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 = "Russia")
y_lab<- "COVID 19 Infection cases in Russia" # 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 <-145966453 # Population size in City for applaying SIR model
# Data Preparation & calculate some of statistics measures
original_data<-Full_original_data$infection
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 9766 616542 658576 1049609 2223500
sd(original_data) # calculate standard deviation
## [1] 611364.2
skewness(original_data) # calculate Cofficient of skewness
## [1] 0.6162814
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 2.449782
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
autoplot(data_series ,xlab=paste ("Time in ", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 85.58861 458.0121 262.2205 NaN Inf 0.03893166 -0.01956833
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.9203543
## Beta: 0.9429986
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 140.04651
## [2,] -10.15089
##
## Sigma: 458.0121
## AIC: 5490.101
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$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 Russia"
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 Russia"
paste(MAPE_Mean_All,"%")
## [1] "0.058 % MAPE 7 days COVID 19 Infection cases in Russia %"
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 Russia"
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 2071858 2072134
## 2 2020-11-23 понедельник 2096749 2096740
## 3 2020-11-24 вторник 2120836 2121347
## 4 2020-11-25 среда 2144229 2145953
## 5 2020-11-26 четверг 2169424 2170559
## 6 2020-11-27 пятница 2196691 2195166
## 7 2020-11-28 суббота 2223500 2219772
## MAPE_bats_Model
## 1 0.013 %
## 2 0 %
## 3 0.024 %
## 4 0.08 %
## 5 0.052 %
## 6 0.069 %
## 7 0.168 %
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 2244379
## 2 2020-11-30 понедельник 2268985
## 3 2020-12-01 вторник 2293591
## 4 2020-12-02 среда 2318198
## 5 2020-12-03 четверг 2342804
## 6 2020-12-04 пятница 2367410
## 7 2020-12-05 суббота 2392017
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 0.9996317 1724.676
## MAPE_Mean_All MAD_bats
## 1 0.058 % MAPE 7 days COVID 19 Infection cases in Russia 230.8637
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 275.858735 0.013 % 0.013 %
## 2 2020-11-23 понедельник 8.763043 0 % 0 %
## 3 2020-11-24 вторник 510.615179 0.024 % 0.024 %
## 4 2020-11-25 среда 1723.993401 0.08 % 0.08 %
## 5 2020-11-26 четверг 1135.371623 0.052 % 0.052 %
## 6 2020-11-27 пятница 1525.250155 0.069 % 0.069 %
## 7 2020-11-28 суббота 3727.871933 0.168 % 0.168 %
## 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 85.67238 457.5259 266.6448 NaN Inf 0.03958853 -0.01949492
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.9202445
## Beta: 0.9401734
## Damping Parameter: 1
## Gamma-1 Values: -0.0006430625
## Gamma-2 Values: -0.0007876699
##
## Seed States:
## [,1]
## [1,] 143.624298
## [2,] -11.152520
## [3,] 13.008154
## [4,] -4.563039
## [5,] -30.414940
## [6,] 5.781084
##
## Sigma: 457.5259
## AIC: 5501.454
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 Russia"
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 Russia"
paste(MAPE_Mean_All,"%")
## [1] "0.058 % MAPE 7 days COVID 19 Infection cases in Russia %"
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 Russia"
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 2071858 2072090
## 2 2020-11-23 понедельник 2096749 2096609
## 3 2020-11-24 вторник 2120836 2121152
## 4 2020-11-25 среда 2144229 2145695
## 5 2020-11-26 четверг 2169424 2170260
## 6 2020-11-27 пятница 2196691 2194865
## 7 2020-11-28 суббота 2223500 2219424
## MAPE_TBATS_Model
## 1 0.011 %
## 2 0.007 %
## 3 0.015 %
## 4 0.068 %
## 5 0.039 %
## 6 0.083 %
## 7 0.183 %
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 2243943
## 2 2020-11-30 понедельник 2268486
## 3 2020-12-01 вторник 2293029
## 4 2020-12-02 среда 2317594
## 5 2020-12-03 четверг 2342199
## 6 2020-12-04 пятница 2366758
## 7 2020-12-05 суббота 2391277
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 0.9996431 1811.54
## MAPE_Mean_All MAD_tbats
## 1 0.058 % MAPE 7 days COVID 19 Infection cases in Russia 455.9455
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 232.0855 0.011 % 0.011 %
## 2 2020-11-23 понедельник 140.2353 0.007 % 0.007 %
## 3 2020-11-24 вторник 315.8708 0.015 % 0.015 %
## 4 2020-11-25 среда 1466.4967 0.068 % 0.068 %
## 5 2020-11-26 четверг 836.2652 0.039 % 0.039 %
## 6 2020-11-27 пятница 1826.0889 0.083 % 0.083 %
## 7 2020-11-28 суббота 4076.0123 0.183 % 0.184 %
## 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 35.50896 451.0444 258.966 NaN Inf 0.03844846 0.07837375
# 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= 0.6277
##
## Smoothing parameters:
## alpha = 0.8597
## beta = 0.8596
##
## Initial states:
## l = -2.0192
## b = 0.0082
##
## sigma: 4.6318
##
## AIC AICc BIC
## 2685.767 2685.968 2704.368
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 35.50896 451.0444 258.966 NaN Inf 0.03844846 0.07837375
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> COVID 19 Infection cases in Russia"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> COVID 19 Infection cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "0.065 % MAPE 7 days COVID 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> COVID 19 Infection cases in Russia"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2020-11-22 воскресенье 2071858 2072281
## 2 2020-11-23 понедельник 2096749 2097178
## 3 2020-11-24 вторник 2120836 2122186
## 4 2020-11-25 среда 2144229 2147304
## 5 2020-11-26 четверг 2169424 2172531
## 6 2020-11-27 пятница 2196691 2197868
## 7 2020-11-28 суббота 2223500 2223315
## MAPE_holt_Model
## 1 0.02 %
## 2 0.02 %
## 3 0.064 %
## 4 0.143 %
## 5 0.143 %
## 6 0.054 %
## 7 0.008 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2020-11-29 воскресенье 2248870
## 2 2020-11-30 понедельник 2274534
## 3 2020-12-01 вторник 2300306
## 4 2020-12-02 среда 2326186
## 5 2020-12-03 четверг 2352173
## 6 2020-12-04 пятница 2378268
## 7 2020-12-05 суббота 2404470
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 0.9997147 1801.404
## MAPE_Mean_All MAD_Holt
## 1 0.065 % MAPE 7 days COVID 19 Infection cases in Russia 1339.541
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 423.3593 0.02 % 0.02 %
## 2 2020-11-23 понедельник 429.3895 0.02 % 0.02 %
## 3 2020-11-24 вторник 1349.9415 0.064 % 0.064 %
## 4 2020-11-25 среда 3074.6812 0.143 % 0.143 %
## 5 2020-11-26 четверг 3107.2777 0.143 % 0.143 %
## 6 2020-11-27 пятница 1177.4038 0.054 % 0.054 %
## 7 2020-11-28 суббота 185.2644 0.008 % 0.008 %
#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 Russia"
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 = 4.953, 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) = 2.1199, 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 = 0.18601, 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 Russia"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 3.0478, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = 1.8121, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = 0.35162, 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 Russia"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
## Warning in kpss.test(diff2_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.83651, Truncation lag parameter = 5, p-value = 0.01
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) = -376.53, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -3.684, Lag order = 6, p-value = 0.02538
## 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) : 4581.701
## ARIMA(0,2,1) : 4580.341
## ARIMA(0,2,2) : 4580.723
## ARIMA(0,2,3) : 4574.303
## ARIMA(0,2,4) : 4576.153
## ARIMA(0,2,5) : 4571.627
## ARIMA(1,2,0) : 4580.033
## ARIMA(1,2,1) : 4582.048
## ARIMA(1,2,2) : 4546.02
## ARIMA(1,2,3) : 4576.163
## ARIMA(1,2,4) : 4578.214
## ARIMA(2,2,0) : 4581.957
## ARIMA(2,2,1) : 4552.919
## ARIMA(2,2,2) : 4570.911
## ARIMA(2,2,3) : 4546.102
## ARIMA(3,2,0) : 4570.731
## ARIMA(3,2,1) : 4545.62
## ARIMA(3,2,2) : 4547.691
## ARIMA(4,2,0) : 4569.455
## ARIMA(4,2,1) : 4547.699
## ARIMA(5,2,0) : 4570.581
##
##
##
## Best model: ARIMA(3,2,1)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(3,2,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.6581 0.1282 0.1872 -0.8806
## s.e. 0.0661 0.0674 0.0600 0.0400
##
## sigma^2 estimated as 187363: log likelihood=-2267.71
## AIC=4545.42 AICc=4545.62 BIC=4563.99
#Make changes in the source of auto arima to run the best model
arima.string <- function (object, padding = FALSE)
{
order <- object$arma[c(1, 6, 2, 3, 7, 4, 5)]
m <- order[7]
result <- paste("ARIMA(", order[1], ",", order[2], ",",
order[3], ")", sep = "")
if (m > 1 && sum(order[4:6]) > 0) {
result <- paste(result, "(", order[4], ",", order[5],
",", order[6], ")[", m, "]", sep = "")
}
if (padding && m > 1 && sum(order[4:6]) == 0) {
result <- paste(result, " ", sep = "")
if (m <= 9) {
result <- paste(result, " ", sep = "")
}
else if (m <= 99) {
result <- paste(result, " ", sep = "")
}
else {
result <- paste(result, " ", sep = "")
}
}
if (!is.null(object$xreg)) {
if (NCOL(object$xreg) == 1 && is.element("drift", names(object$coef))) {
result <- paste(result, "with drift ")
}
else {
result <- paste("Regression with", result, "errors")
}
}
else {
if (is.element("constant", names(object$coef)) || is.element("intercept",
names(object$coef))) {
result <- paste(result, "with non-zero mean")
}
else if (order[2] == 0 && order[5] == 0) {
result <- paste(result, "with zero mean ")
}
else {
result <- paste(result, " ")
}
}
if (!padding) {
result <- gsub("[ ]*$", "", result)
}
return(result)
}
source("stringthearima.R")
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 3 2 1
strtoi(bestmodel[3])
## [1] 1
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.6581 0.1282 0.1872 -0.8806
## s.e. 0.0661 0.0674 0.0600 0.0400
##
## sigma^2 estimated as 184890: log likelihood = -2267.71, aic = 4545.42
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> COVID 19 Infection cases in Russia"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 30.74252 428.5761 248.6959 0.4703187 2.405285 0.03692368
## ACF1
## Training set -0.004877712
x1_model1$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(3,2,1)
## Q* = 25.348, df = 6, p-value = 0.0002943
##
## 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 Russia"
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 = 308.67, 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 = 330.55, 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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> COVID 19 Infection cases in Russia"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> COVID 19 Infection cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "0.126 % MAPE 7 days COVID 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> COVID 19 Infection cases in Russia"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2020-11-22 воскресенье 2071858 2072284
## 2 2020-11-23 понедельник 2096749 2097322
## 3 2020-11-24 вторник 2120836 2122682
## 4 2020-11-25 среда 2144229 2148328
## 5 2020-11-26 четверг 2169424 2174264
## 6 2020-11-27 пятница 2196691 2200486
## 7 2020-11-28 суббота 2223500 2226989
## MAPE_auto.arima_Model
## 1 0.021 %
## 2 0.027 %
## 3 0.087 %
## 4 0.191 %
## 5 0.223 %
## 6 0.173 %
## 7 0.157 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2020-11-29 воскресенье 2253767
## 2 2020-11-30 понедельник 2280815
## 3 2020-12-01 вторник 2308129
## 4 2020-12-02 среда 2335705
## 5 2020-12-03 четверг 2363537
## 6 2020-12-04 пятница 2391621
## 7 2020-12-05 суббота 2419952
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 0.9998159 3178.45
## MAPE_Mean_All MAD_auto.arima
## 1 0.126 % MAPE 7 days COVID 19 Infection cases in Russia 2723.947
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 425.9929 0.021 %
## 2 2020-11-23 понедельник 572.9698 0.027 %
## 3 2020-11-24 вторник 1845.6813 0.087 %
## 4 2020-11-25 среда 4099.0151 0.191 %
## 5 2020-11-26 четверг 4839.5553 0.223 %
## 6 2020-11-27 пятница 3795.3918 0.173 %
## 7 2020-11-28 суббота 3489.0254 0.157 %
## REOF_F_auto.arima
## 1 0.021 %
## 2 0.027 %
## 3 0.087 %
## 4 0.191 %
## 5 0.223 %
## 6 0.172 %
## 7 0.157 %
# SIR Model
#install.packages("dplyr")
library(deSolve)
first<-rows-13
secondr<-rows-7
vector_SIR<-original_data[first:secondr]
Infected <- c(vector_SIR)
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.07043379 0.05787138
# 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 0.9997362 168547.8
## MAPE_Mean_All MAD_SIR
## 1 7.849 % MAPE 7 days COVID 19 Infection cases in Russia 168470
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 161709.0 7.805 % 8.466 %
## 2 2020-11-23 понедельник 164296.7 7.836 % 8.502 %
## 3 2020-11-24 вторник 165946.6 7.825 % 8.489 %
## 4 2020-11-25 среда 166771.5 7.778 % 8.434 %
## 5 2020-11-26 четверг 169270.1 7.803 % 8.463 %
## 6 2020-11-27 пятница 173715.4 7.908 % 8.587 %
## 7 2020-11-28 суббота 177580.4 7.987 % 8.68 %
## validation_forecast testing_data
## 1 1910149 2071858
## 2 1932452 2096749
## 3 1954889 2120836
## 4 1977458 2144229
## 5 2000154 2169424
## 6 2022976 2196691
## 7 2045920 2223500
## 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.0633381 0.0506286
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)
## FD forecating_date forecasting_by_SIR
## 1 2020-11-29 воскресенье 2071858
## 2 2020-11-30 понедельник 2096414
## 3 2020-12-01 вторник 2121140
## 4 2020-12-02 среда 2146035
## 5 2020-12-03 четверг 2171096
## 6 2020-12-04 пятница 2196321
## 7 2020-12-05 суббота 2221707
# 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 Russia"
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 Russia"
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 Russia"
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 Russia"
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 Russia"
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 Russia"
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 0.0133145580 0.011201805
## 2 2020-11-23 понедельник 0.0004179348 0.006688226
## 3 2020-11-24 вторник 0.0240761275 0.014893692
## 4 2020-11-25 среда 0.0804015523 0.068392730
## 5 2020-11-26 четверг 0.0523351647 0.038547797
## 6 2020-11-27 пятница 0.0694339875 0.083129075
## 7 2020-11-28 суббота 0.1676578337 0.183315149
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.020433798 0.02056091
## 2 0.020478823 0.02732658
## 3 0.063651387 0.08702612
## 4 0.143393321 0.19116499
## 5 0.143230539 0.22308020
## 6 0.053598973 0.17277768
## 7 0.008332108 0.15691592
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 Russia"
best_recommended_model
## [1] 0.05802407
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> COVID 19 Infection cases in Russia"
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 Russia"
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 Russia
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 Russia
## 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,] 0.3293841 0.3333576 0.3372583
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")
