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$`daily total`
y_lab <- "Daily Covid 19 Infection cases in Southern 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 <-4
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.
## 0.0 405.0 580.5 727.2 1151.5 1595.0
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 1.952742
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.3005857
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 462.6494
#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(2,5)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 2-5-1 network with 21 weights
## options were - linear output units
##
## sigma^2 estimated as 1316
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 4 days by using NNAR Model for ==> Daily Covid 19 Infection cases in Southern 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 4 days in NNAR Model for ==> Daily Covid 19 Infection cases in Southern Federal District"
paste(MAPE_Mean_All,"%")
## [1] "0.703 % MAPE 4 days Daily Covid 19 Infection cases in Southern 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 4 days in NNAR Model for ==> Daily Covid 19 Infection cases in Southern 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 | 2021-03-19 | Friday | 661.00 | 664.51 | 0.532 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-20 | Saturday | 660.00 | 663.82 | 0.578 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-21 | Sunday | 658.00 | 662.63 | 0.703 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-22 | Monday | 655.00 | 661.53 | 0.997 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 660.42 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 659.32 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 658.22 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 657.13 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 656.04 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 654.96 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 653.88 |
## +---+------------+-----------------+---------------------+
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 -1.023735 37.24777 24.28411 -Inf Inf 0.9233784 0.04654875
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.6127683
## Beta: 0.03245637
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -0.9734446
## [2,] 1.2687392
##
## Sigma: 37.24777
## AIC: 4901.317
#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 4 days by using bats Model for ==> Daily Covid 19 Infection cases in Southern 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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Southern Federal District"
paste(MAPE_Mean_All.bats,"%")
## [1] "4.238 % MAPE 4 days Daily Covid 19 Infection cases in Southern 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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Southern 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 | 2021-03-19 | Friday | 661.00 | 647.26 | 2.078 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-20 | Saturday | 660.00 | 636.17 | 3.61 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-21 | Sunday | 658.00 | 625.08 | 5.003 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-22 | Monday | 655.00 | 613.99 | 6.261 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 602.90 | 521.17 | 477.91 | 521.17 | 477.91 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 591.81 | 502.09 | 454.60 | 502.09 | 454.60 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 580.71 | 483.07 | 431.38 | 483.07 | 431.38 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 569.62 | 464.07 | 408.19 | 464.07 | 408.19 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 558.53 | 445.06 | 384.99 | 445.06 | 384.99 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 547.44 | 426.02 | 361.75 | 426.02 | 361.75 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 536.35 | 406.95 | 338.45 | 406.95 | 338.45 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 -1.017058 37.23881 24.26635 NaN Inf 0.9227034 0.0469672
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.6121857
## Beta: 0.03254105
## Damping Parameter: 1
## Gamma-1 Values: -0.0002762664
## Gamma-2 Values: -0.0001356059
##
## Seed States:
## [,1]
## [1,] -0.9738944
## [2,] 1.2412269
## [3,] -1.1948477
## [4,] -0.5447630
## [5,] 0.4528658
## [6,] 0.3030529
##
## Sigma: 37.23881
## AIC: 4913.138
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 4 days by using TBATS Model for ==> Daily Covid 19 Infection cases in Southern 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 4 days in TBATS Model for ==> Daily Covid 19 Infection cases in Southern Federal District"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "4.174 % MAPE 4 days Daily Covid 19 Infection cases in Southern 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 4 days in TBATS Model for ==> Daily Covid 19 Infection cases in Southern 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 | 2021-03-19 | Friday | 661.00 | 645.84 | 2.293 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-20 | Saturday | 660.00 | 636.86 | 3.506 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-21 | Sunday | 658.00 | 626.46 | 4.794 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-22 | Monday | 655.00 | 615.03 | 6.103 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 604.05 | 528.67 | 488.76 | 679.44 | 719.34 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 591.25 | 510.42 | 467.63 | 672.08 | 714.87 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 579.42 | 493.50 | 448.01 | 665.34 | 710.83 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 570.44 | 479.72 | 431.70 | 661.16 | 709.18 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 560.04 | 464.76 | 414.33 | 655.31 | 705.74 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 548.60 | 448.99 | 396.25 | 648.22 | 700.95 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 537.63 | 433.85 | 378.91 | 641.41 | 696.34 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 -1.547524 37.31651 24.53225 -Inf Inf 0.9328139 0.09717997
# 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= 0.7868
##
## Smoothing parameters:
## alpha = 0.5564
## beta = 0.0322
##
## Initial states:
## l = -3.0801
## b = 0.8812
##
## sigma: 9.6501
##
## AIC AICc BIC
## 3894.430 3894.594 3914.025
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -1.547524 37.31651 24.53225 -Inf Inf 0.9328139 0.09717997
# 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 4 days by using holt Model for ==> Daily Covid 19 Infection cases in Southern 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 4 days in holt Model for ==> Daily Covid 19 Infection cases in Southern Federal District"
paste(MAPE_Mean_All.Holt,"%")
## [1] "4.172 % MAPE 4 days Daily Covid 19 Infection cases in Southern 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 4 days in holt Model for ==> Daily Covid 19 Infection cases in Southern 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 | 2021-03-19 | Friday | 661.00 | 646.72 | 2.16 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-20 | Saturday | 660.00 | 636.26 | 3.597 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-21 | Sunday | 658.00 | 625.83 | 4.889 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-22 | Monday | 655.00 | 615.44 | 6.04 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 605.08 | 527.62 | 487.56 | 684.72 | 727.71 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 594.77 | 510.50 | 467.04 | 681.66 | 728.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 584.49 | 493.49 | 446.69 | 678.62 | 729.63 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 574.25 | 476.57 | 426.49 | 675.62 | 730.67 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 564.05 | 459.72 | 406.41 | 672.68 | 731.78 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 553.89 | 442.95 | 386.46 | 669.80 | 733.00 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 543.76 | 426.24 | 366.62 | 667.00 | 734.33 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 ==> Daily Covid 19 Infection cases in Southern 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 = 4.9554, 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) = 1.9282, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = 0.52897, Lag order = 7, p-value = 0.99
## 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 ==> Daily Covid 19 Infection cases in Southern 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 = 0.7738, 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 smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -422.21, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -4.8399, Lag order = 7, p-value = 0.01
## 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 Daily Covid 19 Infection cases in Southern Federal District"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
## Warning in kpss.test(diff2_x1): p-value greater than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.0093252, Truncation lag parameter = 5, p-value = 0.1
pp.test(diff2_x1) # applay pp test after taking Second differences
## Warning in pp.test(diff2_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff2_x1
## Dickey-Fuller Z(alpha) = -471.62, 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 = -14.104, 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) : 4102.512
## ARIMA(0,2,1) : 3774.91
## ARIMA(0,2,2) : 3738.44
## ARIMA(0,2,3) : 3733.667
## ARIMA(0,2,4) : 3735.723
## ARIMA(0,2,5) : 3736.228
## ARIMA(1,2,0) : 3964.727
## ARIMA(1,2,1) : 3751.14
## ARIMA(1,2,2) : 3734.161
## ARIMA(1,2,3) : 3735.723
## ARIMA(1,2,4) : Inf
## ARIMA(2,2,0) : 3872.473
## ARIMA(2,2,1) : 3738.059
## ARIMA(2,2,2) : 3735.947
## ARIMA(2,2,3) : 3737.648
## ARIMA(3,2,0) : 3832.995
## ARIMA(3,2,1) : 3739.687
## ARIMA(3,2,2) : 3739.14
## ARIMA(4,2,0) : 3830.771
## ARIMA(4,2,1) : 3741.425
## ARIMA(5,2,0) : 3810.576
##
##
##
## Best model: ARIMA(0,2,3)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(0,2,3)
##
## Coefficients:
## ma1 ma2 ma3
## -1.3047 0.2043 0.1443
## s.e. 0.0516 0.0846 0.0532
##
## sigma^2 estimated as 1381: log likelihood=-1862.78
## AIC=3733.56 AICc=3733.67 BIC=3749.21
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 0 2 3
strtoi(bestmodel[3])
## [1] 3
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ma1 ma2 ma3
## -1.3047 0.2043 0.1443
## s.e. 0.0516 0.0846 0.0532
##
## sigma^2 estimated as 1369: log likelihood = -1862.78, aic = 3733.56
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Daily Covid 19 Infection cases in Southern Federal District"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.6352187 36.90701 24.26852 NaN Inf 0.9227857 -0.003773422
x1_model1$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(0,2,3)
## Q* = 34.896, df = 7, p-value = 1.17e-05
##
## Model df: 3. 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 ==> Daily Covid 19 Infection cases in Southern 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 = 57.333, df = 20, p-value = 1.827e-05
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 851.32, 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 4 days by using bats Model for ==> Daily Covid 19 Infection cases in Southern 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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Southern Federal District"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "4.328 % MAPE 4 days Daily Covid 19 Infection cases in Southern 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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Southern 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 | 2021-03-19 | Friday | 661.00 | 648.23 | 1.932 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-20 | Saturday | 660.00 | 634.29 | 3.895 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-21 | Sunday | 658.00 | 623.97 | 5.172 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-22 | Monday | 655.00 | 613.65 | 6.314 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 603.32 | 525.22 | 483.88 | 681.42 | 722.77 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 593.00 | 507.63 | 462.44 | 678.37 | 723.56 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 582.68 | 489.82 | 440.66 | 675.54 | 724.70 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 572.36 | 471.78 | 418.54 | 672.93 | 726.17 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 562.03 | 453.53 | 396.09 | 670.54 | 727.98 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 551.71 | 435.07 | 373.33 | 668.35 | 730.09 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 541.39 | 416.42 | 350.26 | 666.36 | 732.52 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "4.328 % MAPE 4 days Daily Covid 19 Infection cases in Southern 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 ==> Daily Covid 19 Infection cases in Southern Federal District"
best_recommended_model
## [1] 0.703
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 ==> Daily Covid 19 Infection cases in Southern 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$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 602.90 | 521.17 | 477.91 | 521.17 | 477.91 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 591.81 | 502.09 | 454.60 | 502.09 | 454.60 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 580.71 | 483.07 | 431.38 | 483.07 | 431.38 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 569.62 | 464.07 | 408.19 | 464.07 | 408.19 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 558.53 | 445.06 | 384.99 | 445.06 | 384.99 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 547.44 | 426.02 | 361.75 | 426.02 | 361.75 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 536.35 | 406.95 | 338.45 | 406.95 | 338.45 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Daily Covid 19 Infection cases in Southern Federal District"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$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 | 604.05 | 528.67 | 488.76 | 679.44 | 719.34 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 591.25 | 510.42 | 467.63 | 672.08 | 714.87 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 579.42 | 493.50 | 448.01 | 665.34 | 710.83 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 570.44 | 479.72 | 431.70 | 661.16 | 709.18 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 560.04 | 464.76 | 414.33 | 655.31 | 705.74 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 548.60 | 448.99 | 396.25 | 648.22 | 700.95 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 537.63 | 433.85 | 378.91 | 641.41 | 696.34 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Daily Covid 19 Infection cases in Southern 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$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 605.08 | 527.62 | 487.56 | 684.72 | 727.71 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 594.77 | 510.50 | 467.04 | 681.66 | 728.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 584.49 | 493.49 | 446.69 | 678.62 | 729.63 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 574.25 | 476.57 | 426.49 | 675.62 | 730.67 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 564.05 | 459.72 | 406.41 | 672.68 | 731.78 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 553.89 | 442.95 | 386.46 | 669.80 | 733.00 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 543.76 | 426.24 | 366.62 | 667.00 | 734.33 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Daily Covid 19 Infection cases in Southern Federal District"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$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 | 603.32 | 525.22 | 483.88 | 681.42 | 722.77 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 593.00 | 507.63 | 462.44 | 678.37 | 723.56 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 582.68 | 489.82 | 440.66 | 675.54 | 724.70 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 572.36 | 471.78 | 418.54 | 672.93 | 726.17 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 562.03 | 453.53 | 396.09 | 670.54 | 727.98 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 551.71 | 435.07 | 373.33 | 668.35 | 730.09 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 541.39 | 416.42 | 350.26 | 666.36 | 732.52 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Daily Covid 19 Infection cases in Southern 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 | 660.42 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 659.32 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 658.22 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 657.13 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 656.04 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 654.96 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 653.88 |
## +---+------------+-----------------+---------------------+
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 | 0.703 | 4.238 | 4.174 | 4.172 | 4.328 | NNAR 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 ==>Daily Covid 19 Infection cases in Southern 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 ==> Daily Covid 19 Infection cases in Southern Federal District