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 = "usa")
y_lab<- "COVID 19 Infection cases in USA" # 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 <-332002416 # Population size in City for applaying SIR model
# Data Preparation & calculate some of statistics measures
original_data<-Full_original_data$Заражений
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1 461344 2438342 3741221 6445505 13244417
sd(original_data) # calculate standard deviation
## [1] 3582014
skewness(original_data) # calculate Cofficient of skewness
## [1] 0.7385609
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 2.494422
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
autoplot(data_series ,xlab=paste ("Time in ", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE
## Training set 311.1806 6609.909 4202.235 -7.184373 11.59995 0.1055417
## ACF1
## Training set -0.01871398
# Print Model Parameters
model_bats
## BATS(0.497, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 0.497035
## Alpha: 1.141635
## Beta: 0.7277369
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -8.482775
## [2,] 4.013806
## attr(,"lambda")
## [1] 0.4970347
##
## Sigma: 3.544621
## AIC: 6425.073
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$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 USA"
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 USA"
paste(MAPE_Mean_All,"%")
## [1] "0.715 % MAPE 7 days COVID 19 Infection cases in USA %"
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 USA"
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 12246766 12283993
## 2 2020-11-23 понедельник 12418228 12467541
## 3 2020-11-24 вторник 12591163 12652457
## 4 2020-11-25 среда 12772653 12838743
## 5 2020-11-26 четверг 12883264 13026398
## 6 2020-11-27 пятница 13088821 13215423
## 7 2020-11-28 суббота 13244417 13405818
## MAPE_bats_Model
## 1 0.304 %
## 2 0.397 %
## 3 0.487 %
## 4 0.517 %
## 5 1.111 %
## 6 0.967 %
## 7 1.219 %
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 13597582
## 2 2020-11-30 понедельник 13790717
## 3 2020-12-01 вторник 13985221
## 4 2020-12-02 среда 14181096
## 5 2020-12-03 четверг 14378341
## 6 2020-12-04 пятница 14576957
## 7 2020-12-05 суббота 14776943
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 0.998822 103169.8
## MAPE_Mean_All MAD_bats
## 1 0.715 % MAPE 7 days COVID 19 Infection cases in USA 92151.53
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 37227.38 0.304 % 0.303 %
## 2 2020-11-23 понедельник 49312.56 0.397 % 0.396 %
## 3 2020-11-24 вторник 61294.00 0.487 % 0.484 %
## 4 2020-11-25 среда 66089.81 0.517 % 0.515 %
## 5 2020-11-26 четверг 143134.13 1.111 % 1.099 %
## 6 2020-11-27 пятница 126602.07 0.967 % 0.958 %
## 7 2020-11-28 суббота 161400.74 1.219 % 1.204 %
## TBATS Model
# Data Modeling
data_series<-ts(training_data)
model_TBATS<-forecast:::fitSpecificTBATS(data_series,use.box.cox=FALSE, use.beta=TRUE, seasonal.periods=c(6),use.damping=FALSE,k.vector=c(2))
accuracy(model_TBATS) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE
## Training set 914.4552 6658.616 4322.161 -56.85973 3007.343 0.1085537
## ACF1
## Training set 0.009782572
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.198583
## Beta: 0.6440573
## Damping Parameter: 1
## Gamma-1 Values: 3.416932e-06
## Gamma-2 Values: -0.0009812341
##
## Seed States:
## [,1]
## [1,] -3370.3399
## [2,] 185.7172
## [3,] -596.6101
## [4,] 259.2758
## [5,] 110.8531
## [6,] 129.5181
##
## Sigma: 6658.616
## AIC: 7134.932
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 USA"
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 USA"
paste(MAPE_Mean_All,"%")
## [1] "0.556 % MAPE 7 days COVID 19 Infection cases in USA %"
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 USA"
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 12246766 12280961
## 2 2020-11-23 понедельник 12418228 12460894
## 3 2020-11-24 вторник 12591163 12640811
## 4 2020-11-25 среда 12772653 12821175
## 5 2020-11-26 четверг 12883264 13001636
## 6 2020-11-27 пятница 13088821 13180795
## 7 2020-11-28 суббота 13244417 13359875
## MAPE_TBATS_Model
## 1 0.279 %
## 2 0.344 %
## 3 0.394 %
## 4 0.38 %
## 5 0.919 %
## 6 0.703 %
## 7 0.872 %
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 13539808
## 2 2020-11-30 понедельник 13719725
## 3 2020-12-01 вторник 13900089
## 4 2020-12-02 среда 14080550
## 5 2020-12-03 четверг 14259709
## 6 2020-12-04 пятница 14438789
## 7 2020-12-05 суббота 14618722
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 0.9988655 78930.92
## MAPE_Mean_All MAD_tbats
## 1 0.556 % MAPE 7 days COVID 19 Infection cases in USA 71547.75
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_tbats,REOF_A_tbats,REOF_F_tbats) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_tbats REOF_A_tbats REOF_F_tbats
## 1 2020-11-22 воскресенье 34194.51 0.279 % 0.278 %
## 2 2020-11-23 понедельник 42666.22 0.344 % 0.342 %
## 3 2020-11-24 вторник 49647.50 0.394 % 0.393 %
## 4 2020-11-25 среда 48522.03 0.38 % 0.378 %
## 5 2020-11-26 четверг 118372.36 0.919 % 0.91 %
## 6 2020-11-27 пятница 91974.13 0.703 % 0.698 %
## 7 2020-11-28 суббота 115457.53 0.872 % 0.864 %
## 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 299.9498 6764.353 4295.35 0.1075389 3.471672 0.1078803 -0.01140103
# 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= 0.5645
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.905
##
## Initial states:
## l = -1.352
## b = -0.0423
##
## sigma: 8.9136
##
## AIC AICc BIC
## 3085.091 3085.291 3103.692
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 299.9498 6764.353 4295.35 0.1075389 3.471672 0.1078803 -0.01140103
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> COVID 19 Infection cases in USA"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> COVID 19 Infection cases in USA"
paste(MAPE_Mean_All,"%")
## [1] "0.683 % MAPE 7 days COVID 19 Infection cases in USA %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> COVID 19 Infection cases in USA"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2020-11-22 воскресенье 12246766 12285028
## 2 2020-11-23 понедельник 12418228 12467191
## 3 2020-11-24 вторник 12591163 12650521
## 4 2020-11-25 среда 12772653 12835015
## 5 2020-11-26 четверг 12883264 13020671
## 6 2020-11-27 пятница 13088821 13207487
## 7 2020-11-28 суббота 13244417 13395462
## MAPE_holt_Model
## 1 0.312 %
## 2 0.394 %
## 3 0.471 %
## 4 0.488 %
## 5 1.067 %
## 6 0.907 %
## 7 1.14 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2020-11-29 воскресенье 13584592
## 2 2020-11-30 понедельник 13774875
## 3 2020-12-01 вторник 13966311
## 4 2020-12-02 среда 14158896
## 5 2020-12-03 четверг 14352629
## 6 2020-12-04 пятница 14547507
## 7 2020-12-05 суббота 14743529
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 0.9988338 97870.52
## MAPE_Mean_All MAD_Holt
## 1 0.683 % MAPE 7 days COVID 19 Infection cases in USA 88008.89
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 38262.07 0.312 % 0.311 %
## 2 2020-11-23 понедельник 48963.09 0.394 % 0.393 %
## 3 2020-11-24 вторник 59357.70 0.471 % 0.469 %
## 4 2020-11-25 среда 62361.70 0.488 % 0.486 %
## 5 2020-11-26 четверг 137406.94 1.067 % 1.055 %
## 6 2020-11-27 пятница 118666.25 0.907 % 0.898 %
## 7 2020-11-28 суббота 151044.50 1.14 % 1.128 %
#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 USA"
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 = 4.9261, 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) = 2.8043, 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 = 2.192, 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 USA"
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 = 3.2879, 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) = 1.7973, 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 = 4.4347, 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 USA"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.63643, Truncation lag parameter = 5, p-value = 0.01932
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) = -235.18, 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 = -5.6385, 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) : 6212
## ARIMA(0,2,1) : 6211.772
## ARIMA(0,2,2) : 6201.66
## ARIMA(0,2,3) : 6199.609
## ARIMA(0,2,4) : 6175.255
## ARIMA(0,2,5) : 6197.879
## ARIMA(1,2,0) : 6212.497
## ARIMA(1,2,1) : 6203.812
## ARIMA(1,2,2) : 6201.308
## ARIMA(1,2,3) : 6199.108
## ARIMA(1,2,4) : 6147.698
## ARIMA(2,2,0) : 6207.999
## ARIMA(2,2,1) : 6198.815
## ARIMA(2,2,2) : 6122.805
## ARIMA(2,2,3) : 6200.991
## ARIMA(3,2,0) : 6202.602
## ARIMA(3,2,1) : 6196.018
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 6197.556
## ARIMA(4,2,1) : 6192.262
## ARIMA(5,2,0) : 6166.48
##
##
##
## Best model: ARIMA(2,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2454 -0.8517 -1.5330 0.8997
## s.e. 0.0371 0.0525 0.0527 0.0271
##
## sigma^2 estimated as 33963590: log likelihood=-3056.3
## AIC=6122.6 AICc=6122.8 BIC=6141.17
#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("[ ]*$", "", result)
}
return(result)
}
source("stringthearima.R")
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2454 -0.8517 -1.5330 0.8997
## s.e. 0.0371 0.0525 0.0527 0.0271
##
## sigma^2 estimated as 33515226: log likelihood = -3056.3, aic = 6122.6
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> COVID 19 Infection cases in USA"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 954.8594 5770.221 3537.249 1.065116 2.660938 0.08884012
## ACF1
## Training set -0.07778797
x1_model1$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* = 79.178, df = 6, p-value = 5.329e-15
##
## 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 USA"
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 = 225.56, 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 = 1120.5, 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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> COVID 19 Infection cases in USA"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> COVID 19 Infection cases in USA"
paste(MAPE_Mean_All,"%")
## [1] "0.281 % MAPE 7 days COVID 19 Infection cases in USA %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> COVID 19 Infection cases in USA"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2020-11-22 воскресенье 12246766 12268907
## 2 2020-11-23 понедельник 12418228 12429410
## 3 2020-11-24 вторник 12591163 12595706
## 4 2020-11-25 среда 12772653 12772943
## 5 2020-11-26 четверг 12883264 12958871
## 6 2020-11-27 пятница 13088821 13146305
## 7 2020-11-28 суббота 13244417 13328213
## MAPE_auto.arima_Model
## 1 0.181 %
## 2 0.09 %
## 3 0.036 %
## 4 0.002 %
## 5 0.587 %
## 6 0.439 %
## 7 0.633 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2020-11-29 воскресенье 13501956
## 2 2020-11-30 понедельник 13670237
## 3 2020-12-01 вторник 13838669
## 4 2020-12-02 среда 14011940
## 5 2020-12-03 четверг 14191110
## 6 2020-12-04 пятница 14373506
## 7 2020-12-05 суббота 14554894
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 0.9981032 48812.35
## MAPE_Mean_All MAD_auto.arima
## 1 0.281 % MAPE 7 days COVID 19 Infection cases in USA 36434.71
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 22141.1357 0.181 %
## 2 2020-11-23 понедельник 11181.5880 0.09 %
## 3 2020-11-24 вторник 4543.3001 0.036 %
## 4 2020-11-25 среда 290.3628 0.002 %
## 5 2020-11-26 четверг 75607.0518 0.587 %
## 6 2020-11-27 пятница 57483.7846 0.439 %
## 7 2020-11-28 суббота 83795.7144 0.633 %
## REOF_F_auto.arima
## 1 0.18 %
## 2 0.09 %
## 3 0.036 %
## 4 0.002 %
## 5 0.583 %
## 6 0.437 %
## 7 0.629 %
# 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
## 0.023168796 0.007366625
# 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 MAPE_Mean_All
## 1 0.9987319 1182565 9.283 % MAPE 7 days COVID 19 Infection cases in USA
## MAD_SIR
## 1 1182338
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 1193462 9.745 % 10.797 %
## 2 2020-11-23 понедельник 1197626 9.644 % 10.673 %
## 3 2020-11-24 вторник 1200931 9.538 % 10.544 %
## 4 2020-11-25 среда 1210432 9.477 % 10.469 %
## 5 2020-11-26 четверг 1146669 8.9 % 9.77 %
## 6 2020-11-27 пятница 1175439 8.98 % 9.867 %
## 7 2020-11-28 суббота 1151810 8.697 % 9.525 %
## validation_forecast testing_data
## 1 11053304 12246766
## 2 11220602 12418228
## 3 11390232 12591163
## 4 11562221 12772653
## 5 11736595 12883264
## 6 11913382 13088821
## 7 12092607 13244417
## 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.11015019 0.09183258
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)
## FD forecating_date forecasting_by_SIR
## 1 2020-11-29 воскресенье 12246766
## 2 2020-11-30 понедельник 12419901
## 3 2020-12-01 вторник 12590001
## 4 2020-12-02 среда 12756823
## 5 2020-12-03 четверг 12920125
## 6 2020-12-04 пятница 13079668
## 7 2020-12-05 суббота 13235212
# 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 USA"
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 USA"
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 USA"
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 USA"
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 USA"
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 USA"
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 0.3039772 0.2792126
## 2 2020-11-23 понедельник 0.3970982 0.3435774
## 3 2020-11-24 вторник 0.4868017 0.3943043
## 4 2020-11-25 среда 0.5174322 0.3798900
## 5 2020-11-26 четверг 1.1110083 0.9188072
## 6 2020-11-27 пятница 0.9672534 0.7026922
## 7 2020-11-28 суббота 1.2186323 0.8717449
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.3124259 0.180791694
## 2 0.3942840 0.090041735
## 3 0.4714235 0.036083245
## 4 0.4882439 0.002273316
## 5 1.0665538 0.586862551
## 6 0.9066229 0.439182296
## 7 1.1404390 0.632687074
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 USA"
best_recommended_model
## [1] 0.2811317
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> COVID 19 Infection cases in USA"
if(best_recommended_model >= M1) {paste("System Recommend Bats Model That's better For forecasting==> ",y_lab, sep=" ")}
if(best_recommended_model >= M2) {paste("System Recommend That's better TBATS For forecasting ==> ",y_lab, sep=" ")}
if(best_recommended_model >= M3) {paste("System Recommend Holt's Linear Model < Exponential Smoothing Model > That's better For forecasting ==> ",y_lab, sep=" ")}
if(best_recommended_model >= M4) {paste("System Recommend auto arima Model That's better For forecasting ==> ",y_lab, sep=" ")}
## [1] "System Recommend auto arima Model That's better For forecasting ==> COVID 19 Infection cases in USA"
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 USA
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 USA
## 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,] 0.3286477 0.3335583 0.3377939
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")
