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("data2.xlsx", sheet = "Northwestern federal") # path of your data ( time series data)
## New names:
## * region -> region...2
## * infection -> infection...3
## * `daily infection` -> `daily infection...4`
## * region -> region...5
## * infection -> infection...6
## * ...
original_data<-Full_original_data$`total cumulative`
y_lab <- "Cumulative Covid 19 Infection cases in Northwestern federal district" # input name of data
Actual_date_interval <- c("2020/03/12","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 <- "Northwestern federal"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3 41761 101522 227453 404191 752960
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.406617
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.9852895
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 249396.4
#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 93366
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 Northwestern federal district"
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 Northwestern federal district"
paste(MAPE_Mean_All,"%")
## [1] "0.373 % MAPE 8 days Cumulative Covid 19 Infection cases in Northwestern federal district %"
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 Northwestern federal district"
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 | 741441.00 | 740869.14 | 0.077 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 743126.00 | 741973.29 | 0.155 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 744787.00 | 743036.55 | 0.235 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 746451.00 | 744060.03 | 0.32 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 748114.00 | 745044.85 | 0.41 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 749767.00 | 745992.10 | 0.503 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 751374.00 | 746902.90 | 0.595 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 752960.00 | 747778.33 | 0.688 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 748619.48 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 749427.43 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 750203.23 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 750947.93 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 751662.56 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 752348.14 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 753005.65 |
## +---+------------+-----------------+---------------------+
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 -1.612712 129.858 71.3306 -0.0594215 1.716986 0.03538951 0.1311178
# Print Model Parameters
model_bats
## BATS(0.784, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 0.783993
## Alpha: 0.8069522
## Beta: 1.119741
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 4.483888
## [2,] 0.218112
## attr(,"lambda")
## [1] 0.7839929
##
## Sigma: 9.762625
## AIC: 5616.92
#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 Northwestern federal district"
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 Northwestern federal district"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.036 % MAPE 8 days Cumulative Covid 19 Infection cases in Northwestern federal district %"
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 Northwestern federal district"
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 | 741441.00 | 741456.52 | 0.002 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 743126.00 | 743188.15 | 0.008 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 744787.00 | 744920.65 | 0.018 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 746451.00 | 746654.03 | 0.027 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 748114.00 | 748388.27 | 0.037 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 749767.00 | 750123.38 | 0.048 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 751374.00 | 751859.36 | 0.065 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 752960.00 | 753596.20 | 0.084 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 755333.91 | 751126.01 | 748900.54 | 751126.01 | 748900.54 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 757072.48 | 752159.25 | 749561.14 | 752159.25 | 749561.14 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 758811.92 | 753157.46 | 750167.87 | 753157.46 | 750167.87 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 760552.22 | 754122.22 | 750723.17 | 754122.22 | 750723.17 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 762293.38 | 755054.94 | 751229.19 | 755054.94 | 751229.19 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 764035.39 | 755956.84 | 751687.83 | 755956.84 | 751687.83 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 765778.27 | 756829.00 | 752100.77 | 756829.00 | 752100.77 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 3.873287 127.376 73.20898 -2.46485 9.245983 0.03632144 0.001952941
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.8532059
## Beta: 1.212943
## Damping Parameter: 1
## Gamma-1 Values: -0.00103686
## Gamma-2 Values: -0.0005047292
##
## Seed States:
## [,1]
## [1,] -0.9670880
## [2,] 21.4344391
## [3,] 24.1887327
## [4,] 0.8512691
## [5,] 1.0317889
## [6,] -1.8261845
##
## Sigma: 127.376
## AIC: 5761.672
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 Northwestern federal district"
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 Northwestern federal district"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.044 % MAPE 8 days Cumulative Covid 19 Infection cases in Northwestern federal district %"
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 Northwestern federal district"
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 | 741441.00 | 741450.56 | 0.001 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-16 | Tuesday | 743126.00 | 743186.20 | 0.008 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-17 | Wednesday | 744787.00 | 744946.01 | 0.021 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-18 | Thursday | 746451.00 | 746725.15 | 0.037 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-19 | Friday | 748114.00 | 748486.46 | 0.05 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-20 | Saturday | 749767.00 | 750222.65 | 0.061 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-21 | Sunday | 751374.00 | 751952.52 | 0.077 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-03-22 | Monday | 752960.00 | 753688.17 | 0.097 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 755447.97 | 755023.66 | 754799.04 | 755872.28 | 756096.89 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 757227.11 | 756780.99 | 756544.82 | 757673.24 | 757909.40 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 758988.42 | 758521.54 | 758274.38 | 759455.31 | 759702.46 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 760724.61 | 760237.87 | 759980.21 | 761211.36 | 761469.02 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 762454.48 | 761948.75 | 761681.04 | 762960.21 | 763227.93 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 764190.13 | 763666.21 | 763388.87 | 764714.04 | 764991.38 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 765949.93 | 765408.45 | 765121.81 | 766491.40 | 766778.04 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 -20.9203 147.8625 85.73987 0.0311053 1.171692 0.04253844 0.4613606
# 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= 0.4004
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.6413
##
## Initial states:
## l = 0.5334
## b = 0.6754
##
## sigma: 0.3316
##
## AIC AICc BIC
## 1367.722 1367.888 1387.262
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -20.9203 147.8625 85.73987 0.0311053 1.171692 0.04253844 0.4613606
# 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 Northwestern federal district"
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 Northwestern federal district"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.039 % MAPE 8 days Cumulative Covid 19 Infection cases in Northwestern federal district %"
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 Northwestern federal district"
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 | 741441.00 | 741454.96 | 0.002 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 743126.00 | 743189.35 | 0.009 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 744787.00 | 744926.17 | 0.019 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 746451.00 | 746665.42 | 0.029 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 748114.00 | 748407.10 | 0.039 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 749767.00 | 750151.22 | 0.051 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 751374.00 | 751897.77 | 0.07 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 752960.00 | 753646.75 | 0.091 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 755398.18 | 738750.25 | 730027.28 | 772269.02 | 781290.49 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 757152.04 | 737947.42 | 727900.64 | 776653.22 | 787097.09 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 758908.34 | 737028.43 | 725600.95 | 781173.12 | 793115.94 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 760667.08 | 735998.44 | 723136.58 | 785824.90 | 799341.76 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 762428.26 | 734862.04 | 720515.11 | 790605.33 | 805770.15 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 764191.89 | 733623.38 | 717743.40 | 795511.58 | 812397.37 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 765957.95 | 732286.25 | 714827.76 | 800541.24 | 819220.28 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 Northwestern federal district"
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 = 5.2296, 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) = -0.29982, Truncation lag parameter = 5,
## p-value = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -3.621, Lag order = 7, p-value = 0.03118
## 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 Northwestern federal district"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 3.7122, 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) = -0.27115, 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 = -1.1907, Lag order = 7, p-value = 0.9071
## 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 Northwestern federal district"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.48078, Truncation lag parameter = 5, p-value = 0.046
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) = -380.32, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
## Warning in adf.test(diff2_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -4.389, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
####Fitting an ARIMA Model
#1. Using auto arima function
model1 <- auto.arima(data_series,stepwise=FALSE, approximation=FALSE, trace=T, test = c("kpss", "adf", "pp")) #applaying auto arima
##
## ARIMA(0,2,0) : 4607.44
## ARIMA(0,2,1) : 4607.363
## ARIMA(0,2,2) : 4601.231
## ARIMA(0,2,3) : 4603.274
## ARIMA(0,2,4) : 4605.217
## ARIMA(0,2,5) : 4605.343
## ARIMA(1,2,0) : 4606.741
## ARIMA(1,2,1) : 4585.683
## ARIMA(1,2,2) : 4603.274
## ARIMA(1,2,3) : Inf
## ARIMA(1,2,4) : 4586.083
## ARIMA(2,2,0) : 4600.859
## ARIMA(2,2,1) : 4587.061
## ARIMA(2,2,2) : 4588.459
## ARIMA(2,2,3) : 4589.976
## ARIMA(3,2,0) : 4602.883
## ARIMA(3,2,1) : Inf
## ARIMA(3,2,2) : 4590.17
## ARIMA(4,2,0) : 4604.595
## ARIMA(4,2,1) : 4586.953
## ARIMA(5,2,0) : 4599.097
##
##
##
## Best model: ARIMA(1,2,1)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,1)
##
## Coefficients:
## ar1 ma1
## 0.9754 -0.9179
## s.e. 0.0157 0.0254
##
## sigma^2 estimated as 15982: log likelihood=-2289.81
## AIC=4585.62 AICc=4585.68 BIC=4597.32
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 1
strtoi(bestmodel[3])
## [1] 1
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1
## 0.9754 -0.9179
## s.e. 0.0157 0.0254
##
## sigma^2 estimated as 15895: log likelihood = -2289.81, aic = 4585.62
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in Northwestern federal district"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 0.836599 125.732 68.97266 0.1302945 1.006391 0.03421966
## ACF1
## Training set -0.03976314
x1_model1$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(1,2,1)
## Q* = 23.896, df = 8, p-value = 0.002386
##
## Model df: 2. 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 Northwestern federal district"
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 = 150.17, 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 = 3460.3, 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 Northwestern federal district"
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 Northwestern federal district"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.002 % MAPE 8 days Cumulative Covid 19 Infection cases in Northwestern federal district %"
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 Northwestern federal district"
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 | 741441.00 | 741435.98 | 0.001 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-16 | Tuesday | 743126.00 | 743132.34 | 0.001 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-17 | Wednesday | 744787.00 | 744812.52 | 0.003 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-18 | Thursday | 746451.00 | 746476.89 | 0.003 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-19 | Friday | 748114.00 | 748125.85 | 0.002 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-20 | Saturday | 749767.00 | 749759.78 | 0.001 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-21 | Sunday | 751374.00 | 751379.04 | 0.001 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-03-22 | Monday | 752960.00 | 752984.00 | 0.003 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 754575.02 | 751387.59 | 749700.27 | 757762.44 | 759449.77 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 756152.42 | 752385.59 | 750391.55 | 759919.26 | 761913.30 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 757716.55 | 753327.81 | 751004.55 | 762105.30 | 764428.56 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 759267.74 | 754214.83 | 751539.98 | 764320.65 | 766995.50 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 760806.29 | 755047.17 | 751998.47 | 766565.42 | 769614.12 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 762332.53 | 755825.31 | 752380.60 | 768839.75 | 772284.47 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 763846.76 | 756549.71 | 752686.89 | 771143.80 | 775006.62 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "0.002 % MAPE 8 days Cumulative Covid 19 Infection cases in Northwestern federal district"
# 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 Northwestern federal district"
best_recommended_model
## [1] 0.002
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 Northwestern federal district"
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 | 755333.91 | 751126.01 | 748900.54 | 751126.01 | 748900.54 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 757072.48 | 752159.25 | 749561.14 | 752159.25 | 749561.14 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 758811.92 | 753157.46 | 750167.87 | 753157.46 | 750167.87 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 760552.22 | 754122.22 | 750723.17 | 754122.22 | 750723.17 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 762293.38 | 755054.94 | 751229.19 | 755054.94 | 751229.19 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 764035.39 | 755956.84 | 751687.83 | 755956.84 | 751687.83 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 765778.27 | 756829.00 | 752100.77 | 756829.00 | 752100.77 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in Northwestern federal district"
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 | 755447.97 | 755023.66 | 754799.04 | 755872.28 | 756096.89 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 757227.11 | 756780.99 | 756544.82 | 757673.24 | 757909.40 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 758988.42 | 758521.54 | 758274.38 | 759455.31 | 759702.46 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 760724.61 | 760237.87 | 759980.21 | 761211.36 | 761469.02 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 762454.48 | 761948.75 | 761681.04 | 762960.21 | 763227.93 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 764190.13 | 763666.21 | 763388.87 | 764714.04 | 764991.38 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 765949.93 | 765408.45 | 765121.81 | 766491.40 | 766778.04 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 Northwestern federal district"
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 | 755398.18 | 738750.25 | 730027.28 | 772269.02 | 781290.49 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 757152.04 | 737947.42 | 727900.64 | 776653.22 | 787097.09 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 758908.34 | 737028.43 | 725600.95 | 781173.12 | 793115.94 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 760667.08 | 735998.44 | 723136.58 | 785824.90 | 799341.76 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 762428.26 | 734862.04 | 720515.11 | 790605.33 | 805770.15 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 764191.89 | 733623.38 | 717743.40 | 795511.58 | 812397.37 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 765957.95 | 732286.25 | 714827.76 | 800541.24 | 819220.28 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in Northwestern federal district"
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 | 754575.02 | 751387.59 | 749700.27 | 757762.44 | 759449.77 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 756152.42 | 752385.59 | 750391.55 | 759919.26 | 761913.30 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 757716.55 | 753327.81 | 751004.55 | 762105.30 | 764428.56 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 759267.74 | 754214.83 | 751539.98 | 764320.65 | 766995.50 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 760806.29 | 755047.17 | 751998.47 | 766565.42 | 769614.12 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 762332.53 | 755825.31 | 752380.60 | 768839.75 | 772284.47 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 763846.76 | 756549.71 | 752686.89 | 771143.80 | 775006.62 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in Northwestern federal district"
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 | 748619.48 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 749427.43 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 750203.23 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 750947.93 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 751662.56 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 752348.14 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 753005.65 |
## +---+------------+-----------------+---------------------+
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 | Northwestern federal | 0.373 | 0.036 | 0.044 | 0.039 | 0.002 | 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 Northwestern federal district
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 Northwestern federal district