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 = "Southern Federal District") # 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$`cumulative total`
y_lab <- "Cumulative Covid 19 Infection cases in Southern Federal" # 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 <- "Southern Federal District"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1 22827 64384 95729 164820 273442
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.088367
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.682925
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 87550.88
#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 9541
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 Southern Federal"
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 Southern Federal"
paste(MAPE_Mean_All,"%")
## [1] "0.327 % MAPE 8 days Cumulative Covid 19 Infection cases in Southern Federal %"
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 Southern Federal"
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 | 268817.00 | 268654.75 | 0.06 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 269483.00 | 269145.48 | 0.125 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 270140.00 | 269617.59 | 0.193 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 270808.00 | 270071.48 | 0.272 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 271469.00 | 270507.59 | 0.354 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 272129.00 | 270926.35 | 0.442 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 272787.00 | 271328.22 | 0.535 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 273442.00 | 271713.66 | 0.632 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 272083.13 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 272437.10 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 272776.06 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 273100.47 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 273410.80 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 273707.53 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 273991.13 |
## +---+------------+-----------------+---------------------+
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
## Training set 1.877316 38.22179 26.40946 0.07289587 2.395833 0.03614577
## ACF1
## Training set 0.02789552
# Print Model Parameters
model_bats
## BATS(0.931, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 0.930722
## Alpha: 1.03506
## Beta: 0.6770765
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -1.6931384
## [2,] 0.4883351
## attr(,"lambda")
## [1] 0.9307222
##
## Sigma: 18.62793
## AIC: 4859.112
#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 Southern Federal"
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 Southern Federal"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.048 % MAPE 8 days Cumulative Covid 19 Infection cases in Southern Federal %"
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 Southern Federal"
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 | 268817.00 | 268837.34 | 0.008 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 269483.00 | 269530.44 | 0.018 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 270140.00 | 270223.65 | 0.031 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 270808.00 | 270916.99 | 0.04 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 271469.00 | 271610.45 | 0.052 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 272129.00 | 272304.04 | 0.064 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 272787.00 | 272997.75 | 0.077 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 273442.00 | 273691.57 | 0.091 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 274385.53 | 273681.25 | 273308.48 | 273681.25 | 273308.48 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275079.60 | 274266.96 | 273836.84 | 274266.96 | 273836.84 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275773.79 | 274847.76 | 274357.63 | 274847.76 | 274357.63 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276468.11 | 275423.84 | 274871.15 | 275423.84 | 274871.15 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277162.54 | 275995.40 | 275377.69 | 275995.40 | 275377.69 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 277857.10 | 276562.60 | 275877.50 | 276562.60 | 275877.50 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278551.78 | 277125.58 | 276370.80 | 277125.58 | 276370.80 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
plot(forecasting_bats)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph1<-autoplot(forecasting_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph1
## TBATS Model
# Data Modeling
data_series<-ts(training_data)
model_TBATS<-forecast:::fitSpecificTBATS(data_series,use.box.cox=FALSE, use.beta=TRUE, seasonal.periods=c(6),use.damping=FALSE,k.vector=c(2))
accuracy(model_TBATS) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE
## Training set 2.605122 38.31939 26.39515 -0.2857782 16.93239 0.03612618
## ACF1
## Training set -0.006820461
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.029283
## Beta: 0.7189152
## Damping Parameter: 1
## Gamma-1 Values: -0.0008719278
## Gamma-2 Values: -0.0007839451
##
## Seed States:
## [,1]
## [1,] -25.21851586
## [2,] 2.50361949
## [3,] -0.96876475
## [4,] -0.31383009
## [5,] -0.81339188
## [6,] 0.02190382
##
## Sigma: 38.31939
## AIC: 4877.598
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 Southern Federal"
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 Southern Federal"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.045 % MAPE 8 days Cumulative Covid 19 Infection cases in Southern Federal %"
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 Southern Federal"
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 | 268817.00 | 268836.90 | 0.007 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-16 | Tuesday | 269483.00 | 269529.29 | 0.017 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-17 | Wednesday | 270140.00 | 270221.87 | 0.03 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-18 | Thursday | 270808.00 | 270912.49 | 0.039 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-19 | Friday | 271469.00 | 271602.58 | 0.049 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-20 | Saturday | 272129.00 | 272294.73 | 0.061 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-21 | Sunday | 272787.00 | 272987.20 | 0.073 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-03-22 | Monday | 273442.00 | 273679.59 | 0.087 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 274372.17 | 274221.56 | 274141.83 | 274522.79 | 274602.52 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275062.79 | 274904.04 | 274820.00 | 275221.53 | 275305.57 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275752.88 | 275586.41 | 275498.29 | 275919.35 | 276007.48 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276445.03 | 276271.17 | 276179.13 | 276618.89 | 276710.93 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277137.50 | 276956.58 | 276860.80 | 277318.43 | 277414.21 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 277829.89 | 277642.21 | 277542.86 | 278017.58 | 278116.93 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278522.47 | 278328.27 | 278225.46 | 278716.68 | 278819.49 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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
## Training set -5.531665 41.94443 31.19858 0.4405242 1.625699 0.04270048
## ACF1
## Training set 0.3790028
# 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= 0.5438
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.3886
##
## Initial states:
## l = 0.1014
## b = -0.266
##
## sigma: 0.6028
##
## AIC AICc BIC
## 1807.581 1807.746 1827.121
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -5.531665 41.94443 31.19858 0.4405242 1.625699 0.04270048
## ACF1
## Training set 0.3790028
# 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 Southern Federal"
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 Southern Federal"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.071 % MAPE 8 days Cumulative Covid 19 Infection cases in Southern Federal %"
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 Southern Federal"
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 | 268817.00 | 268849.91 | 0.012 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 269483.00 | 269555.67 | 0.027 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 270140.00 | 270262.26 | 0.045 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 270808.00 | 270969.70 | 0.06 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 271469.00 | 271677.99 | 0.077 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 272129.00 | 272387.12 | 0.095 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 272787.00 | 273097.09 | 0.114 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 273442.00 | 273807.91 | 0.134 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 274519.56 | 272596.03 | 271580.28 | 276449.26 | 277473.28 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275232.06 | 273038.15 | 271880.00 | 277433.99 | 278602.86 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275945.41 | 273469.41 | 272162.83 | 278431.58 | 279751.80 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276659.59 | 273890.22 | 272429.35 | 279441.67 | 280919.55 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277374.62 | 274300.91 | 272680.12 | 280463.95 | 282105.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 278090.49 | 274701.81 | 272915.62 | 281498.12 | 283309.67 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278807.20 | 275093.19 | 273136.31 | 282543.93 | 284531.21 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 Southern Federal"
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 = 5.8251, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -0.96265, Truncation lag parameter = 5,
## p-value = 0.9879
## 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 = -4.3493, 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 Southern Federal"
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 = 5.0107, 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) = 2.1123, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = 0.56681, Lag order = 7, p-value = 0.99
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), 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 Southern Federal"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
## Warning in kpss.test(diff2_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.7522, Truncation lag parameter = 5, p-value = 0.01
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) = -416.46, 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 = -4.7988, 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) : 3733.606
## ARIMA(0,2,1) : 3712.593
## ARIMA(0,2,2) : 3714.362
## ARIMA(0,2,3) : 3713.732
## ARIMA(0,2,4) : 3715.578
## ARIMA(0,2,5) : 3716.926
## ARIMA(1,2,0) : 3716.38
## ARIMA(1,2,1) : 3714.486
## ARIMA(1,2,2) : 3715.475
## ARIMA(1,2,3) : 3715.733
## ARIMA(1,2,4) : 3717.619
## ARIMA(2,2,0) : 3711.719
## ARIMA(2,2,1) : 3713.254
## ARIMA(2,2,2) : 3693.589
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 3712.643
## ARIMA(3,2,1) : 3698.963
## ARIMA(3,2,2) : 3693.201
## ARIMA(4,2,0) : 3713.446
## ARIMA(4,2,1) : 3713.65
## ARIMA(5,2,0) : 3710.445
##
##
##
## Best model: ARIMA(3,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(3,2,2)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## -0.4684 -0.9451 -0.0900 0.2337 0.8810
## s.e. 0.0824 0.0455 0.0571 0.0599 0.0702
##
## sigma^2 estimated as 1382: log likelihood=-1840.48
## AIC=3692.97 AICc=3693.2 BIC=3716.38
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 3 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## -0.4684 -0.9451 -0.0900 0.2337 0.8810
## s.e. 0.0824 0.0455 0.0571 0.0599 0.0702
##
## sigma^2 estimated as 1363: log likelihood = -1840.48, aic = 3692.97
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in Southern Federal"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 2.211414 36.81707 25.2839 0.2864193 1.516996 0.03460526
## ACF1
## Training set -0.007113562
x1_model1$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(3,2,2)
## Q* = 32.713, df = 5, p-value = 4.291e-06
##
## 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 Southern Federal"
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 = 89.126, df = 20, p-value = 1.054e-10
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 521.48, 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 Southern Federal"
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 Southern Federal"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.039 % MAPE 8 days Cumulative Covid 19 Infection cases in Southern Federal %"
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 Southern Federal"
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 | 268817.00 | 268838.77 | 0.008 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-16 | Tuesday | 269483.00 | 269523.75 | 0.015 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-17 | Wednesday | 270140.00 | 270206.41 | 0.025 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-18 | Thursday | 270808.00 | 270897.75 | 0.033 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-19 | Friday | 271469.00 | 271588.02 | 0.044 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-20 | Saturday | 272129.00 | 272270.79 | 0.052 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-21 | Sunday | 272787.00 | 272957.31 | 0.062 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-03-22 | Monday | 273442.00 | 273649.26 | 0.076 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 274335.79 | 273649.35 | 273285.97 | 275022.23 | 275385.61 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275019.39 | 274223.83 | 273802.68 | 275814.96 | 276236.11 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275708.99 | 274797.66 | 274315.23 | 276620.33 | 277102.76 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276399.05 | 275366.64 | 274820.12 | 277431.45 | 277977.97 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277083.48 | 275926.32 | 275313.76 | 278240.64 | 278853.20 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 277769.58 | 276482.75 | 275801.55 | 279056.41 | 279737.61 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278460.17 | 277038.22 | 276285.49 | 279882.11 | 280634.85 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "0.039 % MAPE 8 days Cumulative Covid 19 Infection cases in Southern Federal"
# 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 Southern Federal"
best_recommended_model
## [1] 0.039
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 Southern Federal"
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 | 274385.53 | 273681.25 | 273308.48 | 273681.25 | 273308.48 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275079.60 | 274266.96 | 273836.84 | 274266.96 | 273836.84 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275773.79 | 274847.76 | 274357.63 | 274847.76 | 274357.63 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276468.11 | 275423.84 | 274871.15 | 275423.84 | 274871.15 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277162.54 | 275995.40 | 275377.69 | 275995.40 | 275377.69 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 277857.10 | 276562.60 | 275877.50 | 276562.60 | 275877.50 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278551.78 | 277125.58 | 276370.80 | 277125.58 | 276370.80 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in Southern Federal"
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 | 274372.17 | 274221.56 | 274141.83 | 274522.79 | 274602.52 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275062.79 | 274904.04 | 274820.00 | 275221.53 | 275305.57 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275752.88 | 275586.41 | 275498.29 | 275919.35 | 276007.48 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276445.03 | 276271.17 | 276179.13 | 276618.89 | 276710.93 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277137.50 | 276956.58 | 276860.80 | 277318.43 | 277414.21 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 277829.89 | 277642.21 | 277542.86 | 278017.58 | 278116.93 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278522.47 | 278328.27 | 278225.46 | 278716.68 | 278819.49 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 Southern Federal"
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 | 274519.56 | 272596.03 | 271580.28 | 276449.26 | 277473.28 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275232.06 | 273038.15 | 271880.00 | 277433.99 | 278602.86 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275945.41 | 273469.41 | 272162.83 | 278431.58 | 279751.80 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276659.59 | 273890.22 | 272429.35 | 279441.67 | 280919.55 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277374.62 | 274300.91 | 272680.12 | 280463.95 | 282105.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 278090.49 | 274701.81 | 272915.62 | 281498.12 | 283309.67 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278807.20 | 275093.19 | 273136.31 | 282543.93 | 284531.21 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in Southern Federal"
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 | 274335.79 | 273649.35 | 273285.97 | 275022.23 | 275385.61 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 275019.39 | 274223.83 | 273802.68 | 275814.96 | 276236.11 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 275708.99 | 274797.66 | 274315.23 | 276620.33 | 277102.76 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 276399.05 | 275366.64 | 274820.12 | 277431.45 | 277977.97 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 277083.48 | 275926.32 | 275313.76 | 278240.64 | 278853.20 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 277769.58 | 276482.75 | 275801.55 | 279056.41 | 279737.61 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 278460.17 | 277038.22 | 276285.49 | 279882.11 | 280634.85 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in Southern Federal"
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 | 272083.13 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 272437.10 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 272776.06 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 273100.47 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 273410.80 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 273707.53 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 273991.13 |
## +---+------------+-----------------+---------------------+
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 | Southern Federal District | 0.327 | 0.048 | 0.045 | 0.071 | 0.039 | 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 Southern Federal
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 Southern Federal