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/Regin In Russia 29_11_2020.xlsx",sheet = "Chelyabinsk region")
y_lab<- "COVID 19 Infection cases in Chelyabinsk region" # 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 <-1130319 # Population size in City for applaying SIR model
# Data Preparation & calculate some of statistics measures
original_data<-Full_original_data$infection
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 1525 9946 9449 15331 24973
sd(original_data) # calculate standard deviation
## [1] 7486.128
skewness(original_data) # calculate Cofficient of skewness
## [1] 0.1732697
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 1.77532
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
autoplot(data_series ,xlab=paste ("Time in ", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 1.303325 13.62489 8.140653 NaN Inf 0.08918101 -0.001222465
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.055851
## Beta: 0.6679532
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -6.176125
## [2,] -5.825195
##
## Sigma: 13.62489
## AIC: 2764.857
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$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 Chelyabinsk region"
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 Chelyabinsk region"
paste(MAPE_Mean_All,"%")
## [1] "0.259 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region %"
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 Chelyabinsk region"
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 23496 23494.25
## 2 2020-11-23 понедельник 23719 23711.29
## 3 2020-11-24 вторник 23947 23928.32
## 4 2020-11-25 среда 24188 24145.36
## 5 2020-11-26 четверг 24440 24362.40
## 6 2020-11-27 пятница 24701 24579.44
## 7 2020-11-28 суббота 24973 24796.48
## MAPE_bats_Model
## 1 0.007 %
## 2 0.033 %
## 3 0.078 %
## 4 0.176 %
## 5 0.318 %
## 6 0.492 %
## 7 0.707 %
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 25013.52
## 2 2020-11-30 понедельник 25230.55
## 3 2020-12-01 вторник 25447.59
## 4 2020-12-02 среда 25664.63
## 5 2020-12-03 четверг 25881.67
## 6 2020-12-04 пятница 26098.71
## 7 2020-12-05 суббота 26315.74
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 0.9993435 87.98434
## MAPE_Mean_All MAD_bats
## 1 0.259 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region 63.78074
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 1.752550 0.007 % 0.007 %
## 2 2020-11-23 понедельник 7.714328 0.033 % 0.033 %
## 3 2020-11-24 вторник 18.676106 0.078 % 0.078 %
## 4 2020-11-25 среда 42.637884 0.176 % 0.177 %
## 5 2020-11-26 четверг 77.599662 0.318 % 0.319 %
## 6 2020-11-27 пятница 121.561440 0.492 % 0.495 %
## 7 2020-11-28 суббота 176.523218 0.707 % 0.712 %
## 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 1.288604 13.40525 8.294981 NaN Inf 0.09087168 -0.002631398
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.0549
## Beta: 0.679838
## Damping Parameter: 1
## Gamma-1 Values: -0.002854131
## Gamma-2 Values: 0.002116084
##
## Seed States:
## [,1]
## [1,] -6.4357280
## [2,] -5.7209404
## [3,] 0.9525842
## [4,] -0.6092764
## [5,] 1.8923816
## [6,] 0.3628063
##
## Sigma: 13.40525
## AIC: 2768.536
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 Chelyabinsk region"
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 Chelyabinsk region"
paste(MAPE_Mean_All,"%")
## [1] "0.23 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region %"
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 Chelyabinsk region"
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 23496 23495.53
## 2 2020-11-23 понедельник 23719 23713.80
## 3 2020-11-24 вторник 23947 23934.98
## 4 2020-11-25 среда 24188 24155.75
## 5 2020-11-26 четверг 24440 24371.91
## 6 2020-11-27 пятница 24701 24588.50
## 7 2020-11-28 суббота 24973 24806.80
## MAPE_TBATS_Model
## 1 0.002 %
## 2 0.022 %
## 3 0.05 %
## 4 0.133 %
## 5 0.279 %
## 6 0.455 %
## 7 0.666 %
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 25025.07
## 2 2020-11-30 понедельник 25246.25
## 3 2020-12-01 вторник 25467.02
## 4 2020-12-02 среда 25683.19
## 5 2020-12-03 четверг 25899.78
## 6 2020-12-04 пятница 26118.08
## 7 2020-12-05 суббота 26336.35
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 0.9992241 81.17533
## MAPE_Mean_All MAD_tbats
## 1 0.23 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region 56.67648
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 0.4730111 0.002 % 0.002 %
## 2 2020-11-23 понедельник 5.2005034 0.022 % 0.022 %
## 3 2020-11-24 вторник 12.0247469 0.05 % 0.05 %
## 4 2020-11-25 среда 32.2506072 0.133 % 0.134 %
## 5 2020-11-26 четверг 68.0892084 0.279 % 0.279 %
## 6 2020-11-27 пятница 112.4986602 0.455 % 0.458 %
## 7 2020-11-28 суббота 166.1986201 0.666 % 0.67 %
## 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 0.5645154 13.72531 8.252742 NaN Inf 0.09040895 0.07040979
# 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= 0.7518
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.6551
##
## Initial states:
## l = -2.0004
## b = -0.1621
##
## sigma: 2.2406
##
## AIC AICc BIC
## 1838.581 1838.821 1856.307
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.5645154 13.72531 8.252742 NaN Inf 0.09040895 0.07040979
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> COVID 19 Infection cases in Chelyabinsk region"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> COVID 19 Infection cases in Chelyabinsk region"
paste(MAPE_Mean_All,"%")
## [1] "0.233 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> COVID 19 Infection cases in Chelyabinsk region"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2020-11-22 воскресенье 23496 23494.65
## 2 2020-11-23 понедельник 23719 23712.80
## 3 2020-11-24 вторник 23947 23931.46
## 4 2020-11-25 среда 24188 24150.60
## 5 2020-11-26 четверг 24440 24370.25
## 6 2020-11-27 пятница 24701 24590.38
## 7 2020-11-28 суббота 24973 24811.01
## MAPE_holt_Model
## 1 0.006 %
## 2 0.026 %
## 3 0.065 %
## 4 0.155 %
## 5 0.285 %
## 6 0.448 %
## 7 0.649 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2020-11-29 воскресенье 25032.13
## 2 2020-11-30 понедельник 25253.73
## 3 2020-12-01 вторник 25475.81
## 4 2020-12-02 среда 25698.38
## 5 2020-12-03 четверг 25921.42
## 6 2020-12-04 пятница 26144.94
## 7 2020-12-05 суббота 26368.94
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 0.9994123 80.19753
## MAPE_Mean_All MAD_Holt
## 1 0.233 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region 57.54857
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 1.349110 0.006 % 0.006 %
## 2 2020-11-23 понедельник 6.196339 0.026 % 0.026 %
## 3 2020-11-24 вторник 15.544264 0.065 % 0.065 %
## 4 2020-11-25 среда 37.395189 0.155 % 0.155 %
## 5 2020-11-26 четверг 69.751389 0.285 % 0.286 %
## 6 2020-11-27 пятница 110.615114 0.448 % 0.45 %
## 7 2020-11-28 суббота 161.988591 0.649 % 0.653 %
#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 Chelyabinsk region"
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 = 4.3421, 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) = -3.7306, Truncation lag parameter = 5, p-value
## = 0.9009
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -2.4425, Lag order = 6, p-value = 0.3895
## 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 Chelyabinsk region"
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 = 1.7061, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -6.6049, Truncation lag parameter = 5, p-value
## = 0.7397
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.98881, Lag order = 6, p-value = 0.9389
## 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 Chelyabinsk region"
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 = 0.13267, 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) = -277.38, 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 = -7.0415, 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) : 2068.079
## ARIMA(0,2,1) : 2053.64
## ARIMA(0,2,2) : 2055.032
## ARIMA(0,2,3) : 2051.817
## ARIMA(0,2,4) : 2052.36
## ARIMA(0,2,5) : 2049.213
## ARIMA(1,2,0) : 2054.906
## ARIMA(1,2,1) : 2053.539
## ARIMA(1,2,2) : 2055.122
## ARIMA(1,2,3) : 2053.426
## ARIMA(1,2,4) : 2050.519
## ARIMA(2,2,0) : 2056.588
## ARIMA(2,2,1) : 2054.786
## ARIMA(2,2,2) : 2056.403
## ARIMA(2,2,3) : 2053.244
## ARIMA(3,2,0) : 2057.104
## ARIMA(3,2,1) : 2054.427
## ARIMA(3,2,2) : 2052.079
## ARIMA(4,2,0) : 2046.353
## ARIMA(4,2,1) : 2046.943
## ARIMA(5,2,0) : 2047.731
##
##
##
## Best model: ARIMA(4,2,0)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(4,2,0)
##
## Coefficients:
## ar1 ar2 ar3 ar4
## -0.2703 -0.0700 -0.1335 -0.2203
## s.e. 0.0610 0.0628 0.0625 0.0607
##
## sigma^2 estimated as 180: log likelihood=-1018.06
## AIC=2046.11 AICc=2046.35 BIC=2063.8
#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("[ ]*$", "", result)
}
return(result)
}
source("stringthearima.R")
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 4 2 0
strtoi(bestmodel[3])
## [1] 0
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ar4
## -0.2703 -0.0700 -0.1335 -0.2203
## s.e. 0.0610 0.0628 0.0625 0.0607
##
## sigma^2 estimated as 177.2: log likelihood = -1018.06, aic = 2046.11
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> COVID 19 Infection cases in Chelyabinsk region"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 1.435101 13.25908 8.083879 0.6111157 2.781743 0.08855906
## ACF1
## Training set -0.0008462041
x1_model1$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(4,2,0)
## Q* = 3.5355, df = 6, p-value = 0.7392
##
## 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 Chelyabinsk region"
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 = 72, df = 20, p-value = 8.558e-08
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 773.82, 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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> COVID 19 Infection cases in Chelyabinsk region"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> COVID 19 Infection cases in Chelyabinsk region"
paste(MAPE_Mean_All,"%")
## [1] "0.263 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> COVID 19 Infection cases in Chelyabinsk region"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2020-11-22 воскресенье 23496 23493.27
## 2 2020-11-23 понедельник 23719 23710.25
## 3 2020-11-24 вторник 23947 23927.80
## 4 2020-11-25 среда 24188 24144.28
## 5 2020-11-26 четверг 24440 24361.30
## 6 2020-11-27 пятница 24701 24578.02
## 7 2020-11-28 суббота 24973 24794.79
## MAPE_auto.arima_Model
## 1 0.012 %
## 2 0.037 %
## 3 0.08 %
## 4 0.181 %
## 5 0.322 %
## 6 0.498 %
## 7 0.714 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2020-11-29 воскресенье 25011.74
## 2 2020-11-30 понедельник 25228.55
## 3 2020-12-01 вторник 25445.45
## 4 2020-12-02 среда 25662.30
## 5 2020-12-03 четверг 25879.14
## 6 2020-12-04 пятница 26096.00
## 7 2020-12-05 суббота 26312.84
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 0.9993289 88.99512
## MAPE_Mean_All
## 1 0.263 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region
## MAD_auto.arima
## 1 64.89781
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 2.725618 0.012 %
## 2 2020-11-23 понедельник 8.754141 0.037 %
## 3 2020-11-24 вторник 19.195955 0.08 %
## 4 2020-11-25 среда 43.716343 0.181 %
## 5 2020-11-26 четверг 78.699214 0.322 %
## 6 2020-11-27 пятница 122.983753 0.498 %
## 7 2020-11-28 суббота 178.209642 0.714 %
## REOF_F_auto.arima
## 1 0.012 %
## 2 0.037 %
## 3 0.08 %
## 4 0.181 %
## 5 0.323 %
## 6 0.5 %
## 7 0.719 %
# 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
## 0.09747856 0.08558046
# 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 0.9989854 1579.909
## MAPE_Mean_All MAD_SIR
## 1 6.517 % MAPE 7 days COVID 19 Infection cases in Chelyabinsk region 1578.448
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 1512.000 6.435 % 6.878 %
## 2 2020-11-23 понедельник 1516.025 6.392 % 6.828 %
## 3 2020-11-24 вторник 1526.966 6.376 % 6.811 %
## 4 2020-11-25 среда 1552.951 6.42 % 6.861 %
## 5 2020-11-26 четверг 1592.113 6.514 % 6.968 %
## 6 2020-11-27 пятница 1642.584 6.65 % 7.124 %
## 7 2020-11-28 суббота 1706.495 6.833 % 7.335 %
## validation_forecast testing_data
## 1 21984.00 23496
## 2 22202.97 23719
## 3 22420.03 23947
## 4 22635.05 24188
## 5 22847.89 24440
## 6 23058.42 24701
## 7 23266.51 24973
## 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.03218839 0.02148695
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)
## FD forecating_date forecasting_by_SIR
## 1 2020-11-29 воскресенье 23496.00
## 2 2020-11-30 понедельник 23732.66
## 3 2020-12-01 вторник 23971.18
## 4 2020-12-02 среда 24211.59
## 5 2020-12-03 четверг 24453.88
## 6 2020-12-04 пятница 24698.05
## 7 2020-12-05 суббота 24944.10
# 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 Chelyabinsk region"
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 Chelyabinsk region"
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 Chelyabinsk region"
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 Chelyabinsk region"
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 Chelyabinsk region"
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 Chelyabinsk region"
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 0.007458928 0.002013156
## 2 2020-11-23 понедельник 0.032523832 0.021925475
## 3 2020-11-24 вторник 0.077989334 0.050214001
## 4 2020-11-25 среда 0.176277013 0.133333088
## 5 2020-11-26 четверг 0.317510892 0.278597416
## 6 2020-11-27 пятница 0.492131654 0.455441724
## 7 2020-11-28 суббота 0.706856277 0.665513235
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.00574187 0.01160035
## 2 0.02612395 0.03690772
## 3 0.06491111 0.08016017
## 4 0.15460224 0.18073567
## 5 0.28539848 0.32200988
## 6 0.44781634 0.49788977
## 7 0.64865491 0.71360927
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 Chelyabinsk region"
best_recommended_model
## [1] 0.2295769
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> COVID 19 Infection cases in Chelyabinsk region"
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 Chelyabinsk region"
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 Chelyabinsk region
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 Chelyabinsk region
## 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,] 0.3300215 0.333295 0.3366835
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")
