South ural state university, Chelyabinsk, Russian federation
#Import
library(fpp2)
## 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
##
library(forecast)
library(ggplot2)
library("readxl")
library(moments)
library(forecast)
require(forecast)
require(tseries)
## Loading required package: tseries
require(markovchain)
## Loading required package: markovchain
## 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
library(Hmisc)
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(ascii)
library(pander)
##
## Attaching package: 'pander'
## The following object is masked from 'package:ascii':
##
## Pandoc
##Global vriable##
Full_original_data <- read_excel("data.xlsx", sheet = "Vaccine") # path of your data ( time series data)
original_data<-Full_original_data$Vaccine
y_lab <- "Cumulative vaccination Covid 19 cases in Russia" # input name of data
Actual_date_interval <- c("2020/12/16","2021/03/22")
Forecast_date_interval <- c("2021/03/23","2021/03/29")
validation_data_days <-8
Number_Neural<-5 # Number of Neural For model NNAR Model
NNAR_Model<- TRUE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Russia"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3357 854298 2742279 3068390 4797696 8092201
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.025165
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.4625011
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 2470098
#processing on data (input data)
rows <- NROW(original_data) # calculate number of rows in time series (number of days)
training_data<-original_data[1:(rows-validation_data_days)] # Training data
testing_data<-original_data[(rows-validation_data_days+1):rows] #testing data
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)) #calculate number of days that you want to forecasting
validation_dates<-tail(AD,validation_data_days) # select validation_dates
validation_data_by_name<-weekdays(validation_dates) # put names of validation dates
forecasting_data_by_name<-weekdays(FD) # put names of Forecasting dates
#NNAR Model
if(NNAR_Model==TRUE){
data_series<-ts(training_data)
model_NNAR<-nnetar(data_series, size = Number_Neural)
saveRDS(model_NNAR, file = "model_NNAR.RDS")
my_model <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
## Series: data_series
## Model: NNAR(1,5)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 1-5-1 network with 16 weights
## options were - linear output units
##
## sigma^2 estimated as 407520513
if(NNAR_Model==FALSE){
data_series<-ts(training_data)
#model_NNAR<-nnetar(data_series, size = Number_Numeral)
model_NNAR <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
# Testing Data Evaluation
forecasting_NNAR <- forecast(model_NNAR, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_NNAR$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 NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 8 days by using NNAR Model for ==> Cumulative vaccination Covid 19 cases in Russia"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Mean_All_NNAR<-round(mean(MAPE_Per_Day),3)
MAPE_NNAR<-paste(round(MAPE_Per_Day,3),"%")
MAPE_NNAR_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 8 days in NNAR Model for ==> Cumulative vaccination Covid 19 cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "4.747 % MAPE 8 days Cumulative vaccination Covid 19 cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in NNAR Model for ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(date_NNAR=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_NNAR=validation_forecast,MAPE_NNAR_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_NNAR | validation_data_by_name | actual_data | forecasting_NNAR | MAPE_NNAR_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-03-15 | Monday | 7344639.00 | 7270453.46 | 1.01 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 7499489.00 | 7323941.07 | 2.341 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 7609472.00 | 7359186.35 | 3.289 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 7700258.00 | 7381895.12 | 4.134 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 7805641.00 | 7396311.22 | 5.244 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 7900944.00 | 7405375.85 | 6.272 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 7995756.00 | 7411041.06 | 7.313 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 8092201.00 | 7414568.21 | 8.374 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-03-23 | Tuesday | 7416758.97 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 7418117.66 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 7418959.53 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 7419480.87 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 7419803.61 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 7420003.35 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 7420126.96 |
## +---+------------+-----------------+---------------------+
plot(forecasting_NNAR,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph1<-autoplot(forecasting_NNAR,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph1
##bats model
# Data Modeling
data_series<-ts(training_data) # make your data to time series
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 1548.089 17746.45 7972.698 16.3128 49.46082 0.09759931 0.005464383
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 1
## Alpha: 0.8716822
## Beta: 1.044995
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -93019.016
## [2,] 3860.791
## attr(,"lambda")
## [1] 1
##
## Sigma: 17746.44
## AIC: 2151.03
#ploting BATS Model
plot(model_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "))
# 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 8 days by using bats Model for ==> Cumulative vaccination Covid 19 cases in Russia"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-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 8 days in bats Model for ==> Cumulative vaccination Covid 19 cases in Russia"
paste(MAPE_Mean_All.bats,"%")
## [1] "1.485 % MAPE 8 days Cumulative vaccination Covid 19 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 8 days in bats Model for ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_bats | validation_data_by_name | actual_data | forecasting_bats | MAPE_bats_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-03-15 | Monday | 7344639.00 | 7339702.11 | 0.067 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 7499489.00 | 7487542.31 | 0.159 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 7609472.00 | 7635382.51 | 0.341 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 7700258.00 | 7783222.72 | 1.077 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 7805641.00 | 7931062.92 | 1.607 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 7900944.00 | 8078903.12 | 2.252 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 7995756.00 | 8226743.32 | 2.889 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 8092201.00 | 8374583.52 | 3.49 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+============+============+============+============+
## | 1 | 2021-03-23 | Tuesday | 8522423.73 | 8131512.25 | 7924576.21 | 8131512.25 | 7924576.21 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 8670263.93 | 8214810.81 | 7973708.50 | 8214810.81 | 7973708.50 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 8818104.13 | 8294904.80 | 8017939.81 | 8294904.80 | 8017939.81 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 8965944.33 | 8371939.75 | 8057492.72 | 8371939.75 | 8057492.72 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 9113784.53 | 8446042.86 | 8092561.77 | 8446042.86 | 8092561.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 9261624.74 | 8517326.60 | 8123318.97 | 8517326.60 | 8123318.97 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 9409464.94 | 8585891.37 | 8149917.85 | 8585891.37 | 8149917.85 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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=" "), ylab=y_lab)
graph1
## 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 3386.069 36603.97 18568.06 50.61896 120.5399 0.2273044
## ACF1
## Training set -0.002627535
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.9842787
## Beta: 0.5003967
## Damping Parameter: 1
## Gamma-1 Values: -0.00336074
## Gamma-2 Values: 0.0005554326
##
## Seed States:
## [,1]
## [1,] -263682.8534
## [2,] 11966.3201
## [3,] 454.0979
## [4,] 3937.1547
## [5,] 9238.1052
## [6,] 2660.4872
##
## Sigma: 36603.97
## AIC: 2289.897
plot(model_TBATS,xlab = paste ("Time in", frequency ,y_lab , sep=" "), 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 8 days by using TBATS Model for ==> Cumulative vaccination Covid 19 cases in Russia"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-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 8 days in TBATS Model for ==> Cumulative vaccination Covid 19 cases in Russia"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "2.375 % MAPE 8 days Cumulative vaccination Covid 19 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 8 days in TBATS Model for ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | | date_TBATS | validation_data_by_name | actual_data | forecasting_TBATS | MAPE_TBATS_Model |
## +===+============+=========================+=============+===================+==================+
## | 1 | 2021-03-15 | Monday | 7344639.00 | 7350189.59 | 0.076 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-16 | Tuesday | 7499489.00 | 7529721.12 | 0.403 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-17 | Wednesday | 7609472.00 | 7697515.57 | 1.157 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-18 | Thursday | 7700258.00 | 7854985.79 | 2.009 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-19 | Friday | 7805641.00 | 8017295.73 | 2.712 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-20 | Saturday | 7900944.00 | 8168591.80 | 3.388 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-21 | Sunday | 7995756.00 | 8326785.22 | 4.14 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-03-22 | Monday | 8092201.00 | 8506316.75 | 5.117 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+============+============+============+============+
## | 1 | 2021-03-23 | Tuesday | 8674111.21 | 8537295.42 | 8464869.52 | 8810926.99 | 8883352.90 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 8831581.43 | 8687604.50 | 8611387.72 | 8975558.35 | 9051775.13 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 8993891.36 | 8843111.51 | 8763293.47 | 9144671.22 | 9224489.26 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 9145187.43 | 8987983.22 | 8904764.33 | 9302391.65 | 9385610.53 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 9303380.86 | 9140090.28 | 9053649.46 | 9466671.44 | 9553112.25 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 9482912.39 | 9313799.85 | 9224277.08 | 9652024.93 | 9741547.70 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 9650706.84 | 9475990.19 | 9383500.79 | 9825423.49 | 9917912.90 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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=" "), ylab=y_lab)
graph2
## 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 -26.93708 11291.17 6149.15 -0.4359066 1.814672 0.075276 0.5493567
# 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= 0.6147
##
## Smoothing parameters:
## alpha = 0.9984
## beta = 0.9984
##
## Initial states:
## l = -17.3592
## b = 260.4519
##
## sigma: 44.2008
##
## AIC AICc BIC
## 1079.792 1080.515 1092.235
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -26.93708 11291.17 6149.15 -0.4359066 1.814672 0.075276 0.5493567
# 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 8 days by using holt Model for ==> Cumulative vaccination Covid 19 cases in Russia"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-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 8 days in holt Model for ==> Cumulative vaccination Covid 19 cases in Russia"
paste(MAPE_Mean_All.Holt,"%")
## [1] "1.752 % MAPE 8 days Cumulative vaccination Covid 19 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 8 days in holt Model for ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_holt | validation_data_by_name | actual_data | forecasting_holt | MAPE_holt_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-03-15 | Monday | 7344639.00 | 7342149.28 | 0.034 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 7499489.00 | 7493581.89 | 0.079 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 7609472.00 | 7646203.02 | 0.483 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 7700258.00 | 7800007.19 | 1.295 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 7805641.00 | 7954989.02 | 1.913 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 7900944.00 | 8111143.19 | 2.66 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 7995756.00 | 8268464.50 | 3.411 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 8092201.00 | 8426947.82 | 4.137 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+============+============+=============+=============+
## | 1 | 2021-03-23 | Tuesday | 8586588.09 | 8142575.66 | 7911222.34 | 9039629.93 | 9283074.59 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 2 | 2021-03-24 | Wednesday | 8747380.35 | 8228409.84 | 7958658.33 | 9278496.85 | 9564513.64 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 3 | 2021-03-25 | Thursday | 8909319.71 | 8311085.97 | 8000921.64 | 9523449.97 | 9854902.93 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 4 | 2021-03-26 | Friday | 9072401.35 | 8390718.98 | 8038214.64 | 9774419.75 | 10154159.33 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 5 | 2021-03-27 | Saturday | 9236620.54 | 8467408.74 | 8070716.53 | 10031351.07 | 10462221.27 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 6 | 2021-03-28 | Sunday | 9401972.59 | 8541243.08 | 8098587.96 | 10294200.22 | 10779044.12 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 7 | 2021-03-29 | Monday | 9568452.92 | 8612300.06 | 8121974.51 | 10562932.69 | 11104596.88 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
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=" "), ylab=y_lab)
graph3
#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 ==> Cumulative vaccination Covid 19 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 = 2.2785, Truncation lag parameter = 3, 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) = -0.65233, Truncation lag parameter = 3,
## p-value = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -0.58768, Lag order = 4, p-value = 0.976
## 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=" "), ylab=y_lab,main = "1nd differenced series")
##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 ==> Cumulative vaccination Covid 19 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 = 1.2711, Truncation lag parameter = 3, 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) = -10.76, Truncation lag parameter = 3, p-value
## = 0.4862
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -3.5844, Lag order = 4, p-value = 0.03935
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##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 Cumulative vaccination Covid 19 cases in Russia"
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 = 0.049076, Truncation lag parameter = 3, 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) = -38.546, Truncation lag parameter = 3, 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 = -3.5403, Lag order = 4, p-value = 0.04332
## 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) : 1875.29
## ARIMA(0,2,1) : 1852.518
## ARIMA(0,2,2) : 1848.255
## ARIMA(0,2,3) : 1848.912
## ARIMA(0,2,4) : 1844.181
## ARIMA(0,2,5) : Inf
## ARIMA(1,2,0) : 1844.406
## ARIMA(1,2,1) : 1846.544
## ARIMA(1,2,2) : 1848.66
## ARIMA(1,2,3) : 1850.911
## ARIMA(1,2,4) : 1838.57
## ARIMA(2,2,0) : 1846.543
## ARIMA(2,2,1) : Inf
## ARIMA(2,2,2) : Inf
## ARIMA(2,2,3) : 1842.612
## ARIMA(3,2,0) : 1848.644
## ARIMA(3,2,1) : Inf
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 1850.896
## ARIMA(4,2,1) : Inf
## ARIMA(5,2,0) : 1852.281
##
##
##
## Best model: ARIMA(1,2,4)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,4)
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4
## -0.7740 1.5186 0.8987 0.3513 0.2825
## s.e. 0.1193 0.1511 0.2162 0.1931 0.1060
##
## sigma^2 estimated as 78032351: log likelihood=-912.76
## AIC=1837.52 AICc=1838.57 BIC=1852.32
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 4
strtoi(bestmodel[3])
## [1] 4
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4
## -0.7740 1.5186 0.8987 0.3513 0.2825
## s.e. 0.1193 0.1511 0.2162 0.1931 0.1060
##
## sigma^2 estimated as 73547733: log likelihood = -912.76, aic = 1837.52
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative vaccination Covid 19 cases in Russia"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 667.1011 8479.09 3850.22 0.4710244 0.6254332 0.0471332
## ACF1
## Training set 0.0003793958
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,2,4)
## Q* = 13.064, df = 5, p-value = 0.02279
##
## Model df: 5. 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 ==> Cumulative vaccination Covid 19 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 = 31.095, df = 20, p-value = 0.05395
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 588.61, 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='black')
#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 8 days by using bats Model for ==> Cumulative vaccination Covid 19 cases in Russia"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-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 8 days in bats Model for ==> Cumulative vaccination Covid 19 cases in Russia"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "1.081 % MAPE 8 days Cumulative vaccination Covid 19 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 8 days in bats Model for ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)), type = "rest")
##
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | | date_auto.arima | validation_data_by_name | actual_data | forecasting_auto.arima | MAPE_auto.arima_Model |
## +===+=================+=========================+=============+========================+=======================+
## | 1 | 2021-03-15 | Monday | 7344639.00 | 7328249.75 | 0.223 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-16 | Tuesday | 7499489.00 | 7471398.11 | 0.375 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-17 | Wednesday | 7609472.00 | 7608716.90 | 0.01 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-18 | Thursday | 7700258.00 | 7749252.94 | 0.636 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-19 | Friday | 7805641.00 | 7887298.91 | 1.046 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-20 | Saturday | 7900944.00 | 8027272.13 | 1.599 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-21 | Sunday | 7995756.00 | 8165753.70 | 2.126 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-03-22 | Monday | 8092201.00 | 8305389.77 | 2.634 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+===========================+============+============+=============+=============+
## | 1 | 2021-03-23 | Tuesday | 8444132.29 | 8080171.51 | 7887502.30 | 8808093.08 | 9000762.28 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 2 | 2021-03-24 | Wednesday | 8583566.40 | 8154224.73 | 7926944.98 | 9012908.06 | 9240187.81 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 3 | 2021-03-25 | Thursday | 8722465.23 | 8224098.64 | 7960279.31 | 9220831.82 | 9484651.16 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 4 | 2021-03-26 | Friday | 8861778.35 | 8291124.16 | 7989038.07 | 9432432.55 | 9734518.63 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 5 | 2021-03-27 | Saturday | 9000770.83 | 8354563.82 | 8012482.49 | 9646977.84 | 9989059.16 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 6 | 2021-03-28 | Sunday | 9140011.47 | 8415230.74 | 8031555.00 | 9864792.21 | 10248467.95 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 7 | 2021-03-29 | Monday | 9279060.04 | 8472716.93 | 8045864.68 | 10085403.15 | 10512255.41 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
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=" "), ylab=y_lab)
graph4
MAPE_Mean_All.ARIMA
## [1] "1.081 % MAPE 8 days Cumulative vaccination Covid 19 cases in Russia"
# Table for MAPE For counry
best_recommended_model <- min(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
paste("System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> Cumulative vaccination Covid 19 cases in Russia"
best_recommended_model
## [1] 1.081
x1<-if(best_recommended_model >= MAPE_Mean_All.bats_Model) {paste("BATS Model")}
x2<-if(best_recommended_model >= MAPE_Mean_All.TBATS_Model) {paste("TBATS Model")}
x3<-if(best_recommended_model >= MAPE_Mean_All.Holt_Model) {paste("Holt Model")}
x4<-if(best_recommended_model >= MAPE_Mean_All.ARIMA_Model) {paste("ARIMA Model")}
x5<-if(best_recommended_model >= MAPE_Mean_All_NNAR) {paste("NNAR Model")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+============+============+============+============+
## | 1 | 2021-03-23 | Tuesday | 8522423.73 | 8131512.25 | 7924576.21 | 8131512.25 | 7924576.21 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 8670263.93 | 8214810.81 | 7973708.50 | 8214810.81 | 7973708.50 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 8818104.13 | 8294904.80 | 8017939.81 | 8294904.80 | 8017939.81 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 8965944.33 | 8371939.75 | 8057492.72 | 8371939.75 | 8057492.72 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 9113784.53 | 8446042.86 | 8092561.77 | 8446042.86 | 8092561.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 9261624.74 | 8517326.60 | 8123318.97 | 8517326.60 | 8123318.97 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 9409464.94 | 8585891.37 | 8149917.85 | 8585891.37 | 8149917.85 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+============+============+============+============+
## | 1 | 2021-03-23 | Tuesday | 8674111.21 | 8537295.42 | 8464869.52 | 8810926.99 | 8883352.90 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 8831581.43 | 8687604.50 | 8611387.72 | 8975558.35 | 9051775.13 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 8993891.36 | 8843111.51 | 8763293.47 | 9144671.22 | 9224489.26 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 9145187.43 | 8987983.22 | 8904764.33 | 9302391.65 | 9385610.53 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 9303380.86 | 9140090.28 | 9053649.46 | 9466671.44 | 9553112.25 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 9482912.39 | 9313799.85 | 9224277.08 | 9652024.93 | 9741547.70 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 9650706.84 | 9475990.19 | 9383500.79 | 9825423.49 | 9917912.90 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+============+============+=============+=============+
## | 1 | 2021-03-23 | Tuesday | 8586588.09 | 8142575.66 | 7911222.34 | 9039629.93 | 9283074.59 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 2 | 2021-03-24 | Wednesday | 8747380.35 | 8228409.84 | 7958658.33 | 9278496.85 | 9564513.64 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 3 | 2021-03-25 | Thursday | 8909319.71 | 8311085.97 | 8000921.64 | 9523449.97 | 9854902.93 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 4 | 2021-03-26 | Friday | 9072401.35 | 8390718.98 | 8038214.64 | 9774419.75 | 10154159.33 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 5 | 2021-03-27 | Saturday | 9236620.54 | 8467408.74 | 8070716.53 | 10031351.07 | 10462221.27 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 6 | 2021-03-28 | Sunday | 9401972.59 | 8541243.08 | 8098587.96 | 10294200.22 | 10779044.12 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
## | 7 | 2021-03-29 | Monday | 9568452.92 | 8612300.06 | 8121974.51 | 10562932.69 | 11104596.88 |
## +---+------------+-----------------+---------------------+------------+------------+-------------+-------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+===========================+============+============+=============+=============+
## | 1 | 2021-03-23 | Tuesday | 8444132.29 | 8080171.51 | 7887502.30 | 8808093.08 | 9000762.28 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 2 | 2021-03-24 | Wednesday | 8583566.40 | 8154224.73 | 7926944.98 | 9012908.06 | 9240187.81 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 3 | 2021-03-25 | Thursday | 8722465.23 | 8224098.64 | 7960279.31 | 9220831.82 | 9484651.16 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 4 | 2021-03-26 | Friday | 8861778.35 | 8291124.16 | 7989038.07 | 9432432.55 | 9734518.63 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 5 | 2021-03-27 | Saturday | 9000770.83 | 8354563.82 | 8012482.49 | 9646977.84 | 9989059.16 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 6 | 2021-03-28 | Sunday | 9140011.47 | 8415230.74 | 8031555.00 | 9864792.21 | 10248467.95 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
## | 7 | 2021-03-29 | Monday | 9279060.04 | 8472716.93 | 8045864.68 | 10085403.15 | 10512255.41 |
## +---+------------+-----------------+---------------------------+------------+------------+-------------+-------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative vaccination Covid 19 cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-03-23 | Tuesday | 7416758.97 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 7418117.66 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 7418959.53 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 7419480.87 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 7419803.61 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 7420003.35 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 7420126.96 |
## +---+------------+-----------------+---------------------+
result<-c(x1,x2,x3,x4,x5)
table.error<-data.frame(country.name,NNAR.model=MAPE_Mean_All_NNAR, BATS.Model=MAPE_Mean_All.bats_Model,TBATS.Model=MAPE_Mean_All.TBATS_Model,Holt.Model=MAPE_Mean_All.Holt_Model,ARIMA.Model=MAPE_Mean_All.ARIMA_Model,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+=============+======+
## | 1 | Russia | 4.747 | 1.485 | 2.375 | 1.752 | 1.081 | ARIMA Model | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend, and ARIMA Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend, and ARIMA Model ==>Cumulative vaccination Covid 19 cases in Russia
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Cumulative vaccination Covid 19 cases in Russia