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 Russia" # 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<-3 # Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Russia"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 152844 1017708 1697559 3290438 4871843
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 1.900261
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.6570666
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 1677499
#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(1,3)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 1-3-1 network with 10 weights
## options were - linear output units
##
## sigma^2 estimated as 7519520
# 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 Russia"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Mean_All_NNAR<-round(mean(MAPE_Per_Day),3)
MAPE_NNAR<-paste(round(MAPE_Per_Day,3),"%")
MAPE_NNAR_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "2.766 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_NNAR=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_NNAR=validation_forecast,MAPE_NNAR_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | | date_NNAR | validation_data_by_name | actual_data | forecasting_NNAR | MAPE_NNAR_Model |
## +====+============+=========================+=============+==================+=================+
## | 1 | 2021-03-25 | Thursday | 4492692.00 | 4488144.64 | 0.101 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4501859.00 | 4492665.09 | 0.204 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4510744.00 | 4497036.68 | 0.304 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4519832.00 | 4501263.66 | 0.411 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4528543.00 | 4505350.23 | 0.512 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4536820.00 | 4509300.49 | 0.607 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4545095.00 | 4513118.48 | 0.704 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4554264.00 | 4516808.13 | 0.822 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4563056.00 | 4520373.31 | 0.935 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4572077.00 | 4523817.81 | 1.056 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4580894.00 | 4527145.33 | 1.173 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4589540.00 | 4530359.47 | 1.289 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4597868.00 | 4533463.77 | 1.401 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4606162.00 | 4536461.66 | 1.513 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4614834.00 | 4539356.52 | 1.636 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4623984.00 | 4542151.60 | 1.77 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4632688.00 | 4544850.10 | 1.896 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4641390.00 | 4547455.13 | 2.024 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4649710.00 | 4549969.70 | 2.145 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4657883.00 | 4552396.77 | 2.265 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 4666209.00 | 4554739.19 | 2.389 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 4675153.00 | 4556999.73 | 2.527 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 4684148.00 | 4559181.12 | 2.668 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 4693469.00 | 4561285.96 | 2.816 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 4702101.00 | 4563316.80 | 2.952 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 4710690.00 | 4565276.13 | 3.087 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 4718854.00 | 4567166.34 | 3.215 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 4727125.00 | 4568989.76 | 3.345 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 4736121.00 | 4570748.65 | 3.492 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 4744961.00 | 4572445.20 | 3.636 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 4753789.00 | 4574081.53 | 3.78 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 4762569.00 | 4575659.70 | 3.925 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 4771372.00 | 4577181.69 | 4.07 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 4779425.00 | 4578649.45 | 4.201 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 4787273.00 | 4580064.83 | 4.328 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 4796557.00 | 4581429.65 | 4.485 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4805288.00 | 4582745.66 | 4.631 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4814558.00 | 4584014.55 | 4.788 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4823255.00 | 4585237.96 | 4.935 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4831744.00 | 4586417.47 | 5.077 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4839514.00 | 4587554.63 | 5.206 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4847489.00 | 4588650.91 | 5.34 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4855128.00 | 4589707.75 | 5.467 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4863514.00 | 4590726.53 | 5.609 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4871843.00 | 4591708.60 | 5.75 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +====+============+=================+=====================+
## | 1 | 2021-05-09 | Sunday | 4592655.24 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 4593567.72 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 4594447.23 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 4595294.96 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 4596112.02 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 4596899.50 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 4597658.47 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 4598389.93 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 4599094.86 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 4599774.22 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 4600428.92 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 4601059.84 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 4601667.84 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 4602253.73 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 4602818.31 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 4603362.35 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 4603886.58 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 4604391.72 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 4604878.46 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 4605347.46 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 4605799.36 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 4606234.78 |
## +----+------------+-----------------+---------------------+
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 21.72611 580.3338 354.758 NaN Inf 0.03529009 -0.001091273
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.03717
## Beta: 0.9136316
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -29.75345
## [2,] -11.74250
##
## Sigma: 580.3338
## AIC: 8424.905
#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 Russia"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.071 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | | date_bats | validation_data_by_name | actual_data | forecasting_bats | MAPE_bats_Model |
## +====+============+=========================+=============+==================+=================+
## | 1 | 2021-03-25 | Thursday | 4492692.00 | 4492345.49 | 0.008 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4501859.00 | 4501206.54 | 0.014 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4510744.00 | 4510067.60 | 0.015 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4519832.00 | 4518928.66 | 0.02 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4528543.00 | 4527789.71 | 0.017 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4536820.00 | 4536650.77 | 0.004 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4545095.00 | 4545511.82 | 0.009 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4554264.00 | 4554372.88 | 0.002 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4563056.00 | 4563233.93 | 0.004 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4572077.00 | 4572094.99 | 0 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4580894.00 | 4580956.05 | 0.001 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4589540.00 | 4589817.10 | 0.006 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4597868.00 | 4598678.16 | 0.018 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4606162.00 | 4607539.21 | 0.03 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4614834.00 | 4616400.27 | 0.034 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4623984.00 | 4625261.32 | 0.028 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4632688.00 | 4634122.38 | 0.031 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4641390.00 | 4642983.44 | 0.034 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4649710.00 | 4651844.49 | 0.046 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4657883.00 | 4660705.55 | 0.061 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 4666209.00 | 4669566.60 | 0.072 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 4675153.00 | 4678427.66 | 0.07 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 4684148.00 | 4687288.71 | 0.067 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 4693469.00 | 4696149.77 | 0.057 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 4702101.00 | 4705010.82 | 0.062 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 4710690.00 | 4713871.88 | 0.068 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 4718854.00 | 4722732.94 | 0.082 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 4727125.00 | 4731593.99 | 0.095 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 4736121.00 | 4740455.05 | 0.092 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 4744961.00 | 4749316.10 | 0.092 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 4753789.00 | 4758177.16 | 0.092 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 4762569.00 | 4767038.21 | 0.094 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 4771372.00 | 4775899.27 | 0.095 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 4779425.00 | 4784760.33 | 0.112 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 4787273.00 | 4793621.38 | 0.133 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 4796557.00 | 4802482.44 | 0.124 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4805288.00 | 4811343.49 | 0.126 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4814558.00 | 4820204.55 | 0.117 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4823255.00 | 4829065.60 | 0.12 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4831744.00 | 4837926.66 | 0.128 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4839514.00 | 4846787.72 | 0.15 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4847489.00 | 4855648.77 | 0.168 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4855128.00 | 4864509.83 | 0.193 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4863514.00 | 4873370.88 | 0.203 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4871843.00 | 4882231.94 | 0.213 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 4891092.99 | 4766162.14 | 4700027.74 | 4766162.14 | 4700027.74 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4899954.05 | 4770983.07 | 4702709.95 | 4770983.07 | 4702709.95 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4908815.11 | 4775761.36 | 4705326.96 | 4775761.36 | 4705326.96 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4917676.16 | 4780497.47 | 4707879.46 | 4780497.47 | 4707879.46 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4926537.22 | 4785191.82 | 4710368.08 | 4785191.82 | 4710368.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4935398.27 | 4789844.82 | 4712793.47 | 4789844.82 | 4712793.47 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4944259.33 | 4794456.87 | 4715156.24 | 4794456.87 | 4715156.24 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4953120.38 | 4799028.37 | 4717456.98 | 4799028.37 | 4717456.98 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4961981.44 | 4803559.70 | 4719696.29 | 4803559.70 | 4719696.29 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4970842.50 | 4808051.22 | 4721874.72 | 4808051.22 | 4721874.72 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4979703.55 | 4812503.29 | 4723992.82 | 4812503.29 | 4723992.82 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4988564.61 | 4816916.27 | 4726051.13 | 4816916.27 | 4726051.13 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4997425.66 | 4821290.49 | 4728050.17 | 4821290.49 | 4728050.17 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 5006286.72 | 4825626.29 | 4729990.44 | 4825626.29 | 4729990.44 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 5015147.77 | 4829924.00 | 4731872.45 | 4829924.00 | 4731872.45 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 5024008.83 | 4834183.91 | 4733696.67 | 4834183.91 | 4733696.67 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 5032869.89 | 4838406.35 | 4735463.57 | 4838406.35 | 4735463.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 5041730.94 | 4842591.61 | 4737173.62 | 4842591.61 | 4737173.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 5050592.00 | 4846739.99 | 4738827.26 | 4846739.99 | 4738827.26 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5059453.05 | 4850851.77 | 4740424.93 | 4850851.77 | 4740424.93 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5068314.11 | 4854927.24 | 4741967.06 | 4854927.24 | 4741967.06 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5077175.16 | 4858966.66 | 4743454.06 | 4858966.66 | 4743454.06 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
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 22.00545 578.8215 364.0443 NaN Inf 0.03621385 0.0002286151
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.049738
## Beta: 0.9036269
## Damping Parameter: 1
## Gamma-1 Values: -0.001403385
## Gamma-2 Values: 0.001001786
##
## Seed States:
## [,1]
## [1,] -30.399350
## [2,] -11.506873
## [3,] -3.666777
## [4,] 12.648037
## [5,] 2.876446
## [6,] -8.251949
##
## Sigma: 578.8215
## AIC: 8434.572
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 Russia"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.079 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | | date_TBATS | validation_data_by_name | actual_data | forecasting_TBATS | MAPE_TBATS_Model |
## +====+============+=========================+=============+===================+==================+
## | 1 | 2021-03-25 | Thursday | 4492692.00 | 4492409.27 | 0.006 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-26 | Friday | 4501859.00 | 4501249.68 | 0.014 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-27 | Saturday | 4510744.00 | 4510104.71 | 0.014 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-28 | Sunday | 4519832.00 | 4519031.81 | 0.018 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-29 | Monday | 4528543.00 | 4527886.12 | 0.015 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-30 | Tuesday | 4536820.00 | 4536749.49 | 0.002 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-31 | Wednesday | 4545095.00 | 4545671.03 | 0.013 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-04-01 | Thursday | 4554264.00 | 4554511.44 | 0.005 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 9 | 2021-04-02 | Friday | 4563056.00 | 4563366.47 | 0.007 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 10 | 2021-04-03 | Saturday | 4572077.00 | 4572293.57 | 0.005 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 11 | 2021-04-04 | Sunday | 4580894.00 | 4581147.89 | 0.006 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 12 | 2021-04-05 | Monday | 4589540.00 | 4590011.26 | 0.01 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 13 | 2021-04-06 | Tuesday | 4597868.00 | 4598932.80 | 0.023 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 14 | 2021-04-07 | Wednesday | 4606162.00 | 4607773.20 | 0.035 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 15 | 2021-04-08 | Thursday | 4614834.00 | 4616628.24 | 0.039 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 16 | 2021-04-09 | Friday | 4623984.00 | 4625555.34 | 0.034 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 17 | 2021-04-10 | Saturday | 4632688.00 | 4634409.65 | 0.037 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 18 | 2021-04-11 | Sunday | 4641390.00 | 4643273.02 | 0.041 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 19 | 2021-04-12 | Monday | 4649710.00 | 4652194.56 | 0.053 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 20 | 2021-04-13 | Tuesday | 4657883.00 | 4661034.97 | 0.068 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 21 | 2021-04-14 | Wednesday | 4666209.00 | 4669890.00 | 0.079 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 22 | 2021-04-15 | Thursday | 4675153.00 | 4678817.10 | 0.078 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 23 | 2021-04-16 | Friday | 4684148.00 | 4687671.41 | 0.075 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 24 | 2021-04-17 | Saturday | 4693469.00 | 4696534.79 | 0.065 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 25 | 2021-04-18 | Sunday | 4702101.00 | 4705456.32 | 0.071 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 26 | 2021-04-19 | Monday | 4710690.00 | 4714296.73 | 0.077 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 27 | 2021-04-20 | Tuesday | 4718854.00 | 4723151.77 | 0.091 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 28 | 2021-04-21 | Wednesday | 4727125.00 | 4732078.87 | 0.105 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 29 | 2021-04-22 | Thursday | 4736121.00 | 4740933.18 | 0.102 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 30 | 2021-04-23 | Friday | 4744961.00 | 4749796.55 | 0.102 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 31 | 2021-04-24 | Saturday | 4753789.00 | 4758718.09 | 0.104 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 32 | 2021-04-25 | Sunday | 4762569.00 | 4767558.50 | 0.105 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 33 | 2021-04-26 | Monday | 4771372.00 | 4776413.53 | 0.106 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 34 | 2021-04-27 | Tuesday | 4779425.00 | 4785340.63 | 0.124 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 35 | 2021-04-28 | Wednesday | 4787273.00 | 4794194.94 | 0.145 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 36 | 2021-04-29 | Thursday | 4796557.00 | 4803058.31 | 0.136 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 37 | 2021-04-30 | Friday | 4805288.00 | 4811979.85 | 0.139 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 38 | 2021-05-01 | Saturday | 4814558.00 | 4820820.26 | 0.13 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 39 | 2021-05-02 | Sunday | 4823255.00 | 4829675.29 | 0.133 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 40 | 2021-05-03 | Monday | 4831744.00 | 4838602.39 | 0.142 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 41 | 2021-05-04 | Tuesday | 4839514.00 | 4847456.70 | 0.164 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 42 | 2021-05-05 | Wednesday | 4847489.00 | 4856320.08 | 0.182 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 43 | 2021-05-06 | Thursday | 4855128.00 | 4865241.61 | 0.208 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 44 | 2021-05-07 | Friday | 4863514.00 | 4874082.02 | 0.217 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 45 | 2021-05-08 | Saturday | 4871843.00 | 4882937.06 | 0.228 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
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 | 4891864.16 | 4886746.30 | 4884037.07 | 4896982.01 | 4899691.24 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4900718.47 | 4895548.44 | 4892811.60 | 4905888.49 | 4908625.33 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4909581.84 | 4904360.64 | 4901596.70 | 4914803.04 | 4917566.98 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4918503.38 | 4913231.78 | 4910441.16 | 4923774.98 | 4926565.59 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4927343.79 | 4922022.24 | 4919205.19 | 4932665.33 | 4935482.38 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4936198.82 | 4930827.93 | 4927984.75 | 4941569.71 | 4944412.89 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4945125.92 | 4939706.13 | 4936837.07 | 4950545.71 | 4953414.77 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4953980.23 | 4948511.99 | 4945617.28 | 4959448.47 | 4962343.18 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4962843.60 | 4957327.77 | 4954407.87 | 4968359.44 | 4971279.34 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4971765.14 | 4966202.39 | 4963257.65 | 4977327.89 | 4980272.63 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4980605.55 | 4974996.26 | 4972026.87 | 4986214.84 | 4989184.23 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4989460.58 | 4983805.25 | 4980811.50 | 4995115.92 | 4998109.67 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4998387.68 | 4992686.69 | 4989668.76 | 5004088.68 | 5007106.61 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 5007241.99 | 5001495.70 | 4998453.79 | 5012988.29 | 5016030.20 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 5016105.37 | 5010314.54 | 5007249.06 | 5021896.19 | 5024961.67 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 5025026.91 | 5019192.14 | 5016103.41 | 5030861.67 | 5033950.40 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 5033867.31 | 5027988.92 | 5024877.09 | 5039745.71 | 5042857.54 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 5042722.35 | 5036800.76 | 5033666.07 | 5048643.93 | 5051778.63 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 5051649.45 | 5045684.99 | 5042527.59 | 5057613.91 | 5060771.30 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5060503.76 | 5054496.73 | 5051316.80 | 5066510.78 | 5069690.71 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5069367.13 | 5063318.23 | 5060116.13 | 5075416.03 | 5078618.13 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5078288.67 | 5072198.42 | 5068974.44 | 5084378.92 | 5087602.90 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -56.75677 614.1658 385.8766 NaN Inf 0.03838565 0.3115108
# 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= 0.5839
##
## Smoothing parameters:
## alpha = 0.9555
## beta = 0.6374
##
## Initial states:
## l = -2.0666
## b = -0.5033
##
## sigma: 3.3382
##
## AIC AICc BIC
## 3811.471 3811.607 3831.984
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -56.75677 614.1658 385.8766 NaN Inf 0.03838565 0.3115108
# 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 Russia"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.099 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)), type = "rest")
##
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | | date_holt | validation_data_by_name | actual_data | forecasting_holt | MAPE_holt_Model |
## +====+============+=========================+=============+==================+=================+
## | 1 | 2021-03-25 | Thursday | 4492692.00 | 4492282.13 | 0.009 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4501859.00 | 4501102.39 | 0.017 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4510744.00 | 4509929.84 | 0.018 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4519832.00 | 4518764.49 | 0.024 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4528543.00 | 4527606.33 | 0.021 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4536820.00 | 4536455.36 | 0.008 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4545095.00 | 4545311.58 | 0.005 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4554264.00 | 4554174.99 | 0.002 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4563056.00 | 4563045.58 | 0 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4572077.00 | 4571923.36 | 0.003 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4580894.00 | 4580808.31 | 0.002 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4589540.00 | 4589700.44 | 0.003 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4597868.00 | 4598599.74 | 0.016 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4606162.00 | 4607506.22 | 0.029 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4614834.00 | 4616419.86 | 0.034 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4623984.00 | 4625340.68 | 0.029 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4632688.00 | 4634268.66 | 0.034 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4641390.00 | 4643203.80 | 0.039 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4649710.00 | 4652146.10 | 0.052 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4657883.00 | 4661095.56 | 0.069 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 4666209.00 | 4670052.18 | 0.082 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 4675153.00 | 4679015.95 | 0.083 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 4684148.00 | 4687986.87 | 0.082 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 4693469.00 | 4696964.94 | 0.074 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 4702101.00 | 4705950.16 | 0.082 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 4710690.00 | 4714942.52 | 0.09 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 4718854.00 | 4723942.03 | 0.108 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 4727125.00 | 4732948.67 | 0.123 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 4736121.00 | 4741962.45 | 0.123 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 4744961.00 | 4750983.37 | 0.127 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 4753789.00 | 4760011.42 | 0.131 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 4762569.00 | 4769046.60 | 0.136 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 4771372.00 | 4778088.91 | 0.141 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 4779425.00 | 4787138.35 | 0.161 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 4787273.00 | 4796194.91 | 0.186 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 4796557.00 | 4805258.59 | 0.181 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4805288.00 | 4814329.40 | 0.188 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4814558.00 | 4823407.32 | 0.184 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4823255.00 | 4832492.35 | 0.192 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4831744.00 | 4841584.50 | 0.204 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4839514.00 | 4850683.76 | 0.231 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4847489.00 | 4859790.12 | 0.254 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4855128.00 | 4868903.59 | 0.284 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4863514.00 | 4878024.17 | 0.298 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4871843.00 | 4887151.85 | 0.314 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 4896286.63 | 4592003.22 | 4434225.87 | 5208650.26 | 5377247.82 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4905428.50 | 4591267.78 | 4428476.81 | 5228193.65 | 5402506.85 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4914577.47 | 4590431.53 | 4422578.97 | 5247874.11 | 5427980.49 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4923733.53 | 4589495.53 | 4416534.18 | 5267691.04 | 5453667.99 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4932896.68 | 4588460.81 | 4410344.19 | 5287643.84 | 5479568.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4942066.92 | 4587328.37 | 4404010.74 | 5307731.96 | 5505681.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4951244.25 | 4586099.18 | 4397535.51 | 5327954.86 | 5532006.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4960428.66 | 4584774.21 | 4390920.14 | 5348312.04 | 5558542.60 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4969620.16 | 4583354.36 | 4384166.25 | 5368802.99 | 5585289.26 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4978818.73 | 4581840.56 | 4377275.41 | 5389427.27 | 5612245.98 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4988024.38 | 4580233.67 | 4370249.17 | 5410184.42 | 5639412.27 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4997237.10 | 4578534.57 | 4363089.05 | 5431074.03 | 5666787.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 5006456.90 | 4576744.09 | 4355796.51 | 5452095.68 | 5694371.61 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 5015683.77 | 4574863.06 | 4348373.04 | 5473248.99 | 5722163.79 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 5024917.70 | 4572892.29 | 4340820.04 | 5494533.59 | 5750163.77 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 5034158.71 | 4570832.57 | 4333138.93 | 5515949.12 | 5778371.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 5043406.77 | 4568684.67 | 4325331.08 | 5537495.25 | 5806785.67 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 5052661.90 | 4566449.35 | 4317397.84 | 5559171.66 | 5835406.91 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 5061924.09 | 4564127.34 | 4309340.55 | 5580978.04 | 5864234.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5071193.34 | 4561719.39 | 4301160.52 | 5602914.10 | 5893268.43 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5080469.64 | 4559226.19 | 4292859.03 | 5624979.55 | 5922508.16 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5089753.00 | 4556648.46 | 4284437.36 | 5647174.13 | 5951953.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
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 Russia"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 6.7863, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -0.86577, Truncation lag parameter = 5,
## p-value = 0.9895
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -4.5406, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Forecasting cumulative Covid 19 Infection cases in Russia"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 4.9323, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = 0.55875, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.94606, Lag order = 7, p-value = 0.9471
## 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 Russia"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.617, Truncation lag parameter = 5, p-value = 0.02109
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) = -445.54, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -3.6431, Lag order = 7, p-value = 0.02877
## 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) : 6932.144
## ARIMA(0,2,1) : 6933.117
## ARIMA(0,2,2) : 6934.51
## ARIMA(0,2,3) : 6936.517
## ARIMA(0,2,4) : 6937.177
## ARIMA(0,2,5) : 6917.505
## ARIMA(1,2,0) : 6933.199
## ARIMA(1,2,1) : 6934.758
## ARIMA(1,2,2) : 6936.535
## ARIMA(1,2,3) : Inf
## ARIMA(1,2,4) : 6893.29
## ARIMA(2,2,0) : 6934.522
## ARIMA(2,2,1) : 6936.51
## ARIMA(2,2,2) : 6938.548
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 6936.45
## ARIMA(3,2,1) : Inf
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 6938.363
## ARIMA(4,2,1) : 6939.415
## ARIMA(5,2,0) : 6939.092
##
##
##
## Best model: ARIMA(1,2,4)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,4)
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4
## 0.7214 -0.8886 -0.0446 0.0836 0.2503
## s.e. 0.0676 0.0742 0.0673 0.0592 0.0524
##
## sigma^2 estimated as 306932: log likelihood=-3440.55
## AIC=6893.1 AICc=6893.29 BIC=6917.69
#Make changes in the source of auto arima to run the best model
arima.string <- function (object, padding = FALSE)
{
order <- object$arma[c(1, 6, 2, 3, 7, 4, 5)]
m <- order[7]
result <- paste("ARIMA(", order[1], ",", order[2], ",",
order[3], ")", sep = "")
if (m > 1 && sum(order[4:6]) > 0) {
result <- paste(result, "(", order[4], ",", order[5],
",", order[6], ")[", m, "]", sep = "")
}
if (padding && m > 1 && sum(order[4:6]) == 0) {
result <- paste(result, " ", sep = "")
if (m <= 9) {
result <- paste(result, " ", sep = "")
}
else if (m <= 99) {
result <- paste(result, " ", sep = "")
}
else {
result <- paste(result, " ", sep = "")
}
}
if (!is.null(object$xreg)) {
if (NCOL(object$xreg) == 1 && is.element("drift", names(object$coef))) {
result <- paste(result, "with drift ")
}
else {
result <- paste("Regression with", result, "errors")
}
}
else {
if (is.element("constant", names(object$coef)) || is.element("intercept",
names(object$coef))) {
result <- paste(result, "with non-zero mean")
}
else if (order[2] == 0 && order[5] == 0) {
result <- paste(result, "with zero mean ")
}
else {
result <- paste(result, " ")
}
}
if (!padding) {
result <- gsub("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 4
strtoi(bestmodel[3])
## [1] 4
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4
## 0.7214 -0.8886 -0.0446 0.0836 0.2503
## s.e. 0.0676 0.0742 0.0673 0.0592 0.0524
##
## sigma^2 estimated as 303483: log likelihood = -3440.55, aic = 6893.1
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting cumulative Covid 19 Infection cases in Russia"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 12.28731 549.6594 338.2559 0.3124402 2.246239 0.03364851
## ACF1
## Training set 0.01098464
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,2,4)
## Q* = 53.974, df = 5, p-value = 2.121e-10
##
## Model df: 5. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
Box.test(x1_model1$residuals^2, lag=20, type="Ljung-Box") # Do test for resdulas by using Box-Ljung test , Ljung-Box test For Modelling
##
## Box-Ljung test
##
## data: x1_model1$residuals^2
## X-squared = 541.88, 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 = 162.6, 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 Russia"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.316 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)), type = "rest")
##
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | | date_auto.arima | validation_data_by_name | actual_data | forecasting_auto.arima | MAPE_auto.arima_Model |
## +====+=================+=========================+=============+========================+=======================+
## | 1 | 2021-03-25 | Thursday | 4492692.00 | 4492391.89 | 0.007 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-26 | Friday | 4501859.00 | 4501209.49 | 0.014 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-27 | Saturday | 4510744.00 | 4509723.90 | 0.023 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-28 | Sunday | 4519832.00 | 4518066.44 | 0.039 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-29 | Monday | 4528543.00 | 4526284.98 | 0.05 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-30 | Tuesday | 4536820.00 | 4534414.07 | 0.053 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-31 | Wednesday | 4545095.00 | 4542478.62 | 0.058 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-04-01 | Thursday | 4554264.00 | 4550496.62 | 0.083 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 9 | 2021-04-02 | Friday | 4563056.00 | 4558481.04 | 0.1 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 10 | 2021-04-03 | Saturday | 4572077.00 | 4566441.22 | 0.123 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 11 | 2021-04-04 | Sunday | 4580894.00 | 4574383.92 | 0.142 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 12 | 2021-04-05 | Monday | 4589540.00 | 4582314.01 | 0.157 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 13 | 2021-04-06 | Tuesday | 4597868.00 | 4590235.01 | 0.166 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 14 | 2021-04-07 | Wednesday | 4606162.00 | 4598149.44 | 0.174 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 15 | 2021-04-08 | Thursday | 4614834.00 | 4606059.14 | 0.19 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 16 | 2021-04-09 | Friday | 4623984.00 | 4613965.42 | 0.217 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 17 | 2021-04-10 | Saturday | 4632688.00 | 4621869.24 | 0.234 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 18 | 2021-04-11 | Sunday | 4641390.00 | 4629771.28 | 0.25 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 19 | 2021-04-12 | Monday | 4649710.00 | 4637672.03 | 0.259 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 20 | 2021-04-13 | Tuesday | 4657883.00 | 4645571.87 | 0.264 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 21 | 2021-04-14 | Wednesday | 4666209.00 | 4653471.03 | 0.273 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 22 | 2021-04-15 | Thursday | 4675153.00 | 4661369.71 | 0.295 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 23 | 2021-04-16 | Friday | 4684148.00 | 4669268.05 | 0.318 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 24 | 2021-04-17 | Saturday | 4693469.00 | 4677166.14 | 0.347 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 25 | 2021-04-18 | Sunday | 4702101.00 | 4685064.04 | 0.362 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 26 | 2021-04-19 | Monday | 4710690.00 | 4692961.81 | 0.376 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 27 | 2021-04-20 | Tuesday | 4718854.00 | 4700859.49 | 0.381 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 28 | 2021-04-21 | Wednesday | 4727125.00 | 4708757.11 | 0.389 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 29 | 2021-04-22 | Thursday | 4736121.00 | 4716654.67 | 0.411 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 30 | 2021-04-23 | Friday | 4744961.00 | 4724552.20 | 0.43 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 31 | 2021-04-24 | Saturday | 4753789.00 | 4732449.70 | 0.449 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 32 | 2021-04-25 | Sunday | 4762569.00 | 4740347.18 | 0.467 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 33 | 2021-04-26 | Monday | 4771372.00 | 4748244.65 | 0.485 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 34 | 2021-04-27 | Tuesday | 4779425.00 | 4756142.11 | 0.487 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 35 | 2021-04-28 | Wednesday | 4787273.00 | 4764039.57 | 0.485 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 36 | 2021-04-29 | Thursday | 4796557.00 | 4771937.02 | 0.513 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 37 | 2021-04-30 | Friday | 4805288.00 | 4779834.46 | 0.53 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 38 | 2021-05-01 | Saturday | 4814558.00 | 4787731.90 | 0.557 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 39 | 2021-05-02 | Sunday | 4823255.00 | 4795629.35 | 0.573 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 40 | 2021-05-03 | Monday | 4831744.00 | 4803526.79 | 0.584 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 41 | 2021-05-04 | Tuesday | 4839514.00 | 4811424.22 | 0.58 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 42 | 2021-05-05 | Wednesday | 4847489.00 | 4819321.66 | 0.581 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 43 | 2021-05-06 | Thursday | 4855128.00 | 4827219.10 | 0.575 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 44 | 2021-05-07 | Friday | 4863514.00 | 4835116.54 | 0.584 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 45 | 2021-05-08 | Saturday | 4871843.00 | 4843013.97 | 0.592 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 4850911.41 | 4684217.55 | 4595975.15 | 5017605.27 | 5105847.67 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4858808.85 | 4686306.09 | 4594988.65 | 5031311.60 | 5122629.04 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4866706.28 | 4688328.29 | 4593900.69 | 5045084.27 | 5139511.87 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4874603.72 | 4690284.90 | 4592712.41 | 5058922.54 | 5156495.03 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4882501.16 | 4692176.64 | 4591424.93 | 5072825.67 | 5173577.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4890398.59 | 4694004.22 | 4590039.31 | 5086792.97 | 5190757.87 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4898296.03 | 4695768.31 | 4588556.62 | 5100823.74 | 5208035.44 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4906193.46 | 4697469.59 | 4586977.84 | 5114917.34 | 5225409.09 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4914090.90 | 4699108.67 | 4585303.96 | 5129073.13 | 5242877.84 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4921988.34 | 4700686.20 | 4583535.92 | 5143290.47 | 5260440.75 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4929885.77 | 4702202.76 | 4581674.65 | 5157568.79 | 5278096.89 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4937783.21 | 4703658.94 | 4579721.03 | 5171907.48 | 5295845.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4945680.64 | 4705055.30 | 4577675.94 | 5186305.99 | 5313685.35 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4953578.08 | 4706392.40 | 4575540.20 | 5200763.76 | 5331615.96 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4961475.52 | 4707670.77 | 4573314.65 | 5215280.26 | 5349636.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4969372.95 | 4708890.93 | 4571000.08 | 5229854.97 | 5367745.83 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4977270.39 | 4710053.39 | 4568597.26 | 5244487.39 | 5385943.52 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4985167.83 | 4711158.65 | 4566106.95 | 5259177.00 | 5404228.70 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4993065.26 | 4712207.17 | 4563529.88 | 5273923.35 | 5422600.64 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5000962.70 | 4713199.45 | 4560866.78 | 5288725.95 | 5441058.61 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5008860.13 | 4714135.92 | 4558118.34 | 5303584.35 | 5459601.92 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5016757.57 | 4715017.04 | 4555285.25 | 5318498.10 | 5478229.89 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.316 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Russia"
## 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 Russia"
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 Russia"
paste(MAPE_Mean_EnsemblingAverage,"%")
## [1] "0.018 %"
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 Russia"
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 | 4492692.00 | 4492241.64 | 0.01 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 2 | 2021-03-26 | Friday | 4501859.00 | 4500991.56 | 0.019 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 4510744.00 | 4509730.72 | 0.022 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 4519832.00 | 4518463.95 | 0.03 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 5 | 2021-03-29 | Monday | 4528543.00 | 4527188.93 | 0.03 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 4536820.00 | 4535908.68 | 0.02 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 4545095.00 | 4544625.13 | 0.01 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 4554264.00 | 4553335.37 | 0.02 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 9 | 2021-04-02 | Friday | 4563056.00 | 4562042.20 | 0.022 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 4572077.00 | 4570747.39 | 0.029 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 4580894.00 | 4579447.58 | 0.032 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 12 | 2021-04-05 | Monday | 4589540.00 | 4588145.02 | 0.03 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 4597868.00 | 4596841.12 | 0.022 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 4606162.00 | 4605532.55 | 0.014 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 4614834.00 | 4614221.84 | 0.013 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 16 | 2021-04-09 | Friday | 4623984.00 | 4622910.52 | 0.023 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 4632688.00 | 4631595.08 | 0.024 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 4641390.00 | 4640277.67 | 0.024 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 19 | 2021-04-12 | Monday | 4649710.00 | 4648959.60 | 0.016 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 4657883.00 | 4657637.47 | 0.005 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 4666209.00 | 4666313.75 | 0.002 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 4675153.00 | 4674989.95 | 0.003 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 23 | 2021-04-16 | Friday | 4684148.00 | 4683662.53 | 0.01 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 4693469.00 | 4692333.59 | 0.024 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 4702101.00 | 4701004.43 | 0.023 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 26 | 2021-04-19 | Monday | 4710690.00 | 4709671.62 | 0.022 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 4718854.00 | 4718337.63 | 0.011 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 4727125.00 | 4727003.95 | 0.003 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 4736121.00 | 4735667.02 | 0.01 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 30 | 2021-04-23 | Friday | 4744961.00 | 4744328.93 | 0.013 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 4753789.00 | 4752990.96 | 0.017 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 4762569.00 | 4761649.69 | 0.019 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 33 | 2021-04-26 | Monday | 4771372.00 | 4770307.56 | 0.022 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 4779425.00 | 4778966.06 | 0.01 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 4787273.00 | 4787621.60 | 0.007 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 4796557.00 | 4796276.28 | 0.006 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 37 | 2021-04-30 | Friday | 4805288.00 | 4804931.38 | 0.007 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 4814558.00 | 4813583.44 | 0.02 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 4823255.00 | 4822234.92 | 0.021 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 40 | 2021-05-03 | Monday | 4831744.00 | 4830887.27 | 0.018 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 4839514.00 | 4839536.93 | 0 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 4847489.00 | 4848185.96 | 0.014 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 4855128.00 | 4856835.65 | 0.035 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 44 | 2021-05-07 | Friday | 4863514.00 | 4865482.53 | 0.04 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 4871843.00 | 4874129.03 | 0.047 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
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 | 4882776.63 |
## +----+------------+-----------------+---------------------------+
## | 2 | 2021-05-10 | Monday | 4891421.73 |
## +----+------------+-----------------+---------------------------+
## | 3 | 2021-05-11 | Tuesday | 4900066.42 |
## +----+------------+-----------------+---------------------------+
## | 4 | 2021-05-12 | Wednesday | 4908711.94 |
## +----+------------+-----------------+---------------------------+
## | 5 | 2021-05-13 | Thursday | 4917354.84 |
## +----+------------+-----------------+---------------------------+
## | 6 | 2021-05-14 | Friday | 4925997.54 |
## +----+------------+-----------------+---------------------------+
## | 7 | 2021-05-15 | Saturday | 4934641.51 |
## +----+------------+-----------------+---------------------------+
## | 8 | 2021-05-16 | Sunday | 4943283.15 |
## +----+------------+-----------------+---------------------------+
## | 9 | 2021-05-17 | Monday | 4951924.53 |
## +----+------------+-----------------+---------------------------+
## | 10 | 2021-05-18 | Tuesday | 4960566.91 |
## +----+------------+-----------------+---------------------------+
## | 11 | 2021-05-19 | Wednesday | 4969206.81 |
## +----+------------+-----------------+---------------------------+
## | 12 | 2021-05-20 | Thursday | 4977846.66 |
## +----+------------+-----------------+---------------------------+
## | 13 | 2021-05-21 | Friday | 4986487.92 |
## +----+------------+-----------------+---------------------------+
## | 14 | 2021-05-22 | Saturday | 4995126.99 |
## +----+------------+-----------------+---------------------------+
## | 15 | 2021-05-23 | Sunday | 5003765.92 |
## +----+------------+-----------------+---------------------------+
## | 16 | 2021-05-24 | Monday | 5012405.97 |
## +----+------------+-----------------+---------------------------+
## | 17 | 2021-05-25 | Tuesday | 5021043.67 |
## +----+------------+-----------------+---------------------------+
## | 18 | 2021-05-26 | Wednesday | 5029681.44 |
## +----+------------+-----------------+---------------------------+
## | 19 | 2021-05-27 | Thursday | 5038320.73 |
## +----+------------+-----------------+---------------------------+
## | 20 | 2021-05-28 | Friday | 5046957.93 |
## +----+------------+-----------------+---------------------------+
## | 21 | 2021-05-29 | Saturday | 5055595.10 |
## +----+------------+-----------------+---------------------------+
## | 22 | 2021-05-30 | Sunday | 5064233.50 |
## +----+------------+-----------------+---------------------------+
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 Russia"
best_recommended_model
## [1] 0.018
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 Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4891092.99 | 4766162.14 | 4700027.74 | 4766162.14 | 4700027.74 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4899954.05 | 4770983.07 | 4702709.95 | 4770983.07 | 4702709.95 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4908815.11 | 4775761.36 | 4705326.96 | 4775761.36 | 4705326.96 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4917676.16 | 4780497.47 | 4707879.46 | 4780497.47 | 4707879.46 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4926537.22 | 4785191.82 | 4710368.08 | 4785191.82 | 4710368.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4935398.27 | 4789844.82 | 4712793.47 | 4789844.82 | 4712793.47 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4944259.33 | 4794456.87 | 4715156.24 | 4794456.87 | 4715156.24 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4953120.38 | 4799028.37 | 4717456.98 | 4799028.37 | 4717456.98 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4961981.44 | 4803559.70 | 4719696.29 | 4803559.70 | 4719696.29 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4970842.50 | 4808051.22 | 4721874.72 | 4808051.22 | 4721874.72 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4979703.55 | 4812503.29 | 4723992.82 | 4812503.29 | 4723992.82 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4988564.61 | 4816916.27 | 4726051.13 | 4816916.27 | 4726051.13 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4997425.66 | 4821290.49 | 4728050.17 | 4821290.49 | 4728050.17 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 5006286.72 | 4825626.29 | 4729990.44 | 4825626.29 | 4729990.44 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 5015147.77 | 4829924.00 | 4731872.45 | 4829924.00 | 4731872.45 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 5024008.83 | 4834183.91 | 4733696.67 | 4834183.91 | 4733696.67 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 5032869.89 | 4838406.35 | 4735463.57 | 4838406.35 | 4735463.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 5041730.94 | 4842591.61 | 4737173.62 | 4842591.61 | 4737173.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 5050592.00 | 4846739.99 | 4738827.26 | 4846739.99 | 4738827.26 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5059453.05 | 4850851.77 | 4740424.93 | 4850851.77 | 4740424.93 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5068314.11 | 4854927.24 | 4741967.06 | 4854927.24 | 4741967.06 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5077175.16 | 4858966.66 | 4743454.06 | 4858966.66 | 4743454.06 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+======================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4891864.16 | 4886746.30 | 4884037.07 | 4896982.01 | 4899691.24 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4900718.47 | 4895548.44 | 4892811.60 | 4905888.49 | 4908625.33 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4909581.84 | 4904360.64 | 4901596.70 | 4914803.04 | 4917566.98 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4918503.38 | 4913231.78 | 4910441.16 | 4923774.98 | 4926565.59 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4927343.79 | 4922022.24 | 4919205.19 | 4932665.33 | 4935482.38 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4936198.82 | 4930827.93 | 4927984.75 | 4941569.71 | 4944412.89 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4945125.92 | 4939706.13 | 4936837.07 | 4950545.71 | 4953414.77 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4953980.23 | 4948511.99 | 4945617.28 | 4959448.47 | 4962343.18 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4962843.60 | 4957327.77 | 4954407.87 | 4968359.44 | 4971279.34 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4971765.14 | 4966202.39 | 4963257.65 | 4977327.89 | 4980272.63 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4980605.55 | 4974996.26 | 4972026.87 | 4986214.84 | 4989184.23 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4989460.58 | 4983805.25 | 4980811.50 | 4995115.92 | 4998109.67 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4998387.68 | 4992686.69 | 4989668.76 | 5004088.68 | 5007106.61 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 5007241.99 | 5001495.70 | 4998453.79 | 5012988.29 | 5016030.20 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 5016105.37 | 5010314.54 | 5007249.06 | 5021896.19 | 5024961.67 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 5025026.91 | 5019192.14 | 5016103.41 | 5030861.67 | 5033950.40 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 5033867.31 | 5027988.92 | 5024877.09 | 5039745.71 | 5042857.54 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 5042722.35 | 5036800.76 | 5033666.07 | 5048643.93 | 5051778.63 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 5051649.45 | 5045684.99 | 5042527.59 | 5057613.91 | 5060771.30 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5060503.76 | 5054496.73 | 5051316.80 | 5066510.78 | 5069690.71 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5069367.13 | 5063318.23 | 5060116.13 | 5075416.03 | 5078618.13 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5078288.67 | 5072198.42 | 5068974.44 | 5084378.92 | 5087602.90 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
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 Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4896286.63 | 4592003.22 | 4434225.87 | 5208650.26 | 5377247.82 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4905428.50 | 4591267.78 | 4428476.81 | 5228193.65 | 5402506.85 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4914577.47 | 4590431.53 | 4422578.97 | 5247874.11 | 5427980.49 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4923733.53 | 4589495.53 | 4416534.18 | 5267691.04 | 5453667.99 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4932896.68 | 4588460.81 | 4410344.19 | 5287643.84 | 5479568.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4942066.92 | 4587328.37 | 4404010.74 | 5307731.96 | 5505681.69 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4951244.25 | 4586099.18 | 4397535.51 | 5327954.86 | 5532006.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4960428.66 | 4584774.21 | 4390920.14 | 5348312.04 | 5558542.60 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4969620.16 | 4583354.36 | 4384166.25 | 5368802.99 | 5585289.26 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4978818.73 | 4581840.56 | 4377275.41 | 5389427.27 | 5612245.98 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4988024.38 | 4580233.67 | 4370249.17 | 5410184.42 | 5639412.27 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4997237.10 | 4578534.57 | 4363089.05 | 5431074.03 | 5666787.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 5006456.90 | 4576744.09 | 4355796.51 | 5452095.68 | 5694371.61 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 5015683.77 | 4574863.06 | 4348373.04 | 5473248.99 | 5722163.79 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 5024917.70 | 4572892.29 | 4340820.04 | 5494533.59 | 5750163.77 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 5034158.71 | 4570832.57 | 4333138.93 | 5515949.12 | 5778371.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 5043406.77 | 4568684.67 | 4325331.08 | 5537495.25 | 5806785.67 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 5052661.90 | 4566449.35 | 4317397.84 | 5559171.66 | 5835406.91 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 5061924.09 | 4564127.34 | 4309340.55 | 5580978.04 | 5864234.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5071193.34 | 4561719.39 | 4301160.52 | 5602914.10 | 5893268.43 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5080469.64 | 4559226.19 | 4292859.03 | 5624979.55 | 5922508.16 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5089753.00 | 4556648.46 | 4284437.36 | 5647174.13 | 5951953.55 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+===========================+============+============+============+============+
## | 1 | 2021-05-09 | Sunday | 4850911.41 | 4684217.55 | 4595975.15 | 5017605.27 | 5105847.67 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 4858808.85 | 4686306.09 | 4594988.65 | 5031311.60 | 5122629.04 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 4866706.28 | 4688328.29 | 4593900.69 | 5045084.27 | 5139511.87 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 4874603.72 | 4690284.90 | 4592712.41 | 5058922.54 | 5156495.03 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 4882501.16 | 4692176.64 | 4591424.93 | 5072825.67 | 5173577.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 4890398.59 | 4694004.22 | 4590039.31 | 5086792.97 | 5190757.87 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 4898296.03 | 4695768.31 | 4588556.62 | 5100823.74 | 5208035.44 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 4906193.46 | 4697469.59 | 4586977.84 | 5114917.34 | 5225409.09 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 4914090.90 | 4699108.67 | 4585303.96 | 5129073.13 | 5242877.84 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 4921988.34 | 4700686.20 | 4583535.92 | 5143290.47 | 5260440.75 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 4929885.77 | 4702202.76 | 4581674.65 | 5157568.79 | 5278096.89 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 4937783.21 | 4703658.94 | 4579721.03 | 5171907.48 | 5295845.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 4945680.64 | 4705055.30 | 4577675.94 | 5186305.99 | 5313685.35 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 4953578.08 | 4706392.40 | 4575540.20 | 5200763.76 | 5331615.96 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 4961475.52 | 4707670.77 | 4573314.65 | 5215280.26 | 5349636.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 4969372.95 | 4708890.93 | 4571000.08 | 5229854.97 | 5367745.83 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 4977270.39 | 4710053.39 | 4568597.26 | 5244487.39 | 5385943.52 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 4985167.83 | 4711158.65 | 4566106.95 | 5259177.00 | 5404228.70 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 4993065.26 | 4712207.17 | 4563529.88 | 5273923.35 | 5422600.64 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 5000962.70 | 4713199.45 | 4560866.78 | 5288725.95 | 5441058.61 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 5008860.13 | 4714135.92 | 4558118.34 | 5303584.35 | 5459601.92 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 5016757.57 | 4715017.04 | 4555285.25 | 5318498.10 | 5478229.89 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting cumulative Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +====+============+=================+=====================+
## | 1 | 2021-05-09 | Sunday | 4592655.24 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 4593567.72 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 4594447.23 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 4595294.96 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 4596112.02 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 4596899.50 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 4597658.47 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 4598389.93 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 4599094.86 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 4599774.22 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 4600428.92 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 4601059.84 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 4601667.84 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 4602253.73 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 4602818.31 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 4603362.35 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 4603886.58 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 4604391.72 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 4604878.46 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 4605347.46 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 4605799.36 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 4606234.78 |
## +----+------------+-----------------+---------------------+
paste("Forecasting by using Ensembling Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Ensembling Model ==> Forecasting cumulative Covid 19 Infection cases in Russia"
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 | 4882776.63 |
## +----+------------+-----------------+------------------------+
## | 2 | 2021-05-10 | Monday | 4891421.73 |
## +----+------------+-----------------+------------------------+
## | 3 | 2021-05-11 | Tuesday | 4900066.42 |
## +----+------------+-----------------+------------------------+
## | 4 | 2021-05-12 | Wednesday | 4908711.94 |
## +----+------------+-----------------+------------------------+
## | 5 | 2021-05-13 | Thursday | 4917354.84 |
## +----+------------+-----------------+------------------------+
## | 6 | 2021-05-14 | Friday | 4925997.54 |
## +----+------------+-----------------+------------------------+
## | 7 | 2021-05-15 | Saturday | 4934641.51 |
## +----+------------+-----------------+------------------------+
## | 8 | 2021-05-16 | Sunday | 4943283.15 |
## +----+------------+-----------------+------------------------+
## | 9 | 2021-05-17 | Monday | 4951924.53 |
## +----+------------+-----------------+------------------------+
## | 10 | 2021-05-18 | Tuesday | 4960566.91 |
## +----+------------+-----------------+------------------------+
## | 11 | 2021-05-19 | Wednesday | 4969206.81 |
## +----+------------+-----------------+------------------------+
## | 12 | 2021-05-20 | Thursday | 4977846.66 |
## +----+------------+-----------------+------------------------+
## | 13 | 2021-05-21 | Friday | 4986487.92 |
## +----+------------+-----------------+------------------------+
## | 14 | 2021-05-22 | Saturday | 4995126.99 |
## +----+------------+-----------------+------------------------+
## | 15 | 2021-05-23 | Sunday | 5003765.92 |
## +----+------------+-----------------+------------------------+
## | 16 | 2021-05-24 | Monday | 5012405.97 |
## +----+------------+-----------------+------------------------+
## | 17 | 2021-05-25 | Tuesday | 5021043.67 |
## +----+------------+-----------------+------------------------+
## | 18 | 2021-05-26 | Wednesday | 5029681.44 |
## +----+------------+-----------------+------------------------+
## | 19 | 2021-05-27 | Thursday | 5038320.73 |
## +----+------------+-----------------+------------------------+
## | 20 | 2021-05-28 | Friday | 5046957.93 |
## +----+------------+-----------------+------------------------+
## | 21 | 2021-05-29 | Saturday | 5055595.10 |
## +----+------------+-----------------+------------------------+
## | 22 | 2021-05-30 | Sunday | 5064233.50 |
## +----+------------+-----------------+------------------------+
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 | Russia | 2.766 | 0.071 | 0.079 | 0.099 | 0.316 | 0.018 | Ensembling | 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 Russia
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Forecasting cumulative Covid 19 Infection cases in Russia