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
library(ascii)
require(tseries) # need to install tseries tj test Stationarity in time series
library(forecast) # install library forecast
library(tseries)
##Global vriable##
Full_original_data <- read.csv("data.csv") # path of your data ( time series data)
original_data<-Full_original_data$cases #Cumulative #cases
y_lab <- "Forecasting cumulative Covid 19 Infection cases in USA" # input name of data
Actual_date_interval <- c("2020/03/01","2021/05/08")
Forecast_date_interval <- c("2021/05/09","2021/05/30")
validation_data_days <-45
frequency<-"day"
Number_Neural<-5# Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "USA"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 1147668 6072726 10617004 20513513 32257416
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.01343
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.7693384
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 11198982
#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
}
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
}
## 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 496887154
# 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 45 days by using NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
paste(MAPE_Mean_All,"%")
## [1] "3.465 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in USA %"
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 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-03-25 | Thursday | 29653604.00 | 29619474.34 | 0.115 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 29718930.00 | 29643242.06 | 0.255 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 29788519.00 | 29666180.46 | 0.411 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 29859706.00 | 29688316.99 | 0.574 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 29921599.00 | 29709678.31 | 0.708 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 29968464.00 | 29730290.28 | 0.795 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 30033063.00 | 29750177.99 | 0.942 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 30095776.00 | 29769365.77 | 1.085 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 30164185.00 | 29787877.20 | 1.248 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 30238692.00 | 29805735.16 | 1.432 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 30304462.00 | 29822961.80 | 1.589 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 30372016.00 | 29839578.60 | 1.753 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 30413124.00 | 29855606.35 | 1.833 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 30475874.00 | 29871065.21 | 1.985 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 30541000.00 | 29885974.66 | 2.145 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 30615849.00 | 29900353.61 | 2.337 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 30692226.00 | 29914220.34 | 2.535 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 30772857.00 | 29927592.52 | 2.747 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 30840411.00 | 29940487.29 | 2.918 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 30888765.00 | 29952921.21 | 3.03 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 30951566.00 | 29964910.30 | 3.188 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 31029700.00 | 29976470.05 | 3.394 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 31103006.00 | 29987615.45 | 3.586 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 31176938.00 | 29998361.00 | 3.78 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 31250635.00 | 30008720.70 | 3.974 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 31311941.00 | 30018708.08 | 4.13 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 31350025.00 | 30028336.25 | 4.216 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 31407189.00 | 30037617.85 | 4.361 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 31467572.00 | 30046565.09 | 4.516 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 31530214.00 | 30055189.80 | 4.678 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 31593420.00 | 30063503.37 | 4.843 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 31656636.00 | 30071516.83 | 5.007 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 31708445.00 | 30079240.83 | 5.138 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 31742914.00 | 30086685.64 | 5.218 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 31783375.00 | 30093861.19 | 5.316 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 31835314.00 | 30100777.06 | 5.448 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 31889171.00 | 30107442.52 | 5.587 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 31948761.00 | 30113866.50 | 5.743 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 32002328.00 | 30120057.62 | 5.882 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 32047478.00 | 30126024.21 | 5.996 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 32083656.00 | 30131774.32 | 6.084 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 32123136.00 | 30137315.68 | 6.182 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 32167970.00 | 30142655.80 | 6.296 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 32210817.00 | 30147801.90 | 6.405 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 32257416.00 | 30152760.94 | 6.525 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-05-09 | Sunday | 30157539.65 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 30162144.52 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 30166581.82 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 30170857.57 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 30174977.62 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 30178947.57 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 30182772.85 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 30186458.68 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 30190010.12 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 30193432.01 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 30196729.06 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 30199905.78 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 30202966.54 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 30205915.53 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 30208756.83 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 30211494.32 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 30214131.79 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 30216672.87 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 30219121.06 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 30221479.74 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 30223752.16 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 30225941.46 |
## +----+------------+-----------------+---------------------+
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 318.276 18242.95 9185.65 -Inf Inf 0.1384295 0.01047745
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.109368
## Beta: 0.3808696
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -108.9141
## [2,] 227.8479
##
## Sigma: 18242.95
## AIC: 11507.36
#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 45 days by using bats Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.627 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in USA %"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-03-25 | Thursday | 29653604.00 | 29650219.13 | 0.011 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 29718930.00 | 29704633.06 | 0.048 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 29788519.00 | 29759046.99 | 0.099 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 29859706.00 | 29813460.91 | 0.155 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 29921599.00 | 29867874.84 | 0.18 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 29968464.00 | 29922288.77 | 0.154 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 30033063.00 | 29976702.69 | 0.188 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 30095776.00 | 30031116.62 | 0.215 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 30164185.00 | 30085530.55 | 0.261 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 30238692.00 | 30139944.47 | 0.327 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 30304462.00 | 30194358.40 | 0.363 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 30372016.00 | 30248772.33 | 0.406 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 30413124.00 | 30303186.25 | 0.361 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 30475874.00 | 30357600.18 | 0.388 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 30541000.00 | 30412014.11 | 0.422 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 30615849.00 | 30466428.03 | 0.488 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 30692226.00 | 30520841.96 | 0.558 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 30772857.00 | 30575255.89 | 0.642 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 30840411.00 | 30629669.81 | 0.683 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 30888765.00 | 30684083.74 | 0.663 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 30951566.00 | 30738497.67 | 0.688 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 31029700.00 | 30792911.59 | 0.763 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 31103006.00 | 30847325.52 | 0.822 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 31176938.00 | 30901739.45 | 0.883 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 31250635.00 | 30956153.37 | 0.942 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 31311941.00 | 31010567.30 | 0.962 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 31350025.00 | 31064981.23 | 0.909 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 31407189.00 | 31119395.16 | 0.916 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 31467572.00 | 31173809.08 | 0.934 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 31530214.00 | 31228223.01 | 0.958 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 31593420.00 | 31282636.94 | 0.984 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 31656636.00 | 31337050.86 | 1.01 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 31708445.00 | 31391464.79 | 1 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 31742914.00 | 31445878.72 | 0.936 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 31783375.00 | 31500292.64 | 0.891 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 31835314.00 | 31554706.57 | 0.881 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 31889171.00 | 31609120.50 | 0.878 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 31948761.00 | 31663534.42 | 0.893 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 32002328.00 | 31717948.35 | 0.889 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 32047478.00 | 31772362.28 | 0.858 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 32083656.00 | 31826776.20 | 0.801 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 32123136.00 | 31881190.13 | 0.753 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 32167970.00 | 31935604.06 | 0.722 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 32210817.00 | 31990017.98 | 0.685 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 32257416.00 | 32044431.91 | 0.66 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-05-09 | Sunday | 32098845.84 | 30367323.33 | 29450710.69 | 30367323.33 | 29450710.69 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32153259.76 | 30367800.04 | 29422634.76 | 30367800.04 | 29422634.76 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32207673.69 | 30367728.45 | 29393720.28 | 30367728.45 | 29393720.28 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32262087.62 | 30367114.03 | 29363975.60 | 30367114.03 | 29363975.60 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32316501.54 | 30365962.05 | 29333408.82 | 30365962.05 | 29333408.82 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32370915.47 | 30364277.67 | 29302027.79 | 30364277.67 | 29302027.79 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32425329.40 | 30362065.88 | 29269840.15 | 30362065.88 | 29269840.15 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32479743.32 | 30359331.55 | 29236853.36 | 30359331.55 | 29236853.36 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32534157.25 | 30356079.39 | 29203074.62 | 30356079.39 | 29203074.62 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32588571.18 | 30352314.02 | 29168510.99 | 30352314.02 | 29168510.99 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32642985.10 | 30348039.91 | 29133169.32 | 30348039.91 | 29133169.32 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32697399.03 | 30343261.44 | 29097056.28 | 30343261.44 | 29097056.28 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32751812.96 | 30337982.86 | 29060178.39 | 30337982.86 | 29060178.39 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32806226.88 | 30332208.31 | 29022541.99 | 30332208.31 | 29022541.99 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32860640.81 | 30325941.86 | 28984153.28 | 30325941.86 | 28984153.28 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32915054.74 | 30319187.44 | 28945018.30 | 30319187.44 | 28945018.30 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 32969468.66 | 30311948.93 | 28905142.96 | 30311948.93 | 28905142.96 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 33023882.59 | 30304230.08 | 28864533.01 | 30304230.08 | 28864533.01 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 33078296.52 | 30296034.58 | 28823194.08 | 30296034.58 | 28823194.08 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 33132710.44 | 30287366.03 | 28781131.69 | 30287366.03 | 28781131.69 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33187124.37 | 30278227.95 | 28738351.20 | 30278227.95 | 28738351.20 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33241538.30 | 30268623.77 | 28694857.89 | 30268623.77 | 28694857.89 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
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 317.1624 18138.84 9511.215 NaN Inf 0.1433358 0.008424101
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.115982
## Beta: 0.3820274
## Damping Parameter: 1
## Gamma-1 Values: -0.00238997
## Gamma-2 Values: 0.00130653
##
## Seed States:
## [,1]
## [1,] 8.32221
## [2,] 174.69300
## [3,] -457.42635
## [4,] -543.09596
## [5,] -723.30575
## [6,] 587.27074
##
## Sigma: 18138.84
## AIC: 11514.24
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 45 days by using TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.633 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in USA %"
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 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-03-25 | Thursday | 29653604.00 | 29649898.68 | 0.012 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-26 | Friday | 29718930.00 | 29705830.40 | 0.044 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-27 | Saturday | 29788519.00 | 29759316.98 | 0.098 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-28 | Sunday | 29859706.00 | 29811673.15 | 0.161 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-29 | Monday | 29921599.00 | 29867130.31 | 0.182 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-30 | Tuesday | 29968464.00 | 29921848.45 | 0.156 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-31 | Wednesday | 30033063.00 | 29975910.71 | 0.19 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-04-01 | Thursday | 30095776.00 | 30031842.43 | 0.212 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 9 | 2021-04-02 | Friday | 30164185.00 | 30085329.01 | 0.261 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 10 | 2021-04-03 | Saturday | 30238692.00 | 30137685.18 | 0.334 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 11 | 2021-04-04 | Sunday | 30304462.00 | 30193142.34 | 0.367 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 12 | 2021-04-05 | Monday | 30372016.00 | 30247860.48 | 0.409 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 13 | 2021-04-06 | Tuesday | 30413124.00 | 30301922.74 | 0.366 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 14 | 2021-04-07 | Wednesday | 30475874.00 | 30357854.46 | 0.387 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 15 | 2021-04-08 | Thursday | 30541000.00 | 30411341.04 | 0.425 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 16 | 2021-04-09 | Friday | 30615849.00 | 30463697.20 | 0.497 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 17 | 2021-04-10 | Saturday | 30692226.00 | 30519154.37 | 0.564 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 18 | 2021-04-11 | Sunday | 30772857.00 | 30573872.51 | 0.647 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 19 | 2021-04-12 | Monday | 30840411.00 | 30627934.77 | 0.689 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 20 | 2021-04-13 | Tuesday | 30888765.00 | 30683866.49 | 0.663 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 21 | 2021-04-14 | Wednesday | 30951566.00 | 30737353.07 | 0.692 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 22 | 2021-04-15 | Thursday | 31029700.00 | 30789709.23 | 0.773 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 23 | 2021-04-16 | Friday | 31103006.00 | 30845166.40 | 0.829 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 24 | 2021-04-17 | Saturday | 31176938.00 | 30899884.54 | 0.889 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 25 | 2021-04-18 | Sunday | 31250635.00 | 30953946.80 | 0.949 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 26 | 2021-04-19 | Monday | 31311941.00 | 31009878.52 | 0.965 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 27 | 2021-04-20 | Tuesday | 31350025.00 | 31063365.10 | 0.914 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 28 | 2021-04-21 | Wednesday | 31407189.00 | 31115721.26 | 0.928 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 29 | 2021-04-22 | Thursday | 31467572.00 | 31171178.43 | 0.942 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 30 | 2021-04-23 | Friday | 31530214.00 | 31225896.57 | 0.965 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 31 | 2021-04-24 | Saturday | 31593420.00 | 31279958.83 | 0.992 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 32 | 2021-04-25 | Sunday | 31656636.00 | 31335890.55 | 1.013 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 33 | 2021-04-26 | Monday | 31708445.00 | 31389377.13 | 1.006 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 34 | 2021-04-27 | Tuesday | 31742914.00 | 31441733.29 | 0.949 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 35 | 2021-04-28 | Wednesday | 31783375.00 | 31497190.46 | 0.9 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 36 | 2021-04-29 | Thursday | 31835314.00 | 31551908.60 | 0.89 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 37 | 2021-04-30 | Friday | 31889171.00 | 31605970.86 | 0.888 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 38 | 2021-05-01 | Saturday | 31948761.00 | 31661902.58 | 0.898 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 39 | 2021-05-02 | Sunday | 32002328.00 | 31715389.16 | 0.897 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 40 | 2021-05-03 | Monday | 32047478.00 | 31767745.32 | 0.873 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 41 | 2021-05-04 | Tuesday | 32083656.00 | 31823202.49 | 0.812 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 42 | 2021-05-05 | Wednesday | 32123136.00 | 31877920.63 | 0.763 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 43 | 2021-05-06 | Thursday | 32167970.00 | 31931982.89 | 0.734 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 44 | 2021-05-07 | Friday | 32210817.00 | 31987914.61 | 0.692 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 45 | 2021-05-08 | Saturday | 32257416.00 | 32041401.19 | 0.67 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
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 | 2021-05-09 | Sunday | 32093757.35 | 31926609.99 | 31838127.52 | 32260904.72 | 32349387.19 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32149214.52 | 31980427.11 | 31891076.45 | 32318001.92 | 32407352.58 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32203932.66 | 32033542.29 | 31943343.08 | 32374323.02 | 32464522.23 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32257994.92 | 32086031.58 | 31994999.68 | 32429958.27 | 32520990.16 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32313926.64 | 32140406.10 | 32048549.88 | 32487447.17 | 32579303.40 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32367413.22 | 32192355.57 | 32099685.65 | 32542470.87 | 32635140.80 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32419769.38 | 32243188.00 | 32149711.46 | 32596350.77 | 32689827.31 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32475226.55 | 32297135.57 | 32202859.90 | 32653317.52 | 32747593.19 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32529944.69 | 32350376.74 | 32255319.21 | 32709512.63 | 32804570.16 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32584006.95 | 32402988.15 | 32307162.59 | 32765025.75 | 32860851.31 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32639938.67 | 32457481.99 | 32360895.27 | 32822395.34 | 32918982.07 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32693425.25 | 32509547.79 | 32412208.94 | 32877302.71 | 32974641.56 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32745781.41 | 32560494.06 | 32462408.85 | 32931068.77 | 33029153.97 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32801238.57 | 32614553.01 | 32515727.64 | 32987924.14 | 33086749.51 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32855956.71 | 32667902.09 | 32568351.99 | 33044011.33 | 33143561.44 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32910018.98 | 32720618.46 | 32620355.87 | 33099419.51 | 33199682.09 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 32965950.70 | 32775215.12 | 32674245.80 | 33156686.27 | 33257655.59 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 33019437.28 | 32827381.44 | 32725713.22 | 33211493.12 | 33313161.34 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 33071793.44 | 32878426.35 | 32776064.00 | 33265160.53 | 33367522.89 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 33127250.60 | 32932582.08 | 32829530.79 | 33321919.13 | 33424970.42 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33181968.74 | 32986025.17 | 32882298.91 | 33377912.32 | 33481638.58 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33236031.01 | 33038833.17 | 32934442.94 | 33433228.85 | 33537619.08 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
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 -797.6627 18542.85 9589.94 NaN Inf 0.1445222 0.1585094
# 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= 0.5411
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.3438
##
## Initial states:
## l = -2.2178
## b = -0.1666
##
## sigma: 13.4909
##
## AIC AICc BIC
## 5060.030 5060.166 5080.543
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -797.6627 18542.85 9589.94 NaN Inf 0.1445222 0.1585094
# 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 45 days by using holt Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.612 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in USA %"
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 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-03-25 | Thursday | 29653604.00 | 29648861.25 | 0.016 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 29718930.00 | 29702919.26 | 0.054 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 29788519.00 | 29757022.46 | 0.106 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 29859706.00 | 29811170.84 | 0.163 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 29921599.00 | 29865364.40 | 0.188 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 29968464.00 | 29919603.12 | 0.163 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 30033063.00 | 29973887.01 | 0.197 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 30095776.00 | 30028216.06 | 0.224 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 30164185.00 | 30082590.25 | 0.271 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 30238692.00 | 30137009.59 | 0.336 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 30304462.00 | 30191474.06 | 0.373 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 30372016.00 | 30245983.66 | 0.415 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 30413124.00 | 30300538.39 | 0.37 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 30475874.00 | 30355138.23 | 0.396 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 30541000.00 | 30409783.17 | 0.43 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 30615849.00 | 30464473.23 | 0.494 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 30692226.00 | 30519208.37 | 0.564 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 30772857.00 | 30573988.61 | 0.646 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 30840411.00 | 30628813.92 | 0.686 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 30888765.00 | 30683684.32 | 0.664 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 30951566.00 | 30738599.78 | 0.688 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 31029700.00 | 30793560.30 | 0.761 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 31103006.00 | 30848565.88 | 0.818 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 31176938.00 | 30903616.51 | 0.877 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 31250635.00 | 30958712.19 | 0.934 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 31311941.00 | 31013852.90 | 0.952 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 31350025.00 | 31069038.63 | 0.896 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 31407189.00 | 31124269.39 | 0.901 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 31467572.00 | 31179545.17 | 0.915 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 31530214.00 | 31234865.96 | 0.937 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 31593420.00 | 31290231.75 | 0.96 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 31656636.00 | 31345642.54 | 0.982 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 31708445.00 | 31401098.31 | 0.969 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 31742914.00 | 31456599.07 | 0.902 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 31783375.00 | 31512144.81 | 0.853 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 31835314.00 | 31567735.52 | 0.841 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 31889171.00 | 31623371.19 | 0.834 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 31948761.00 | 31679051.82 | 0.844 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 32002328.00 | 31734777.40 | 0.836 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 32047478.00 | 31790547.93 | 0.802 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 32083656.00 | 31846363.39 | 0.74 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 32123136.00 | 31902223.79 | 0.688 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 32167970.00 | 31958129.11 | 0.652 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 32210817.00 | 32014079.34 | 0.611 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 32257416.00 | 32070074.50 | 0.581 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-05-09 | Sunday | 32126114.55 | 28978910.65 | 27373326.61 | 35421584.20 | 37225711.08 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32182199.51 | 28936677.50 | 27282876.64 | 35585346.48 | 37450224.41 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32238329.36 | 28893500.71 | 27191118.51 | 35750527.03 | 37677036.10 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32294504.09 | 28849391.93 | 27098073.32 | 35917121.88 | 37906143.04 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32350723.71 | 28804362.57 | 27003761.79 | 36085127.29 | 38137542.49 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32406988.20 | 28758423.78 | 26908204.25 | 36254539.76 | 38371232.08 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32463297.56 | 28711586.48 | 26811420.67 | 36425356.06 | 38607209.82 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32519651.77 | 28663861.35 | 26713430.67 | 36597573.14 | 38845474.02 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32576050.85 | 28615258.86 | 26614253.53 | 36771188.20 | 39086023.36 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32632494.77 | 28565789.27 | 26513908.26 | 36946198.62 | 39328856.78 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32688983.53 | 28515462.64 | 26412413.51 | 37122602.00 | 39573973.54 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32745517.13 | 28464288.85 | 26309787.70 | 37300396.09 | 39821373.17 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32802095.55 | 28412277.59 | 26206048.94 | 37479578.85 | 40071055.48 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32858718.80 | 28359438.38 | 26101215.10 | 37660148.39 | 40323020.50 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32915386.87 | 28305780.57 | 25995303.80 | 37842102.99 | 40577268.53 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32972099.74 | 28251313.37 | 25888332.39 | 38025441.08 | 40833800.11 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 33028857.42 | 28196045.81 | 25780318.04 | 38210161.25 | 41092615.98 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 33085659.90 | 28139986.79 | 25671277.66 | 38396262.22 | 41353717.11 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 33142507.16 | 28083145.07 | 25561227.98 | 38583742.84 | 41617104.65 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 33199399.21 | 28025529.28 | 25450185.50 | 38772602.13 | 41882779.99 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33256336.04 | 27967147.90 | 25338166.55 | 38962839.18 | 42150744.66 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33313317.65 | 27908009.32 | 25225187.27 | 39154453.25 | 42421000.40 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
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
##################
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Forecasting cumulative Covid 19 Infection cases in USA"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 6.5024, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
## Warning in pp.test(data_series): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -0.4596, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -3.5943, Lag order = 7, p-value = 0.03345
## 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 ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 = 4.5112, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -18.398, Truncation lag parameter = 5, p-value
## = 0.09526
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.76434, Lag order = 7, p-value = 0.9646
## 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 Forecasting cumulative Covid 19 Infection cases in USA"
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 = 0.10419, 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) = -487.25, 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 = -7.8527, 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) : 10098.88
## ARIMA(0,2,1) : 10008.93
## ARIMA(0,2,2) : 10003.59
## ARIMA(0,2,3) : 10001.12
## ARIMA(0,2,4) : 10001.59
## ARIMA(0,2,5) : 9997.4
## ARIMA(1,2,0) : 10039.4
## ARIMA(1,2,1) : 10002.17
## ARIMA(1,2,2) : 10004.14
## ARIMA(1,2,3) : 10002.75
## ARIMA(1,2,4) : 9997.538
## ARIMA(2,2,0) : 10033.29
## ARIMA(2,2,1) : 10004.03
## ARIMA(2,2,2) : 10003.98
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 10019.78
## ARIMA(3,2,1) : 9996.959
## ARIMA(3,2,2) : 9942.13
## ARIMA(4,2,0) : 10006.36
## ARIMA(4,2,1) : 9991.898
## ARIMA(5,2,0) : 9981.209
##
##
##
## 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
## 0.7838 -0.3911 -0.4443 -1.3134 0.9189
## s.e. 0.0473 0.0545 0.0450 0.0294 0.0239
##
## sigma^2 estimated as 289247715: log likelihood=-4964.97
## AIC=9941.94 AICc=9942.13 BIC=9966.53
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 3 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.7838 -0.3911 -0.4443 -1.3134 0.9189
## s.e. 0.0473 0.0545 0.0450 0.0294 0.0239
##
## sigma^2 estimated as 2.86e+08: log likelihood = -4964.97, aic = 9941.94
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting cumulative Covid 19 Infection cases in USA"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 202.3156 16873.59 7962.389 0.5154827 2.617159 0.1199947
## ACF1
## Training set -0.07500919
x1_model1$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* = 30.074, df = 5, p-value = 1.426e-05
##
## 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 ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 = 132.28, df = 20, p-value < 2.2e-16
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 22801, 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 45 days by using bats Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.795 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in USA %"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-03-25 | Thursday | 29653604.00 | 29647942.05 | 0.019 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-26 | Friday | 29718930.00 | 29704348.77 | 0.049 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-27 | Saturday | 29788519.00 | 29756920.82 | 0.106 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-28 | Sunday | 29859706.00 | 29807231.81 | 0.176 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-29 | Monday | 29921599.00 | 29855798.34 | 0.22 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-30 | Tuesday | 29968464.00 | 29905585.60 | 0.21 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-31 | Wednesday | 30033063.00 | 29958016.43 | 0.25 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-04-01 | Thursday | 30095776.00 | 30012816.75 | 0.276 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 9 | 2021-04-02 | Friday | 30164185.00 | 30067897.91 | 0.319 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 10 | 2021-04-03 | Saturday | 30238692.00 | 30121097.97 | 0.389 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 11 | 2021-04-04 | Sunday | 30304462.00 | 30171661.14 | 0.438 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 12 | 2021-04-05 | Monday | 30372016.00 | 30220768.59 | 0.498 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 13 | 2021-04-06 | Tuesday | 30413124.00 | 30270602.17 | 0.469 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 14 | 2021-04-07 | Wednesday | 30475874.00 | 30322745.70 | 0.502 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 15 | 2021-04-08 | Thursday | 30541000.00 | 30377062.42 | 0.537 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 16 | 2021-04-09 | Friday | 30615849.00 | 30431856.34 | 0.601 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 17 | 2021-04-10 | Saturday | 30692226.00 | 30485148.04 | 0.675 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 18 | 2021-04-11 | Sunday | 30772857.00 | 30536110.25 | 0.769 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 19 | 2021-04-12 | Monday | 30840411.00 | 30585622.22 | 0.826 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 20 | 2021-04-13 | Tuesday | 30888765.00 | 30635576.06 | 0.82 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 21 | 2021-04-14 | Wednesday | 30951566.00 | 30687478.35 | 0.853 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 22 | 2021-04-15 | Thursday | 31029700.00 | 30741379.24 | 0.929 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 23 | 2021-04-16 | Friday | 31103006.00 | 30795888.17 | 0.987 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 24 | 2021-04-17 | Saturday | 31176938.00 | 30849226.33 | 1.051 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 25 | 2021-04-18 | Sunday | 31250635.00 | 30900521.16 | 1.12 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 26 | 2021-04-19 | Monday | 31311941.00 | 30950402.26 | 1.155 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 27 | 2021-04-20 | Tuesday | 31350025.00 | 31000494.67 | 1.115 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 28 | 2021-04-21 | Wednesday | 31407189.00 | 31052213.43 | 1.13 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 29 | 2021-04-22 | Thursday | 31467572.00 | 31105752.28 | 1.15 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 30 | 2021-04-23 | Friday | 31530214.00 | 31159987.68 | 1.174 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 31 | 2021-04-24 | Saturday | 31593420.00 | 31213334.59 | 1.203 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 32 | 2021-04-25 | Sunday | 31656636.00 | 31264904.10 | 1.237 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 33 | 2021-04-26 | Monday | 31708445.00 | 31315118.59 | 1.24 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 34 | 2021-04-27 | Tuesday | 31742914.00 | 31365360.98 | 1.189 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 35 | 2021-04-28 | Wednesday | 31783375.00 | 31416944.85 | 1.153 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 36 | 2021-04-29 | Thursday | 31835314.00 | 31470171.21 | 1.147 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 37 | 2021-04-30 | Friday | 31889171.00 | 31524147.82 | 1.145 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 38 | 2021-05-01 | Saturday | 31948761.00 | 31577474.05 | 1.162 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 39 | 2021-05-02 | Sunday | 32002328.00 | 31629267.40 | 1.166 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 40 | 2021-05-03 | Monday | 32047478.00 | 31679780.38 | 1.147 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 41 | 2021-05-04 | Tuesday | 32083656.00 | 31730178.36 | 1.102 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 42 | 2021-05-05 | Wednesday | 32123136.00 | 31781667.99 | 1.063 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 43 | 2021-05-06 | Thursday | 32167970.00 | 31834627.02 | 1.036 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 44 | 2021-05-07 | Friday | 32210817.00 | 31888361.83 | 1.001 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 45 | 2021-05-08 | Saturday | 32257416.00 | 31941644.99 | 0.979 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2021-05-09 | Sunday | 31993617.91 | 29679407.99 | 28454339.26 | 34307827.83 | 35532896.56 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32044395.91 | 29655983.76 | 28391634.74 | 34432808.06 | 35697157.08 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32094950.50 | 29631673.13 | 28327692.86 | 34558227.87 | 35862208.14 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32146379.44 | 29607351.27 | 28263270.94 | 34685407.61 | 36029487.94 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32199111.91 | 29583317.21 | 28198599.13 | 34814906.62 | 36199624.69 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32252623.32 | 29559101.92 | 28133237.83 | 34946144.72 | 36372008.82 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32305846.95 | 29533836.18 | 28066422.32 | 35077857.72 | 36545271.58 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32357961.25 | 29506894.45 | 27997630.85 | 35209028.05 | 36718291.64 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32408972.59 | 29478342.94 | 27926961.32 | 35339602.24 | 36890983.86 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32459681.21 | 29448875.54 | 27855051.29 | 35470486.89 | 37064311.13 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32511076.81 | 29419298.90 | 27782610.54 | 35602854.71 | 37239543.07 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32563619.23 | 29389951.88 | 27709913.87 | 35737286.58 | 37417324.59 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32616926.30 | 29360480.91 | 27636622.85 | 35873371.68 | 37597229.74 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32670078.92 | 29330121.67 | 27562055.10 | 36010036.16 | 37778102.73 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32722301.91 | 29298267.18 | 27485692.68 | 36146336.65 | 37958911.14 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32773517.01 | 29264904.12 | 27407556.66 | 36282129.89 | 38139477.36 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 32824374.36 | 29230607.67 | 27328182.50 | 36418141.05 | 38320566.22 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 32875758.53 | 29196112.25 | 27248225.17 | 36555404.82 | 38503291.90 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 32928143.32 | 29161780.96 | 27167989.17 | 36694505.67 | 38688297.46 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 32981265.22 | 29127359.87 | 27087225.61 | 36835170.58 | 38875304.83 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33034339.45 | 29092185.01 | 27005334.51 | 36976493.88 | 39063344.38 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33086643.46 | 29055677.77 | 26921813.43 | 37117609.15 | 39251473.49 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
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] "0.795 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in USA"
## Ensembling (Average)
weight.model<-0.90# optimization the weights ( weight average)
re_NNAR<-forecasting_NNAR$mean
re_BATS<-forecasting_bats$mean
re_TBATS<-forecasting_tbats$mean
re_holt<-forecasting_holt$mean
re_autoarima<-forecasting_auto_arima$mean
re_bestmodel<-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)
y1<-if(re_bestmodel >= MAPE_Mean_All.bats_Model) {re_BATS*weight.model
} else {
(re_BATS*(1-weight.model))/4
}
y2<-if(re_bestmodel >= MAPE_Mean_All.TBATS_Model) {re_TBATS*weight.model
} else {
(re_TBATS*(1-weight.model))/4
}
y3<-if(re_bestmodel >= MAPE_Mean_All.Holt_Model) {re_holt*weight.model
} else {
(re_holt*(1-weight.model))/4
}
y4<-if(re_bestmodel >= MAPE_Mean_All.ARIMA_Model) {re_autoarima*weight.model
} else {
(re_autoarima*(1-weight.model))/4
}
y5<-if(re_bestmodel >= MAPE_Mean_All_NNAR) {re_NNAR*weight.model
} else {
(re_NNAR*(1-weight.model))/4
}
Ensembling.Average<-(y1+y2+y3+y4+y5)
# Testing Data Evaluation
validation_forecast<-head(Ensembling.Average,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 Ensembling (Average) for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using Ensembling (Average) for ==> Forecasting cumulative Covid 19 Infection cases in USA"
MAPE_Mean_EnsemblingAverage<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_Ensembling<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Ensembling<-paste(round(MAPE_Per_Day,3),"%")
MAPE_Ensembling_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in Ensembling Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in Ensembling Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
paste(MAPE_Mean_EnsemblingAverage,"%")
## [1] "0.689 %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in Ensembling Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in Ensembling Model for ==> Forecasting cumulative Covid 19 Infection cases in USA"
print(ascii(data.frame(date_Ensembling=validation_dates,validation_data_by_name,actual_data=testing_data,Ensembling=validation_forecast,MAPE_Ensembling)), type = "rest")
##
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | | date_Ensembling | validation_data_by_name | actual_data | Ensembling | MAPE_Ensembling |
## +====+=================+=========================+=============+=============+=================+
## | 1 | 2021-03-25 | Thursday | 29653604.00 | 29648163.48 | 0.018 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 2 | 2021-03-26 | Friday | 29718930.00 | 29701578.69 | 0.058 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 29788519.00 | 29754856.84 | 0.113 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 29859706.00 | 29808070.83 | 0.173 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 5 | 2021-03-29 | Monday | 29921599.00 | 29861340.00 | 0.201 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 29968464.00 | 29914643.14 | 0.18 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 30033063.00 | 29968018.51 | 0.217 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 30095776.00 | 30021522.99 | 0.247 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 9 | 2021-04-02 | Friday | 30164185.00 | 30074997.09 | 0.296 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 30238692.00 | 30128420.20 | 0.365 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 30304462.00 | 30181879.75 | 0.405 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 12 | 2021-04-05 | Monday | 30372016.00 | 30235309.80 | 0.45 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 30413124.00 | 30288767.49 | 0.409 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 30475874.00 | 30342356.04 | 0.438 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 30541000.00 | 30395964.66 | 0.475 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 16 | 2021-04-09 | Friday | 30615849.00 | 30449584.28 | 0.543 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 30692226.00 | 30503271.65 | 0.616 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 30772857.00 | 30556910.53 | 0.702 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 19 | 2021-04-12 | Monday | 30840411.00 | 30610525.38 | 0.745 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 30888765.00 | 30664227.07 | 0.727 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 30951566.00 | 30717945.79 | 0.755 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 31029700.00 | 30771716.03 | 0.831 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 23 | 2021-04-16 | Friday | 31103006.00 | 30825609.19 | 0.892 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 31176938.00 | 30879485.15 | 0.954 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 31250635.00 | 30933324.52 | 1.015 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 26 | 2021-04-19 | Monday | 31311941.00 | 30987206.51 | 1.037 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 31350025.00 | 31041064.20 | 0.986 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 31407189.00 | 31094966.15 | 0.994 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 31467572.00 | 31149023.28 | 1.012 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 30 | 2021-04-23 | Friday | 31530214.00 | 31203111.79 | 1.037 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 31593420.00 | 31257194.42 | 1.064 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 31656636.00 | 31311312.34 | 1.091 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 33 | 2021-04-26 | Monday | 31708445.00 | 31365368.51 | 1.082 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 31742914.00 | 31419430.63 | 1.019 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 31783375.00 | 31473637.56 | 0.975 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 31835314.00 | 31527901.05 | 0.966 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 37 | 2021-04-30 | Friday | 31889171.00 | 31582201.11 | 0.963 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 31948761.00 | 31636566.08 | 0.977 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 32002328.00 | 31690866.22 | 0.973 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 40 | 2021-05-03 | Monday | 32047478.00 | 31745140.94 | 0.943 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 32083656.00 | 31799525.34 | 0.886 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 32123136.00 | 31853953.77 | 0.838 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 32167970.00 | 31908437.94 | 0.807 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 44 | 2021-05-07 | Friday | 32210817.00 | 31963023.82 | 0.769 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 32257416.00 | 32017573.02 | 0.744 % |
## +----+-----------------+-------------------------+-------------+-------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_Ensembling=tail(Ensembling.Average,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+
## | | FD | forecating_date | forecasting_by_Ensembling |
## +====+============+=================+===========================+
## | 1 | 2021-05-09 | Sunday | 32072097.12 |
## +----+------------+-----------------+---------------------------+
## | 2 | 2021-05-10 | Monday | 32126704.93 |
## +----+------------+-----------------+---------------------------+
## | 3 | 2021-05-11 | Tuesday | 32181324.89 |
## +----+------------+-----------------+---------------------------+
## | 4 | 2021-05-12 | Wednesday | 32235986.67 |
## +----+------------+-----------------+---------------------------+
## | 5 | 2021-05-13 | Thursday | 32290764.28 |
## +----+------------+-----------------+---------------------------+
## | 6 | 2021-05-14 | Friday | 32345536.87 |
## +----+------------+-----------------+---------------------------+
## | 7 | 2021-05-15 | Saturday | 32400310.76 |
## +----+------------+-----------------+---------------------------+
## | 8 | 2021-05-16 | Sunday | 32455171.34 |
## +----+------------+-----------------+---------------------------+
## | 9 | 2021-05-17 | Monday | 32510022.88 |
## +----+------------+-----------------+---------------------------+
## | 10 | 2021-05-18 | Tuesday | 32564887.57 |
## +----+------------+-----------------+---------------------------+
## | 11 | 2021-05-19 | Wednesday | 32619853.42 |
## +----+------------+-----------------+---------------------------+
## | 12 | 2021-05-20 | Thursday | 32674824.15 |
## +----+------------+-----------------+---------------------------+
## | 13 | 2021-05-21 | Friday | 32729823.18 |
## +----+------------+-----------------+---------------------------+
## | 14 | 2021-05-22 | Saturday | 32784933.42 |
## +----+------------+-----------------+---------------------------+
## | 15 | 2021-05-23 | Sunday | 32840039.59 |
## +----+------------+-----------------+---------------------------+
## | 16 | 2021-05-24 | Monday | 32895141.89 |
## +----+------------+-----------------+---------------------------+
## | 17 | 2021-05-25 | Tuesday | 32950319.82 |
## +----+------------+-----------------+---------------------------+
## | 18 | 2021-05-26 | Wednesday | 33005487.69 |
## +----+------------+-----------------+---------------------------+
## | 19 | 2021-05-27 | Thursday | 33060690.30 |
## +----+------------+-----------------+---------------------------+
## | 20 | 2021-05-28 | Friday | 33116026.94 |
## +----+------------+-----------------+---------------------------+
## | 21 | 2021-05-29 | Saturday | 33171382.06 |
## +----+------------+-----------------+---------------------------+
## | 22 | 2021-05-30 | Sunday | 33226739.74 |
## +----+------------+-----------------+---------------------------+
graph5<-autoplot(Ensembling.Average,xlab = paste ("Time in", frequency ,y_lab,"by using Ensembling models" , sep=" "), ylab=y_lab)
graph5
# 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,MAPE_Mean_EnsemblingAverage)
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 ==> Forecasting cumulative Covid 19 Infection cases in USA"
best_recommended_model
## [1] 0.612
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")}
x6<-if(best_recommended_model >= MAPE_Mean_EnsemblingAverage) {paste("Ensembling")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-05-09 | Sunday | 32098845.84 | 30367323.33 | 29450710.69 | 30367323.33 | 29450710.69 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32153259.76 | 30367800.04 | 29422634.76 | 30367800.04 | 29422634.76 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32207673.69 | 30367728.45 | 29393720.28 | 30367728.45 | 29393720.28 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32262087.62 | 30367114.03 | 29363975.60 | 30367114.03 | 29363975.60 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32316501.54 | 30365962.05 | 29333408.82 | 30365962.05 | 29333408.82 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32370915.47 | 30364277.67 | 29302027.79 | 30364277.67 | 29302027.79 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32425329.40 | 30362065.88 | 29269840.15 | 30362065.88 | 29269840.15 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32479743.32 | 30359331.55 | 29236853.36 | 30359331.55 | 29236853.36 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32534157.25 | 30356079.39 | 29203074.62 | 30356079.39 | 29203074.62 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32588571.18 | 30352314.02 | 29168510.99 | 30352314.02 | 29168510.99 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32642985.10 | 30348039.91 | 29133169.32 | 30348039.91 | 29133169.32 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32697399.03 | 30343261.44 | 29097056.28 | 30343261.44 | 29097056.28 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32751812.96 | 30337982.86 | 29060178.39 | 30337982.86 | 29060178.39 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32806226.88 | 30332208.31 | 29022541.99 | 30332208.31 | 29022541.99 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32860640.81 | 30325941.86 | 28984153.28 | 30325941.86 | 28984153.28 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32915054.74 | 30319187.44 | 28945018.30 | 30319187.44 | 28945018.30 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 32969468.66 | 30311948.93 | 28905142.96 | 30311948.93 | 28905142.96 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 33023882.59 | 30304230.08 | 28864533.01 | 30304230.08 | 28864533.01 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 33078296.52 | 30296034.58 | 28823194.08 | 30296034.58 | 28823194.08 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 33132710.44 | 30287366.03 | 28781131.69 | 30287366.03 | 28781131.69 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33187124.37 | 30278227.95 | 28738351.20 | 30278227.95 | 28738351.20 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33241538.30 | 30268623.77 | 28694857.89 | 30268623.77 | 28694857.89 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-05-09 | Sunday | 32093757.35 | 31926609.99 | 31838127.52 | 32260904.72 | 32349387.19 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32149214.52 | 31980427.11 | 31891076.45 | 32318001.92 | 32407352.58 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32203932.66 | 32033542.29 | 31943343.08 | 32374323.02 | 32464522.23 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32257994.92 | 32086031.58 | 31994999.68 | 32429958.27 | 32520990.16 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32313926.64 | 32140406.10 | 32048549.88 | 32487447.17 | 32579303.40 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32367413.22 | 32192355.57 | 32099685.65 | 32542470.87 | 32635140.80 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32419769.38 | 32243188.00 | 32149711.46 | 32596350.77 | 32689827.31 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32475226.55 | 32297135.57 | 32202859.90 | 32653317.52 | 32747593.19 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32529944.69 | 32350376.74 | 32255319.21 | 32709512.63 | 32804570.16 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32584006.95 | 32402988.15 | 32307162.59 | 32765025.75 | 32860851.31 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32639938.67 | 32457481.99 | 32360895.27 | 32822395.34 | 32918982.07 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32693425.25 | 32509547.79 | 32412208.94 | 32877302.71 | 32974641.56 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32745781.41 | 32560494.06 | 32462408.85 | 32931068.77 | 33029153.97 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32801238.57 | 32614553.01 | 32515727.64 | 32987924.14 | 33086749.51 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32855956.71 | 32667902.09 | 32568351.99 | 33044011.33 | 33143561.44 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32910018.98 | 32720618.46 | 32620355.87 | 33099419.51 | 33199682.09 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 32965950.70 | 32775215.12 | 32674245.80 | 33156686.27 | 33257655.59 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 33019437.28 | 32827381.44 | 32725713.22 | 33211493.12 | 33313161.34 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 33071793.44 | 32878426.35 | 32776064.00 | 33265160.53 | 33367522.89 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 33127250.60 | 32932582.08 | 32829530.79 | 33321919.13 | 33424970.42 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33181968.74 | 32986025.17 | 32882298.91 | 33377912.32 | 33481638.58 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33236031.01 | 33038833.17 | 32934442.94 | 33433228.85 | 33537619.08 |
## +----+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-05-09 | Sunday | 32126114.55 | 28978910.65 | 27373326.61 | 35421584.20 | 37225711.08 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32182199.51 | 28936677.50 | 27282876.64 | 35585346.48 | 37450224.41 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32238329.36 | 28893500.71 | 27191118.51 | 35750527.03 | 37677036.10 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32294504.09 | 28849391.93 | 27098073.32 | 35917121.88 | 37906143.04 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32350723.71 | 28804362.57 | 27003761.79 | 36085127.29 | 38137542.49 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32406988.20 | 28758423.78 | 26908204.25 | 36254539.76 | 38371232.08 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32463297.56 | 28711586.48 | 26811420.67 | 36425356.06 | 38607209.82 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32519651.77 | 28663861.35 | 26713430.67 | 36597573.14 | 38845474.02 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32576050.85 | 28615258.86 | 26614253.53 | 36771188.20 | 39086023.36 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32632494.77 | 28565789.27 | 26513908.26 | 36946198.62 | 39328856.78 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32688983.53 | 28515462.64 | 26412413.51 | 37122602.00 | 39573973.54 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32745517.13 | 28464288.85 | 26309787.70 | 37300396.09 | 39821373.17 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32802095.55 | 28412277.59 | 26206048.94 | 37479578.85 | 40071055.48 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32858718.80 | 28359438.38 | 26101215.10 | 37660148.39 | 40323020.50 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32915386.87 | 28305780.57 | 25995303.80 | 37842102.99 | 40577268.53 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32972099.74 | 28251313.37 | 25888332.39 | 38025441.08 | 40833800.11 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 33028857.42 | 28196045.81 | 25780318.04 | 38210161.25 | 41092615.98 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 33085659.90 | 28139986.79 | 25671277.66 | 38396262.22 | 41353717.11 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 33142507.16 | 28083145.07 | 25561227.98 | 38583742.84 | 41617104.65 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 33199399.21 | 28025529.28 | 25450185.50 | 38772602.13 | 41882779.99 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33256336.04 | 27967147.90 | 25338166.55 | 38962839.18 | 42150744.66 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33313317.65 | 27908009.32 | 25225187.27 | 39154453.25 | 42421000.40 |
## +----+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-05-09 | Sunday | 31993617.91 | 29679407.99 | 28454339.26 | 34307827.83 | 35532896.56 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-05-10 | Monday | 32044395.91 | 29655983.76 | 28391634.74 | 34432808.06 | 35697157.08 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-05-11 | Tuesday | 32094950.50 | 29631673.13 | 28327692.86 | 34558227.87 | 35862208.14 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-05-12 | Wednesday | 32146379.44 | 29607351.27 | 28263270.94 | 34685407.61 | 36029487.94 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-05-13 | Thursday | 32199111.91 | 29583317.21 | 28198599.13 | 34814906.62 | 36199624.69 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-05-14 | Friday | 32252623.32 | 29559101.92 | 28133237.83 | 34946144.72 | 36372008.82 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-05-15 | Saturday | 32305846.95 | 29533836.18 | 28066422.32 | 35077857.72 | 36545271.58 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 8 | 2021-05-16 | Sunday | 32357961.25 | 29506894.45 | 27997630.85 | 35209028.05 | 36718291.64 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 9 | 2021-05-17 | Monday | 32408972.59 | 29478342.94 | 27926961.32 | 35339602.24 | 36890983.86 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 10 | 2021-05-18 | Tuesday | 32459681.21 | 29448875.54 | 27855051.29 | 35470486.89 | 37064311.13 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 11 | 2021-05-19 | Wednesday | 32511076.81 | 29419298.90 | 27782610.54 | 35602854.71 | 37239543.07 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 12 | 2021-05-20 | Thursday | 32563619.23 | 29389951.88 | 27709913.87 | 35737286.58 | 37417324.59 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 13 | 2021-05-21 | Friday | 32616926.30 | 29360480.91 | 27636622.85 | 35873371.68 | 37597229.74 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 14 | 2021-05-22 | Saturday | 32670078.92 | 29330121.67 | 27562055.10 | 36010036.16 | 37778102.73 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 15 | 2021-05-23 | Sunday | 32722301.91 | 29298267.18 | 27485692.68 | 36146336.65 | 37958911.14 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 16 | 2021-05-24 | Monday | 32773517.01 | 29264904.12 | 27407556.66 | 36282129.89 | 38139477.36 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 17 | 2021-05-25 | Tuesday | 32824374.36 | 29230607.67 | 27328182.50 | 36418141.05 | 38320566.22 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 18 | 2021-05-26 | Wednesday | 32875758.53 | 29196112.25 | 27248225.17 | 36555404.82 | 38503291.90 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 19 | 2021-05-27 | Thursday | 32928143.32 | 29161780.96 | 27167989.17 | 36694505.67 | 38688297.46 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 20 | 2021-05-28 | Friday | 32981265.22 | 29127359.87 | 27087225.61 | 36835170.58 | 38875304.83 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 21 | 2021-05-29 | Saturday | 33034339.45 | 29092185.01 | 27005334.51 | 36976493.88 | 39063344.38 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 22 | 2021-05-30 | Sunday | 33086643.46 | 29055677.77 | 26921813.43 | 37117609.15 | 39251473.49 |
## +----+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting cumulative Covid 19 Infection cases in USA"
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 | 2021-05-09 | Sunday | 30157539.65 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 30162144.52 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 30166581.82 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 30170857.57 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 30174977.62 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 30178947.57 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 30182772.85 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 30186458.68 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 30190010.12 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 30193432.01 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 30196729.06 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 30199905.78 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 30202966.54 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 30205915.53 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 30208756.83 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 30211494.32 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 30214131.79 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 30216672.87 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 30219121.06 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 30221479.74 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 30223752.16 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 30225941.46 |
## +----+------------+-----------------+---------------------+
paste("Forecasting by using Ensembling Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Ensembling Model ==> Forecasting cumulative Covid 19 Infection cases in USA"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting.Ensembling=tail(Ensembling.Average,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+------------------------+
## | | FD | forecating_date | forecasting.Ensembling |
## +====+============+=================+========================+
## | 1 | 2021-05-09 | Sunday | 32072097.12 |
## +----+------------+-----------------+------------------------+
## | 2 | 2021-05-10 | Monday | 32126704.93 |
## +----+------------+-----------------+------------------------+
## | 3 | 2021-05-11 | Tuesday | 32181324.89 |
## +----+------------+-----------------+------------------------+
## | 4 | 2021-05-12 | Wednesday | 32235986.67 |
## +----+------------+-----------------+------------------------+
## | 5 | 2021-05-13 | Thursday | 32290764.28 |
## +----+------------+-----------------+------------------------+
## | 6 | 2021-05-14 | Friday | 32345536.87 |
## +----+------------+-----------------+------------------------+
## | 7 | 2021-05-15 | Saturday | 32400310.76 |
## +----+------------+-----------------+------------------------+
## | 8 | 2021-05-16 | Sunday | 32455171.34 |
## +----+------------+-----------------+------------------------+
## | 9 | 2021-05-17 | Monday | 32510022.88 |
## +----+------------+-----------------+------------------------+
## | 10 | 2021-05-18 | Tuesday | 32564887.57 |
## +----+------------+-----------------+------------------------+
## | 11 | 2021-05-19 | Wednesday | 32619853.42 |
## +----+------------+-----------------+------------------------+
## | 12 | 2021-05-20 | Thursday | 32674824.15 |
## +----+------------+-----------------+------------------------+
## | 13 | 2021-05-21 | Friday | 32729823.18 |
## +----+------------+-----------------+------------------------+
## | 14 | 2021-05-22 | Saturday | 32784933.42 |
## +----+------------+-----------------+------------------------+
## | 15 | 2021-05-23 | Sunday | 32840039.59 |
## +----+------------+-----------------+------------------------+
## | 16 | 2021-05-24 | Monday | 32895141.89 |
## +----+------------+-----------------+------------------------+
## | 17 | 2021-05-25 | Tuesday | 32950319.82 |
## +----+------------+-----------------+------------------------+
## | 18 | 2021-05-26 | Wednesday | 33005487.69 |
## +----+------------+-----------------+------------------------+
## | 19 | 2021-05-27 | Thursday | 33060690.30 |
## +----+------------+-----------------+------------------------+
## | 20 | 2021-05-28 | Friday | 33116026.94 |
## +----+------------+-----------------+------------------------+
## | 21 | 2021-05-29 | Saturday | 33171382.06 |
## +----+------------+-----------------+------------------------+
## | 22 | 2021-05-30 | Sunday | 33226739.74 |
## +----+------------+-----------------+------------------------+
result<-c(x1,x2,x3,x4,x5,x6)
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,Ensemblingt=MAPE_Mean_EnsemblingAverage,Best.Model=result)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Ensemblingt | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+=============+============+======+
## | 1 | USA | 3.465 | 0.627 | 0.633 | 0.612 | 0.795 | 0.689 | Holt 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,MAPE_Mean_EnsemblingAverage)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model","Ensembling.weight")
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,ARIMA Model, and Ensembling Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and Ensembling Model ==>Forecasting cumulative Covid 19 Infection cases in USA
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Forecasting cumulative Covid 19 Infection cases in USA