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 = "China")
y_lab<- "COVID 19 Infection cases in China" # 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 <-1442182072 # Population size in City for applaying SIR model
# Data Preparation & calculate some of statistics measures
original_data<-Full_original_data$infection
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 549 83244 85160 81617 90649 93329
sd(original_data) # calculate standard deviation
## [1] 18491.18
skewness(original_data) # calculate Cofficient of skewness
## [1] -3.26615
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 13.04048
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
autoplot(data_series ,xlab=paste ("Time in ", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE
## Training set -0.07248013 889.3494 183.8106 0.6722956 1.161568 0.6067079
## ACF1
## Training set -0.02534514
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 1
## Alpha: 1.123249
## Beta: 0.2700065
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 7.32516
## [2,] 44.27698
## attr(,"lambda")
## [1] 0.9999999
##
## Sigma: 889.348
## AIC: 5896.894
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$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 China"
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 China"
paste(MAPE_Mean_All,"%")
## [1] "0.236 % MAPE 7 days COVID 19 Infection cases in China %"
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 China"
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 92733 92689.62
## 2 2020-11-23 понедельник 92829 92727.93
## 3 2020-11-24 вторник 92914 92766.24
## 4 2020-11-25 среда 93025 92804.55
## 5 2020-11-26 четверг 93113 92842.86
## 6 2020-11-27 пятница 93225 92881.17
## 7 2020-11-28 суббота 93329 92919.48
## MAPE_bats_Model
## 1 0.047 %
## 2 0.109 %
## 3 0.159 %
## 4 0.237 %
## 5 0.29 %
## 6 0.369 %
## 7 0.439 %
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 92957.79
## 2 2020-11-30 понедельник 92996.10
## 3 2020-12-01 вторник 93034.41
## 4 2020-12-02 среда 93072.72
## 5 2020-12-03 четверг 93111.03
## 6 2020-12-04 пятница 93149.33
## 7 2020-12-05 суббота 93187.64
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 0.9993874 251.1196
## MAPE_Mean_All MAD_bats
## 1 0.236 % MAPE 7 days COVID 19 Infection cases in China 219.4485
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 43.3761 0.047 % 0.047 %
## 2 2020-11-23 понедельник 101.0669 0.109 % 0.109 %
## 3 2020-11-24 вторник 147.7577 0.159 % 0.159 %
## 4 2020-11-25 среда 220.4485 0.237 % 0.238 %
## 5 2020-11-26 четверг 270.1393 0.29 % 0.291 %
## 6 2020-11-27 пятница 343.8301 0.369 % 0.37 %
## 7 2020-11-28 суббота 409.5208 0.439 % 0.441 %
## 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 8.264055 1008.811 266.2988 3.992163 6.787387 0.878979 -0.007658573
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.081409
## Beta: 0.225458
## Damping Parameter: 1
## Gamma-1 Values: -0.001777534
## Gamma-2 Values: 0.001856258
##
## Seed States:
## [,1]
## [1,] -7346.869868
## [2,] -528.916366
## [3,] 104.390921
## [4,] -17.323721
## [5,] 2.245731
## [6,] 17.411924
##
## Sigma: 1008.811
## AIC: 5983.777
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 China"
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 China"
paste(MAPE_Mean_All,"%")
## [1] "0.21 % MAPE 7 days COVID 19 Infection cases in China %"
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 China"
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 92733 92753.00
## 2 2020-11-23 понедельник 92829 92861.34
## 3 2020-11-24 вторник 92914 92885.93
## 4 2020-11-25 среда 93025 92776.67
## 5 2020-11-26 четверг 93113 92758.92
## 6 2020-11-27 пятница 93225 92877.92
## 7 2020-11-28 суббота 93329 92989.15
## MAPE_TBATS_Model
## 1 0.022 %
## 2 0.035 %
## 3 0.03 %
## 4 0.267 %
## 5 0.38 %
## 6 0.372 %
## 7 0.364 %
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 93097.49
## 2 2020-11-30 понедельник 93122.08
## 3 2020-12-01 вторник 93012.82
## 4 2020-12-02 среда 92995.08
## 5 2020-12-03 четверг 93114.08
## 6 2020-12-04 пятница 93225.31
## 7 2020-12-05 суббота 93333.64
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 0.5598285 246.4691
## MAPE_Mean_All MAD_tbats
## 1 0.21 % MAPE 7 days COVID 19 Infection cases in China 180.7234
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 20.00182 0.022 % 0.022 %
## 2 2020-11-23 понедельник 32.33588 0.035 % 0.035 %
## 3 2020-11-24 вторник 28.07203 0.03 % 0.03 %
## 4 2020-11-25 среда 248.33091 0.267 % 0.268 %
## 5 2020-11-26 четверг 354.07678 0.38 % 0.382 %
## 6 2020-11-27 пятница 347.07585 0.372 % 0.374 %
## 7 2020-11-28 суббота 339.84594 0.364 % 0.365 %
## 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 -88.69075 944.9715 221.3907 -0.1161827 0.7896821 0.7307496 0.16232
# 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= 0.4106
##
## Smoothing parameters:
## alpha = 0.9727
## beta = 0.2383
##
## Initial states:
## l = 22.9523
## b = 6.8933
##
## sigma: 1.7769
##
## AIC AICc BIC
## 2101.341 2101.541 2119.942
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -88.69075 944.9715 221.3907 -0.1161827 0.7896821 0.7307496 0.16232
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> COVID 19 Infection cases in China"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> COVID 19 Infection cases in China"
paste(MAPE_Mean_All,"%")
## [1] "0.243 % MAPE 7 days COVID 19 Infection cases in China %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> COVID 19 Infection cases in China"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2020-11-22 воскресенье 92733 92684.76
## 2 2020-11-23 понедельник 92829 92722.36
## 3 2020-11-24 вторник 92914 92759.96
## 4 2020-11-25 среда 93025 92797.57
## 5 2020-11-26 четверг 93113 92835.19
## 6 2020-11-27 пятница 93225 92872.82
## 7 2020-11-28 суббота 93329 92910.46
## MAPE_holt_Model
## 1 0.052 %
## 2 0.115 %
## 3 0.166 %
## 4 0.244 %
## 5 0.298 %
## 6 0.378 %
## 7 0.448 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2020-11-29 воскресенье 92948.11
## 2 2020-11-30 понедельник 92985.77
## 3 2020-12-01 вторник 93023.44
## 4 2020-12-02 среда 93061.11
## 5 2020-12-03 четверг 93098.80
## 6 2020-12-04 пятница 93136.49
## 7 2020-12-05 суббота 93174.19
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 0.9993929 257.8833
## MAPE_Mean_All MAD_Holt
## 1 0.243 % MAPE 7 days COVID 19 Infection cases in China 226.409
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 48.23692 0.052 % 0.052 %
## 2 2020-11-23 понедельник 106.64259 0.115 % 0.115 %
## 3 2020-11-24 вторник 154.03928 0.166 % 0.166 %
## 4 2020-11-25 среда 227.42698 0.244 % 0.245 %
## 5 2020-11-26 четверг 277.80570 0.298 % 0.299 %
## 6 2020-11-27 пятница 352.17542 0.378 % 0.379 %
## 7 2020-11-28 суббота 418.53615 0.448 % 0.45 %
#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 China"
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 = 2.165, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -10.556, Truncation lag parameter = 5, p-value
## = 0.5185
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -6.4174, Lag order = 6, p-value = 0.01
## 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 China"
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 = 1.1956, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -171.26, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -3.39, Lag order = 6, p-value = 0.05636
## 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 China"
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 = 0.016755, Truncation lag parameter = 5, p-value = 0.1
pp.test(diff2_x1) # applay pp test after taking Second differences
## Warning in pp.test(diff2_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff2_x1
## Dickey-Fuller Z(alpha) = -331.42, 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 = -9.848, 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) : 5086.059
## ARIMA(0,2,1) : 4984.327
## ARIMA(0,2,2) : 4981.711
## ARIMA(0,2,3) : 4982.516
## ARIMA(0,2,4) : 4984.535
## ARIMA(0,2,5) : 4986.603
## ARIMA(1,2,0) : 5042.866
## ARIMA(1,2,1) : 4982.607
## ARIMA(1,2,2) : 4982.808
## ARIMA(1,2,3) : Inf
## ARIMA(1,2,4) : Inf
## ARIMA(2,2,0) : 5009.106
## ARIMA(2,2,1) : 4982.432
## ARIMA(2,2,2) : 4984.49
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 4995.963
## ARIMA(3,2,1) : 4984.486
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 4991.274
## ARIMA(4,2,1) : 4986.1
## ARIMA(5,2,0) : 4992.003
##
##
##
## Best model: ARIMA(0,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(0,2,2)
##
## Coefficients:
## ma1 ma2
## -0.6281 -0.1344
## s.e. 0.0598 0.0620
##
## sigma^2 estimated as 796021: log likelihood=-2487.82
## AIC=4981.63 AICc=4981.71 BIC=4992.77
#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("[ ]*$", "", result)
}
return(result)
}
source("stringthearima.R")
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 0 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ma1 ma2
## -0.6281 -0.1344
## s.e. 0.0598 0.0620
##
## sigma^2 estimated as 790767: log likelihood = -2487.82, aic = 4981.63
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> COVID 19 Infection cases in China"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set -4.435145 886.3304 186.5041 0.4206983 0.774974 0.6155986
## ACF1
## Training set -0.008331372
x1_model1$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(0,2,2)
## Q* = 9.0745, df = 8, p-value = 0.3361
##
## 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 Infection cases in China"
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 = 3.1714, df = 20, p-value = 1
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 346108, 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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> COVID 19 Infection cases in China"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> COVID 19 Infection cases in China"
paste(MAPE_Mean_All,"%")
## [1] "0.24 % MAPE 7 days COVID 19 Infection cases in China %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> COVID 19 Infection cases in China"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2020-11-22 воскресенье 92733 92688.88
## 2 2020-11-23 понедельник 92829 92726.13
## 3 2020-11-24 вторник 92914 92763.38
## 4 2020-11-25 среда 93025 92800.64
## 5 2020-11-26 четверг 93113 92837.89
## 6 2020-11-27 пятница 93225 92875.14
## 7 2020-11-28 суббота 93329 92912.40
## MAPE_auto.arima_Model
## 1 0.048 %
## 2 0.111 %
## 3 0.162 %
## 4 0.241 %
## 5 0.295 %
## 6 0.375 %
## 7 0.446 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2020-11-29 воскресенье 92949.65
## 2 2020-11-30 понедельник 92986.90
## 3 2020-12-01 вторник 93024.16
## 4 2020-12-02 среда 93061.41
## 5 2020-12-03 четверг 93098.66
## 6 2020-12-04 пятница 93135.92
## 7 2020-12-05 суббота 93173.17
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 0.9993874 255.5654
## MAPE_Mean_All MAD_auto.arima
## 1 0.24 % MAPE 7 days COVID 19 Infection cases in China 223.3629
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 44.12297 0.048 %
## 2 2020-11-23 понедельник 102.86962 0.111 %
## 3 2020-11-24 вторник 150.61628 0.162 %
## 4 2020-11-25 среда 224.36293 0.241 %
## 5 2020-11-26 четверг 275.10958 0.295 %
## 6 2020-11-27 пятница 349.85623 0.375 %
## 7 2020-11-28 суббота 416.60288 0.446 %
## REOF_F_auto.arima
## 1 0.048 %
## 2 0.111 %
## 3 0.162 %
## 4 0.242 %
## 5 0.296 %
## 6 0.377 %
## 7 0.448 %
# 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
## 0.5003480 0.4999817
# 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 0.9969257 510.187
## MAPE_Mean_All MAD_SIR
## 1 0.525 % MAPE 7 days COVID 19 Infection cases in China 488.8972
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 281.0000 0.303 % 0.304 %
## 2 2020-11-23 понедельник 346.8375 0.374 % 0.375 %
## 3 2020-11-24 вторник 403.1503 0.434 % 0.436 %
## 4 2020-11-25 среда 486.9400 0.523 % 0.526 %
## 5 2020-11-26 четверг 549.2084 0.59 % 0.593 %
## 6 2020-11-27 пятница 636.9570 0.683 % 0.688 %
## 7 2020-11-28 суббота 718.1875 0.77 % 0.775 %
## validation_forecast testing_data
## 1 92452.00 92733
## 2 92482.16 92829
## 3 92510.85 92914
## 4 92538.06 93025
## 5 92563.79 93113
## 6 92588.04 93225
## 7 92610.81 93329
## 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.5010644 0.4999440
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)
## FD forecating_date forecasting_by_SIR
## 1 2020-11-29 воскресенье 92733.00
## 2 2020-11-30 понедельник 92833.22
## 3 2020-12-01 вторник 92932.05
## 4 2020-12-02 среда 93029.48
## 5 2020-12-03 четверг 93125.50
## 6 2020-12-04 пятница 93220.11
## 7 2020-12-05 суббота 93313.30
# 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 China"
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 China"
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 China"
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 China"
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 China"
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 China"
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 0.04677526 0.02156926
## 2 2020-11-23 понедельник 0.10887426 0.03483381
## 3 2020-11-24 вторник 0.15902628 0.03021292
## 4 2020-11-25 среда 0.23697766 0.26695072
## 5 2020-11-26 четверг 0.29011981 0.38026567
## 6 2020-11-27 пятница 0.36881743 0.37229911
## 7 2020-11-28 суббота 0.43879270 0.36413756
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.05201699 0.04758066
## 2 0.11488069 0.11081626
## 3 0.16578694 0.16210289
## 4 0.24447942 0.24118562
## 5 0.29835329 0.29545775
## 6 0.37776929 0.37528156
## 7 0.44845242 0.44638095
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 China"
best_recommended_model
## [1] 0.2100384
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> COVID 19 Infection cases in China"
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 China"
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 China
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 China
## 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,] 0.333009 0.3333162 0.3336748
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")
