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 = "Infection and deaths") # path of your data ( time series data)
original_data<-Full_original_data$Cumulative_cases
y_lab <- "Cumulative Covid 19 Infection cases in Russia" # input name of data
Actual_date_interval <- c("2020/03/01","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.
## 0 62773 902701 1383053 2322056 4466153
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.389869
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.874069
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 1439672
#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 3346033
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 Covid 19 Infection cases in Russia"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_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 Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "0.399 % MAPE 8 days Cumulative Covid 19 Infection 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 Covid 19 Infection 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 | 4400045.00 | 4396619.43 | 0.078 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 4409438.00 | 4402402.14 | 0.16 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 4418436.00 | 4407962.24 | 0.237 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 4428239.00 | 4413305.87 | 0.337 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 4437938.00 | 4418439.21 | 0.439 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 4447570.00 | 4423368.42 | 0.544 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 4456869.00 | 4428099.66 | 0.646 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 4466153.00 | 4432639.05 | 0.75 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 4436992.69 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 4441166.61 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 4445166.78 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 4448999.08 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 4452669.32 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 4456183.21 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 4459546.35 |
## +---+------------+-----------------+---------------------+
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 25.15711 582.7157 354.5365 NaN Inf 0.0352065 -0.001728585
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.039472
## Beta: 0.9161858
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -29.75345
## [2,] -11.74250
##
## Sigma: 582.7157
## AIC: 8230.3
#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 Covid 19 Infection 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 Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.063 % MAPE 8 days Cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in bats Model for ==> Cumulative Covid 19 Infection 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 | 4400045.00 | 4400676.45 | 0.014 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 4409438.00 | 4410736.93 | 0.029 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 4418436.00 | 4420797.42 | 0.053 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 4428239.00 | 4430857.91 | 0.059 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 4437938.00 | 4440918.40 | 0.067 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 4447570.00 | 4450978.89 | 0.077 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 4456869.00 | 4461039.38 | 0.094 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 4466153.00 | 4471099.86 | 0.111 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 4481160.35 | 4469365.72 | 4463122.01 | 4469365.72 | 4463122.01 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4491220.84 | 4477538.98 | 4470296.24 | 4477538.98 | 4470296.24 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4501281.33 | 4485621.52 | 4477331.72 | 4485621.52 | 4477331.72 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4511341.82 | 4493617.30 | 4484234.51 | 4493617.30 | 4484234.51 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4521402.31 | 4501529.81 | 4491009.95 | 4501529.81 | 4491009.95 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4531462.79 | 4509362.14 | 4497662.76 | 4509362.14 | 4497662.76 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4541523.28 | 4517117.07 | 4504197.21 | 4517117.07 | 4504197.21 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 ACF1
## Training set 25.27537 579.8485 363.7035 NaN Inf 0.0361168 -0.001662375
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.043996
## Beta: 0.9176685
## Damping Parameter: 1
## Gamma-1 Values: -0.001292311
## Gamma-2 Values: 0.001648065
##
## Seed States:
## [,1]
## [1,] -31.661891
## [2,] -11.043865
## [3,] -0.458230
## [4,] 7.717451
## [5,] 14.705122
## [6,] -10.889494
##
## Sigma: 579.8485
## AIC: 8237.989
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 Covid 19 Infection 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 Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.071 % MAPE 8 days Cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in TBATS Model for ==> Cumulative Covid 19 Infection 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 | 4400045.00 | 4400764.69 | 0.016 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-16 | Tuesday | 4409438.00 | 4410944.95 | 0.034 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-17 | Wednesday | 4418436.00 | 4421021.77 | 0.059 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-18 | Thursday | 4428239.00 | 4431164.66 | 0.066 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-19 | Friday | 4437938.00 | 4441318.23 | 0.076 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-20 | Saturday | 4447570.00 | 4451369.82 | 0.085 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-21 | Sunday | 4456869.00 | 4461514.17 | 0.104 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-03-22 | Monday | 4466153.00 | 4471694.43 | 0.124 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 4481771.25 | 4479466.02 | 4478245.71 | 4484076.47 | 4485296.78 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4491914.14 | 4489484.32 | 4488198.05 | 4494343.95 | 4495630.22 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4502067.71 | 4499519.29 | 4498170.24 | 4504616.13 | 4505965.18 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4512119.30 | 4509458.81 | 4508050.44 | 4514779.78 | 4516188.16 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4522263.65 | 4519496.16 | 4518031.13 | 4525031.14 | 4526496.16 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4532443.91 | 4529573.01 | 4528053.25 | 4535314.81 | 4536834.58 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4542520.73 | 4539550.34 | 4537977.91 | 4545491.12 | 4547063.55 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -55.9422 620.1378 388.3759 NaN Inf 0.03856685 0.3258833
# 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= 0.5767
##
## Smoothing parameters:
## alpha = 0.9539
## beta = 0.6273
##
## Initial states:
## l = -2.116
## b = -0.4662
##
## sigma: 3.1369
##
## AIC AICc BIC
## 3662.093 3662.232 3682.493
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -55.9422 620.1378 388.3759 NaN Inf 0.03856685 0.3258833
# 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 Covid 19 Infection 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 Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.059 % MAPE 8 days Cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in holt Model for ==> Cumulative Covid 19 Infection 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 | 4400045.00 | 4400599.40 | 0.013 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 4409438.00 | 4410613.24 | 0.027 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 4418436.00 | 4420636.70 | 0.05 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 4428239.00 | 4430669.79 | 0.055 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 4437938.00 | 4440712.51 | 0.063 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 4447570.00 | 4450764.86 | 0.072 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 4456869.00 | 4460826.82 | 0.089 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 4466153.00 | 4470898.40 | 0.106 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 4480979.59 | 4450870.30 | 4434966.20 | 4511174.75 | 4527193.84 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4491070.39 | 4456309.86 | 4437955.04 | 4525945.17 | 4544452.97 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4501170.79 | 4461537.75 | 4440617.38 | 4540952.10 | 4562071.00 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4511280.80 | 4466562.76 | 4442966.84 | 4556187.26 | 4580035.47 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4521400.41 | 4471392.62 | 4445015.45 | 4571643.42 | 4598335.54 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4531529.61 | 4476034.22 | 4446773.98 | 4587314.18 | 4616961.62 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4541668.41 | 4480493.75 | 4448252.09 | 4603193.86 | 4635905.22 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 Covid 19 Infection cases in Russia"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 6.5745, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
## Warning in pp.test(data_series): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -0.48438, Truncation lag parameter = 5,
## p-value = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -4.5839, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), 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 Covid 19 Infection cases in Russia"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 5.0793, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = 0.29677, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -1.0773, Lag order = 7, p-value = 0.9258
## 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 Covid 19 Infection cases in Russia"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.54629, Truncation lag parameter = 5, p-value = 0.03124
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) = -434.59, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -3.6028, Lag order = 7, p-value = 0.03267
## 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) : 6779.927
## ARIMA(0,2,1) : 6781.103
## ARIMA(0,2,2) : 6782.424
## ARIMA(0,2,3) : 6784.46
## ARIMA(0,2,4) : 6785.434
## ARIMA(0,2,5) : 6767.101
## ARIMA(1,2,0) : 6781.174
## ARIMA(1,2,1) : 6782.767
## ARIMA(1,2,2) : 6784.464
## ARIMA(1,2,3) : Inf
## ARIMA(1,2,4) : 6742.862
## ARIMA(2,2,0) : 6782.404
## ARIMA(2,2,1) : 6784.436
## ARIMA(2,2,2) : 6786.477
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 6784.417
## ARIMA(3,2,1) : Inf
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 6786.343
## ARIMA(4,2,1) : 6787.598
## ARIMA(5,2,0) : 6787.26
##
##
##
## 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
## 0.7260 -0.8919 -0.0502 0.0903 0.2498
## s.e. 0.0659 0.0728 0.0678 0.0603 0.0529
##
## sigma^2 estimated as 309952: log likelihood=-3365.33
## AIC=6742.67 AICc=6742.86 BIC=6767.12
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 4
strtoi(bestmodel[3])
## [1] 4
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4
## 0.7260 -0.8919 -0.0502 0.0903 0.2498
## s.e. 0.0659 0.0728 0.0678 0.0603 0.0529
##
## sigma^2 estimated as 306389: log likelihood = -3365.33, aic = 6742.67
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in Russia"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 15.82418 552.2563 338.285 0.3190848 2.3107 0.03359268 0.01194082
x1_model1$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* = 52.45, df = 5, p-value = 4.361e-10
##
## 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 Covid 19 Infection cases in Russia"
Box.test(x1_model1$residuals^2, lag=20, type="Ljung-Box") # Do test for resdulas by using Box-Ljung test , Ljung-Box test For Modelling
##
## Box-Ljung test
##
## data: x1_model1$residuals^2
## X-squared = 533.65, df = 20, p-value < 2.2e-16
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 157.49, 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 Covid 19 Infection 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 Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.009 % MAPE 8 days Cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in bats Model for ==> Cumulative Covid 19 Infection 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 | 4400045.00 | 4400169.26 | 0.003 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-16 | Tuesday | 4409438.00 | 4409488.83 | 0.001 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-17 | Wednesday | 4418436.00 | 4418823.26 | 0.009 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-18 | Thursday | 4428239.00 | 4428352.24 | 0.003 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-19 | Friday | 4437938.00 | 4438022.45 | 0.002 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-20 | Saturday | 4447570.00 | 4447795.21 | 0.005 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-21 | Sunday | 4456869.00 | 4457642.42 | 0.017 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-03-22 | Monday | 4466153.00 | 4467543.68 | 0.031 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 4477484.18 | 4466772.94 | 4461102.76 | 4488195.42 | 4493865.61 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4487453.17 | 4474612.97 | 4467815.78 | 4500293.38 | 4507090.57 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4497442.85 | 4482288.24 | 4474265.87 | 4512597.46 | 4520619.83 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4507447.55 | 4489804.22 | 4480464.40 | 4525090.88 | 4534430.69 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4517463.14 | 4497166.97 | 4486422.83 | 4537759.31 | 4548503.46 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4527486.66 | 4504382.69 | 4492152.19 | 4550590.62 | 4562821.12 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4537515.92 | 4511457.40 | 4497662.85 | 4563574.43 | 4577368.98 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.009 % MAPE 8 days Cumulative Covid 19 Infection 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 Covid 19 Infection cases in Russia"
best_recommended_model
## [1] 0.009
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 Covid 19 Infection 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 | 4481160.35 | 4469365.72 | 4463122.01 | 4469365.72 | 4463122.01 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4491220.84 | 4477538.98 | 4470296.24 | 4477538.98 | 4470296.24 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4501281.33 | 4485621.52 | 4477331.72 | 4485621.52 | 4477331.72 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4511341.82 | 4493617.30 | 4484234.51 | 4493617.30 | 4484234.51 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4521402.31 | 4501529.81 | 4491009.95 | 4501529.81 | 4491009.95 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4531462.79 | 4509362.14 | 4497662.76 | 4509362.14 | 4497662.76 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4541523.28 | 4517117.07 | 4504197.21 | 4517117.07 | 4504197.21 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection 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 | 4481771.25 | 4479466.02 | 4478245.71 | 4484076.47 | 4485296.78 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4491914.14 | 4489484.32 | 4488198.05 | 4494343.95 | 4495630.22 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4502067.71 | 4499519.29 | 4498170.24 | 4504616.13 | 4505965.18 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4512119.30 | 4509458.81 | 4508050.44 | 4514779.78 | 4516188.16 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4522263.65 | 4519496.16 | 4518031.13 | 4525031.14 | 4526496.16 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4532443.91 | 4529573.01 | 4528053.25 | 4535314.81 | 4536834.58 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4542520.73 | 4539550.34 | 4537977.91 | 4545491.12 | 4547063.55 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Cumulative Covid 19 Infection 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 | 4480979.59 | 4450870.30 | 4434966.20 | 4511174.75 | 4527193.84 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4491070.39 | 4456309.86 | 4437955.04 | 4525945.17 | 4544452.97 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4501170.79 | 4461537.75 | 4440617.38 | 4540952.10 | 4562071.00 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4511280.80 | 4466562.76 | 4442966.84 | 4556187.26 | 4580035.47 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4521400.41 | 4471392.62 | 4445015.45 | 4571643.42 | 4598335.54 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4531529.61 | 4476034.22 | 4446773.98 | 4587314.18 | 4616961.62 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4541668.41 | 4480493.75 | 4448252.09 | 4603193.86 | 4635905.22 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection 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 | 4477484.18 | 4466772.94 | 4461102.76 | 4488195.42 | 4493865.61 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-03-24 | Wednesday | 4487453.17 | 4474612.97 | 4467815.78 | 4500293.38 | 4507090.57 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-03-25 | Thursday | 4497442.85 | 4482288.24 | 4474265.87 | 4512597.46 | 4520619.83 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-03-26 | Friday | 4507447.55 | 4489804.22 | 4480464.40 | 4525090.88 | 4534430.69 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-03-27 | Saturday | 4517463.14 | 4497166.97 | 4486422.83 | 4537759.31 | 4548503.46 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-03-28 | Sunday | 4527486.66 | 4504382.69 | 4492152.19 | 4550590.62 | 4562821.12 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-03-29 | Monday | 4537515.92 | 4511457.40 | 4497662.85 | 4563574.43 | 4577368.98 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection 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 | 4436992.69 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 4441166.61 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 4445166.78 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 4448999.08 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 4452669.32 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 4456183.21 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 4459546.35 |
## +---+------------+-----------------+---------------------+
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 | 0.399 | 0.063 | 0.071 | 0.059 | 0.009 | 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 Covid 19 Infection 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 Covid 19 Infection cases in Russia