mid Infections", "Hight Infections")
byRow = TRUE
CovidMatrix = matrix(data = c(proba_vector1,
proba_vector2,
proba_vector3), byrow = byRow, nrow = 3,
dimnames = list(CovidStates, CovidStates))
mcCovid = new("markovchain", states = CovidStates, byrow = byRow,
transitionMatrix = CovidMatrix, name = "Cvid 19")
mcCovid = new("markovchain", states = c("Low Infections", "Mid Infections", "Hight Infections"),
transitionMatrix = matrix(data = c(proba_vector1,
proba_vector2,
proba_vector3), byrow = byRow, nrow = 3),
name = "Cvid 19")
name = ("Cvid 19")
initialState = c(0,1,0)
after2Days = initialState * (mcCovid * mcCovid)
after7Days = initialState * (mcCovid^7)
after30days =initialState * (mcCovid^30)
after7Days
## Low Infections Mid Infections Hight Infections
## [1,] 0.3280355 0.3332229 0.3387416
plot(mcCovid,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main = "Markov Chain")
