South ural state university, Chelyabinsk, Russian federation
#Import
library(fpp2)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v ggplot2 3.3.2 v fma 2.4
## v forecast 8.13 v expsmooth 2.3
##
library(forecast)
library(ggplot2)
library("readxl")
library(moments)
library(forecast)
require(forecast)
require(tseries)
## Loading required package: tseries
require(markovchain)
## Loading required package: markovchain
## Package: markovchain
## Version: 0.8.5-3
## Date: 2020-12-03
## BugReport: https://github.com/spedygiorgio/markovchain/issues
require(data.table)
## Loading required package: data.table
library(Hmisc)
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(ascii)
library(pander)
##
## Attaching package: 'pander'
## The following object is masked from 'package:ascii':
##
## Pandoc
##Global vriable##
Full_original_data <- read.csv("data.csv") # path of your data ( time series data)
original_data<-Full_original_data$daily.infection
y_lab <- "Forecasting Covid 19 infection cases in Chelyabinsk" # input name of data
Actual_date_interval <- c("2020/03/12","2021/04/09")
Forecast_date_interval <- c("2021/04/10","2021/04/30")
validation_data_days <-4
frequency<-"day"
Number_Neural<-5 # Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
Population <-1130319 # population in England for SIR Model
country.name <- "Chelyabinsk"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 71.0 130.0 143.4 217.2 317.0
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.065293
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.3784112
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 94.52591
#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(6,5)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 6-5-1 network with 41 weights
## options were - linear output units
##
## sigma^2 estimated as 65.39
# Testing Data Evaluation
forecasting_NNAR <- forecast(model_NNAR, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_NNAR$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 4 days by using NNAR Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Mean_All_NNAR<-round(mean(MAPE_Per_Day),3)
MAPE_NNAR<-paste(round(MAPE_Per_Day,3),"%")
MAPE_NNAR_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 4 days in NNAR Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
paste(MAPE_Mean_All,"%")
## [1] "0.64 % MAPE 4 days Forecasting Covid 19 infection cases in Chelyabinsk %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 4 days in NNAR Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-06 | Tuesday | 122.00 | 122.11 | 0.09 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-04-07 | Wednesday | 121.00 | 121.52 | 0.427 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-04-08 | Thursday | 120.00 | 121.14 | 0.953 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-04-09 | Friday | 119.00 | 120.30 | 1.092 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-04-10 | Saturday | 119.51 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-04-11 | Sunday | 118.91 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-04-12 | Monday | 118.43 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-04-13 | Tuesday | 118.05 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-04-14 | Wednesday | 117.58 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-04-15 | Thursday | 117.10 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-04-16 | Friday | 116.64 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-04-17 | Saturday | 116.20 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-04-18 | Sunday | 115.79 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-04-19 | Monday | 115.36 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-04-20 | Tuesday | 114.92 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-04-21 | Wednesday | 114.48 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-04-22 | Thursday | 114.03 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-04-23 | Friday | 113.58 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-04-24 | Saturday | 113.11 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-04-25 | Sunday | 112.64 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-04-26 | Monday | 112.15 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-04-27 | Tuesday | 111.65 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-04-28 | Wednesday | 111.14 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-04-29 | Thursday | 110.61 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-04-30 | Friday | 110.06 |
## +----+------------+-----------------+---------------------+
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 0.1774571 10.8119 6.337771 NaN Inf 1.0026 0.03331582
# Print Model Parameters
model_bats
## BATS(1, {4,4}, 0.963, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.1211636
## Beta: 0.01034443
## Damping Parameter: 0.963279
## AR coefficients: -0.637902 0.510351 0.701003 -0.155703
## MA coefficients: 1.290587 0.426238 -0.33795 -0.058416
##
## Seed States:
## [,1]
## [1,] -6.5739305
## [2,] 0.3030306
## [3,] 0.0000000
## [4,] 0.0000000
## [5,] 0.0000000
## [6,] 0.0000000
## [7,] 0.0000000
## [8,] 0.0000000
## [9,] 0.0000000
## [10,] 0.0000000
##
## Sigma: 10.8119
## AIC: 4225.702
#ploting BATS Model
plot(model_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "))
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 4 days by using bats Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 4 days in bats Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
paste(MAPE_Mean_All.bats,"%")
## [1] "1.713 % MAPE 4 days Forecasting Covid 19 infection cases in Chelyabinsk %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 4 days in bats Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-06 | Tuesday | 122.00 | 123.14 | 0.938 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-04-07 | Wednesday | 121.00 | 122.59 | 1.313 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-04-08 | Thursday | 120.00 | 122.58 | 2.151 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-04-09 | Friday | 119.00 | 121.91 | 2.449 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-04-10 | Saturday | 121.59 | 97.38 | 84.56 | 97.38 | 84.56 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 121.31 | 95.18 | 81.34 | 95.18 | 81.34 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 120.64 | 93.05 | 78.44 | 93.05 | 78.44 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 120.59 | 91.22 | 75.67 | 91.22 | 75.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 119.93 | 89.02 | 72.65 | 89.02 | 72.65 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 119.71 | 87.22 | 70.03 | 87.22 | 70.03 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 119.39 | 85.17 | 67.05 | 85.17 | 67.05 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 118.84 | 83.14 | 64.24 | 83.14 | 64.24 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 118.80 | 81.30 | 61.45 | 81.30 | 61.45 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 118.19 | 79.10 | 58.41 | 79.10 | 58.41 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 118.06 | 77.27 | 55.68 | 77.27 | 55.68 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 117.73 | 75.15 | 52.60 | 75.15 | 52.60 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 117.30 | 73.10 | 49.70 | 73.10 | 49.70 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 117.27 | 71.17 | 46.77 | 71.17 | 46.77 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 116.72 | 68.94 | 43.65 | 68.94 | 43.65 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 116.67 | 67.06 | 40.81 | 67.06 | 40.81 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 116.34 | 64.88 | 37.64 | 64.88 | 37.64 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 116.02 | 62.84 | 34.68 | 62.84 | 34.68 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 115.98 | 60.85 | 31.67 | 60.85 | 31.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 115.50 | 58.62 | 28.52 | 58.62 | 28.52 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 115.50 | 56.73 | 25.62 | 56.73 | 25.62 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 -0.2457791 11.24058 6.564229 NaN Inf 1.038424 0.006991486
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.7634547
## Beta: 0.02166803
## Damping Parameter: 1
## Gamma-1 Values: -0.001518676
## Gamma-2 Values: 0.002474274
##
## Seed States:
## [,1]
## [1,] -6.7609532
## [2,] 0.3568741
## [3,] 1.3360746
## [4,] -0.4861759
## [5,] 0.1601151
## [6,] 0.8083682
##
## Sigma: 11.24058
## AIC: 4234.031
plot(model_TBATS,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
# Testing Data Evaluation
forecasting_tbats <- predict(model_TBATS, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_tbats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 4 days by using TBATS Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 4 days in TBATS Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "1.873 % MAPE 4 days Forecasting Covid 19 infection cases in Chelyabinsk %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 4 days in TBATS Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-06 | Tuesday | 122.00 | 122.92 | 0.754 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-04-07 | Wednesday | 121.00 | 122.10 | 0.908 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-04-08 | Thursday | 120.00 | 117.11 | 2.405 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-04-09 | Friday | 119.00 | 114.92 | 3.427 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2021-04-10 | Saturday | 114.94 | 88.70 | 74.81 | 141.18 | 155.08 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 112.79 | 84.40 | 69.36 | 141.19 | 156.22 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 112.60 | 82.22 | 66.13 | 142.98 | 159.07 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 111.78 | 79.51 | 62.43 | 144.04 | 161.12 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 106.79 | 72.76 | 54.74 | 140.83 | 158.84 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 104.60 | 68.89 | 49.98 | 140.32 | 159.22 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 104.62 | 67.30 | 47.54 | 141.94 | 161.70 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 102.47 | 63.64 | 43.09 | 141.30 | 161.86 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 102.28 | 62.01 | 40.69 | 142.55 | 163.87 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 101.46 | 59.78 | 37.72 | 143.13 | 165.19 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 96.47 | 53.45 | 30.67 | 139.50 | 162.28 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 94.28 | 49.95 | 26.48 | 138.62 | 162.09 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 94.30 | 48.69 | 24.55 | 139.91 | 164.05 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 92.15 | 45.33 | 20.55 | 138.98 | 163.76 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 91.96 | 43.96 | 18.56 | 139.95 | 165.36 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 91.14 | 41.99 | 15.97 | 140.29 | 166.31 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 86.15 | 35.88 | 9.27 | 136.42 | 163.04 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 83.96 | 32.59 | 5.40 | 135.33 | 162.52 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 83.98 | 31.53 | 3.77 | 136.43 | 164.19 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 81.83 | 28.35 | 0.04 | 135.31 | 163.62 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 81.64 | 27.15 | -1.69 | 136.12 | 164.96 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 -0.4196004 11.3857 6.476959 -Inf Inf 1.024619 0.02127749
# 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= 0.8498
##
## Smoothing parameters:
## alpha = 0.7519
## beta = 0.0173
##
## Initial states:
## l = -1.6453
## b = 0.4991
##
## sigma: 5.8046
##
## AIC AICc BIC
## 3704.529 3704.686 3724.360
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.4196004 11.3857 6.476959 -Inf Inf 1.024619 0.02127749
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 4 days by using holt Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 4 days in holt Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.85 % MAPE 4 days Forecasting Covid 19 infection cases in Chelyabinsk %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 4 days in holt Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-06 | Tuesday | 122.00 | 121.72 | 0.232 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-04-07 | Wednesday | 121.00 | 120.22 | 0.641 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-04-08 | Thursday | 120.00 | 118.73 | 1.055 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-04-09 | Friday | 119.00 | 117.25 | 1.473 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-04-10 | Saturday | 115.76 | 87.79 | 73.49 | 144.79 | 160.54 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 114.28 | 83.78 | 68.26 | 146.06 | 163.34 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 112.80 | 79.92 | 63.26 | 147.21 | 165.95 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 111.33 | 76.16 | 58.44 | 148.27 | 168.43 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 109.85 | 72.49 | 53.77 | 149.26 | 170.80 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 108.38 | 68.91 | 49.24 | 150.19 | 173.08 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 106.92 | 65.40 | 44.83 | 151.07 | 175.30 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 105.45 | 61.95 | 40.54 | 151.91 | 177.45 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 103.99 | 58.55 | 36.35 | 152.72 | 179.56 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 102.53 | 55.21 | 32.26 | 153.51 | 181.63 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 101.08 | 51.91 | 28.28 | 154.27 | 183.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 99.63 | 48.66 | 24.40 | 155.02 | 185.69 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 98.18 | 45.46 | 20.63 | 155.76 | 187.69 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 96.73 | 42.30 | 16.97 | 156.48 | 189.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 95.29 | 39.18 | 13.43 | 157.20 | 191.65 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 93.85 | 36.10 | 10.04 | 157.91 | 193.61 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 92.42 | 33.07 | 6.82 | 158.61 | 195.57 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 90.99 | 30.08 | 3.82 | 159.31 | 197.53 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 89.56 | 27.13 | 1.17 | 160.01 | 199.48 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 88.13 | 24.24 | -0.82 | 160.71 | 201.44 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 86.71 | 21.39 | -3.40 | 161.41 | 203.40 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 = 3.9414, 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) = -1.7002, Truncation lag parameter = 5, p-value
## = 0.9763
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -0.44379, Lag order = 7, p-value = 0.9842
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 1
#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 Covid 19 infection cases in Chelyabinsk"
kpss.test(diff1_x1) # applay kpss test after taking first differences
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 0.37156, Truncation lag parameter = 5, p-value = 0.08941
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -440.32, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -6.6478, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking Second differences in",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking Second differences in Forecasting Covid 19 infection cases in Chelyabinsk"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
## Warning in kpss.test(diff2_x1): p-value greater than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.007219, Truncation lag parameter = 5, p-value = 0.1
pp.test(diff2_x1) # applay pp test after taking Second differences
## Warning in pp.test(diff2_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff2_x1
## Dickey-Fuller Z(alpha) = -526.21, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
## Warning in adf.test(diff2_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -13.724, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
####Fitting an ARIMA Model
#1. Using auto arima function
model1 <- auto.arima(data_series,stepwise=FALSE, approximation=FALSE, trace=T, test = c("kpss", "adf", "pp")) #applaying auto arima
##
## ARIMA(0,1,0) : 3015.501
## ARIMA(0,1,0) with drift : 3017.235
## ARIMA(0,1,1) : 3001.133
## ARIMA(0,1,1) with drift : 3002.685
## ARIMA(0,1,2) : 3003.088
## ARIMA(0,1,2) with drift : 3004.668
## ARIMA(0,1,3) : 3000.669
## ARIMA(0,1,3) with drift : 3002.156
## ARIMA(0,1,4) : 3001.086
## ARIMA(0,1,4) with drift : 3002.54
## ARIMA(0,1,5) : 2994.082
## ARIMA(0,1,5) with drift : 2995.639
## ARIMA(1,1,0) : 3000.782
## ARIMA(1,1,0) with drift : 3002.375
## ARIMA(1,1,1) : 3002.806
## ARIMA(1,1,1) with drift : 3004.413
## ARIMA(1,1,2) : 3004.798
## ARIMA(1,1,2) with drift : 3006.404
## ARIMA(1,1,3) : 3002.333
## ARIMA(1,1,3) with drift : 3003.815
## ARIMA(1,1,4) : 2997.253
## ARIMA(1,1,4) with drift : 2998.718
## ARIMA(2,1,0) : 3002.808
## ARIMA(2,1,0) with drift : 3004.414
## ARIMA(2,1,1) : Inf
## ARIMA(2,1,1) with drift : 3005.734
## ARIMA(2,1,2) : 3005.726
## ARIMA(2,1,2) with drift : 3007.258
## ARIMA(2,1,3) : 2994.742
## ARIMA(2,1,3) with drift : 2996.303
## ARIMA(3,1,0) : 3004.268
## ARIMA(3,1,0) with drift : 3005.847
## ARIMA(3,1,1) : 3004.177
## ARIMA(3,1,1) with drift : 3005.66
## ARIMA(3,1,2) : 2997.901
## ARIMA(3,1,2) with drift : 2999.427
## ARIMA(4,1,0) : 2994.287
## ARIMA(4,1,0) with drift : 2995.665
## ARIMA(4,1,1) : 2991.522
## ARIMA(4,1,1) with drift : 2992.981
## ARIMA(5,1,0) : 2992.139
## ARIMA(5,1,0) with drift : 2993.662
##
##
##
## Best model: ARIMA(4,1,1)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(4,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## -0.6738 -0.0996 -0.0776 -0.1983 0.4832
## s.e. 0.1466 0.0664 0.0600 0.0505 0.1447
##
## sigma^2 estimated as 125.6: log likelihood=-1489.65
## AIC=2991.3 AICc=2991.52 BIC=3015.08
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 4 1 1
strtoi(bestmodel[3])
## [1] 1
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## -0.6738 -0.0996 -0.0776 -0.1983 0.4832
## s.e. 0.1466 0.0664 0.0600 0.0505 0.1447
##
## sigma^2 estimated as 124: log likelihood = -1489.65, aic = 2991.3
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting Covid 19 infection cases in Chelyabinsk"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.4399124 11.12191 6.467357 NaN Inf 1.0231 0.001076781
x1_model1$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(4,1,1)
## Q* = 9.3817, df = 5, p-value = 0.09477
##
## 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 Covid 19 infection cases in Chelyabinsk"
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 = 170.45, df = 20, p-value < 2.2e-16
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 2362.3, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 4 days by using bats Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 4 days in bats Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "2.951 % MAPE 4 days Forecasting Covid 19 infection cases in Chelyabinsk %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 4 days in bats Model for ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-06 | Tuesday | 122.00 | 123.62 | 1.329 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-04-07 | Wednesday | 121.00 | 123.83 | 2.341 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-04-08 | Thursday | 120.00 | 124.38 | 3.649 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-04-09 | Friday | 119.00 | 124.34 | 4.486 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2021-04-10 | Saturday | 124.17 | 98.14 | 84.35 | 150.21 | 163.99 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 124.20 | 96.00 | 81.07 | 152.41 | 167.34 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 124.09 | 94.25 | 78.45 | 153.94 | 169.73 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 124.19 | 92.49 | 75.72 | 155.88 | 172.66 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 124.16 | 90.81 | 73.16 | 157.52 | 175.17 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 124.17 | 89.30 | 70.83 | 159.05 | 177.51 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 124.18 | 87.76 | 68.48 | 160.61 | 179.89 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 124.16 | 86.35 | 66.33 | 161.97 | 181.99 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 124.18 | 84.95 | 64.19 | 163.40 | 184.16 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 124.16 | 83.61 | 62.15 | 164.72 | 186.18 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 124.17 | 82.33 | 60.18 | 166.02 | 188.17 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 124.17 | 81.06 | 58.24 | 167.28 | 190.10 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 124.17 | 79.85 | 56.39 | 168.49 | 191.95 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 124.17 | 78.66 | 54.56 | 169.69 | 193.78 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 124.17 | 77.50 | 52.80 | 170.84 | 195.54 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 124.17 | 76.37 | 51.07 | 171.97 | 197.27 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 124.17 | 75.27 | 49.38 | 173.07 | 198.96 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 124.17 | 74.19 | 47.73 | 174.15 | 200.61 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 124.17 | 73.13 | 46.12 | 175.21 | 202.23 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 124.17 | 72.10 | 44.53 | 176.24 | 203.81 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 124.17 | 71.08 | 42.98 | 177.26 | 205.36 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "2.951 % MAPE 4 days Forecasting Covid 19 infection cases in Chelyabinsk"
# SIR Model
#install.packages("dplyr")
library(deSolve)
first<-rows-(validation_data_days+N_forecasting_days-1)
secondr<-rows-N_forecasting_days
vector_SIR<-original_data[first:secondr]
Infected <- c(vector_SIR)
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.000000000 0.008803695
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR<-data.frame(out)
validation_forecast<-result_SIR$I
MAPE_Mean_SIR<-round(mean(abs(((testing_data-validation_forecast)/testing_data)*100)),3)
## forecasting by SIR model
Infected <- c(tail(original_data,N_forecasting_days))
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 1.967236 1.971169
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +----+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +====+============+=================+====================+
## | 1 | 2021-04-10 | Saturday | 141.00 |
## +----+------------+-----------------+--------------------+
## | 2 | 2021-04-11 | Sunday | 140.38 |
## +----+------------+-----------------+--------------------+
## | 3 | 2021-04-12 | Monday | 139.69 |
## +----+------------+-----------------+--------------------+
## | 4 | 2021-04-13 | Tuesday | 138.94 |
## +----+------------+-----------------+--------------------+
## | 5 | 2021-04-14 | Wednesday | 138.13 |
## +----+------------+-----------------+--------------------+
## | 6 | 2021-04-15 | Thursday | 137.26 |
## +----+------------+-----------------+--------------------+
## | 7 | 2021-04-16 | Friday | 136.33 |
## +----+------------+-----------------+--------------------+
## | 8 | 2021-04-17 | Saturday | 135.34 |
## +----+------------+-----------------+--------------------+
## | 9 | 2021-04-18 | Sunday | 134.30 |
## +----+------------+-----------------+--------------------+
## | 10 | 2021-04-19 | Monday | 133.21 |
## +----+------------+-----------------+--------------------+
## | 11 | 2021-04-20 | Tuesday | 132.06 |
## +----+------------+-----------------+--------------------+
## | 12 | 2021-04-21 | Wednesday | 130.87 |
## +----+------------+-----------------+--------------------+
## | 13 | 2021-04-22 | Thursday | 129.63 |
## +----+------------+-----------------+--------------------+
## | 14 | 2021-04-23 | Friday | 128.34 |
## +----+------------+-----------------+--------------------+
## | 15 | 2021-04-24 | Saturday | 127.01 |
## +----+------------+-----------------+--------------------+
## | 16 | 2021-04-25 | Sunday | 125.64 |
## +----+------------+-----------------+--------------------+
## | 17 | 2021-04-26 | Monday | 124.23 |
## +----+------------+-----------------+--------------------+
## | 18 | 2021-04-27 | Tuesday | 122.78 |
## +----+------------+-----------------+--------------------+
## | 19 | 2021-04-28 | Wednesday | 121.31 |
## +----+------------+-----------------+--------------------+
## | 20 | 2021-04-29 | Thursday | 119.79 |
## +----+------------+-----------------+--------------------+
## | 21 | 2021-04-30 | Friday | 118.25 |
## +----+------------+-----------------+--------------------+
# 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_SIR)
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 Covid 19 infection cases in Chelyabinsk"
best_recommended_model
## [1] 0.64
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_SIR) {paste("SIR Model")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-10 | Saturday | 121.59 | 97.38 | 84.56 | 97.38 | 84.56 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 121.31 | 95.18 | 81.34 | 95.18 | 81.34 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 120.64 | 93.05 | 78.44 | 93.05 | 78.44 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 120.59 | 91.22 | 75.67 | 91.22 | 75.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 119.93 | 89.02 | 72.65 | 89.02 | 72.65 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 119.71 | 87.22 | 70.03 | 87.22 | 70.03 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 119.39 | 85.17 | 67.05 | 85.17 | 67.05 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 118.84 | 83.14 | 64.24 | 83.14 | 64.24 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 118.80 | 81.30 | 61.45 | 81.30 | 61.45 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 118.19 | 79.10 | 58.41 | 79.10 | 58.41 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 118.06 | 77.27 | 55.68 | 77.27 | 55.68 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 117.73 | 75.15 | 52.60 | 75.15 | 52.60 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 117.30 | 73.10 | 49.70 | 73.10 | 49.70 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 117.27 | 71.17 | 46.77 | 71.17 | 46.77 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 116.72 | 68.94 | 43.65 | 68.94 | 43.65 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 116.67 | 67.06 | 40.81 | 67.06 | 40.81 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 116.34 | 64.88 | 37.64 | 64.88 | 37.64 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 116.02 | 62.84 | 34.68 | 62.84 | 34.68 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 115.98 | 60.85 | 31.67 | 60.85 | 31.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 115.50 | 58.62 | 28.52 | 58.62 | 28.52 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 115.50 | 56.73 | 25.62 | 56.73 | 25.62 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-10 | Saturday | 114.94 | 88.70 | 74.81 | 141.18 | 155.08 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 112.79 | 84.40 | 69.36 | 141.19 | 156.22 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 112.60 | 82.22 | 66.13 | 142.98 | 159.07 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 111.78 | 79.51 | 62.43 | 144.04 | 161.12 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 106.79 | 72.76 | 54.74 | 140.83 | 158.84 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 104.60 | 68.89 | 49.98 | 140.32 | 159.22 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 104.62 | 67.30 | 47.54 | 141.94 | 161.70 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 102.47 | 63.64 | 43.09 | 141.30 | 161.86 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 102.28 | 62.01 | 40.69 | 142.55 | 163.87 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 101.46 | 59.78 | 37.72 | 143.13 | 165.19 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 96.47 | 53.45 | 30.67 | 139.50 | 162.28 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 94.28 | 49.95 | 26.48 | 138.62 | 162.09 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 94.30 | 48.69 | 24.55 | 139.91 | 164.05 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 92.15 | 45.33 | 20.55 | 138.98 | 163.76 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 91.96 | 43.96 | 18.56 | 139.95 | 165.36 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 91.14 | 41.99 | 15.97 | 140.29 | 166.31 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 86.15 | 35.88 | 9.27 | 136.42 | 163.04 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 83.96 | 32.59 | 5.40 | 135.33 | 162.52 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 83.98 | 31.53 | 3.77 | 136.43 | 164.19 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 81.83 | 28.35 | 0.04 | 135.31 | 163.62 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 81.64 | 27.15 | -1.69 | 136.12 | 164.96 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-10 | Saturday | 115.76 | 87.79 | 73.49 | 144.79 | 160.54 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 114.28 | 83.78 | 68.26 | 146.06 | 163.34 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 112.80 | 79.92 | 63.26 | 147.21 | 165.95 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 111.33 | 76.16 | 58.44 | 148.27 | 168.43 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 109.85 | 72.49 | 53.77 | 149.26 | 170.80 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 108.38 | 68.91 | 49.24 | 150.19 | 173.08 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 106.92 | 65.40 | 44.83 | 151.07 | 175.30 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 105.45 | 61.95 | 40.54 | 151.91 | 177.45 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 103.99 | 58.55 | 36.35 | 152.72 | 179.56 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 102.53 | 55.21 | 32.26 | 153.51 | 181.63 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 101.08 | 51.91 | 28.28 | 154.27 | 183.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 99.63 | 48.66 | 24.40 | 155.02 | 185.69 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 98.18 | 45.46 | 20.63 | 155.76 | 187.69 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 96.73 | 42.30 | 16.97 | 156.48 | 189.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 95.29 | 39.18 | 13.43 | 157.20 | 191.65 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 93.85 | 36.10 | 10.04 | 157.91 | 193.61 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 92.42 | 33.07 | 6.82 | 158.61 | 195.57 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 90.99 | 30.08 | 3.82 | 159.31 | 197.53 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 89.56 | 27.13 | 1.17 | 160.01 | 199.48 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 88.13 | 24.24 | -0.82 | 160.71 | 201.44 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 86.71 | 21.39 | -3.40 | 161.41 | 203.40 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-10 | Saturday | 124.17 | 98.14 | 84.35 | 150.21 | 163.99 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-11 | Sunday | 124.20 | 96.00 | 81.07 | 152.41 | 167.34 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-12 | Monday | 124.09 | 94.25 | 78.45 | 153.94 | 169.73 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-04-13 | Tuesday | 124.19 | 92.49 | 75.72 | 155.88 | 172.66 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-04-14 | Wednesday | 124.16 | 90.81 | 73.16 | 157.52 | 175.17 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-04-15 | Thursday | 124.17 | 89.30 | 70.83 | 159.05 | 177.51 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-04-16 | Friday | 124.18 | 87.76 | 68.48 | 160.61 | 179.89 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-04-17 | Saturday | 124.16 | 86.35 | 66.33 | 161.97 | 181.99 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-04-18 | Sunday | 124.18 | 84.95 | 64.19 | 163.40 | 184.16 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-04-19 | Monday | 124.16 | 83.61 | 62.15 | 164.72 | 186.18 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-04-20 | Tuesday | 124.17 | 82.33 | 60.18 | 166.02 | 188.17 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-04-21 | Wednesday | 124.17 | 81.06 | 58.24 | 167.28 | 190.10 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-04-22 | Thursday | 124.17 | 79.85 | 56.39 | 168.49 | 191.95 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 14 | 2021-04-23 | Friday | 124.17 | 78.66 | 54.56 | 169.69 | 193.78 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 15 | 2021-04-24 | Saturday | 124.17 | 77.50 | 52.80 | 170.84 | 195.54 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 16 | 2021-04-25 | Sunday | 124.17 | 76.37 | 51.07 | 171.97 | 197.27 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 17 | 2021-04-26 | Monday | 124.17 | 75.27 | 49.38 | 173.07 | 198.96 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 18 | 2021-04-27 | Tuesday | 124.17 | 74.19 | 47.73 | 174.15 | 200.61 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 19 | 2021-04-28 | Wednesday | 124.17 | 73.13 | 46.12 | 175.21 | 202.23 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 20 | 2021-04-29 | Thursday | 124.17 | 72.10 | 44.53 | 176.24 | 203.81 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 21 | 2021-04-30 | Friday | 124.17 | 71.08 | 42.98 | 177.26 | 205.36 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting Covid 19 infection cases in Chelyabinsk"
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 | 2021-04-10 | Saturday | 119.51 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-04-11 | Sunday | 118.91 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-04-12 | Monday | 118.43 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-04-13 | Tuesday | 118.05 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-04-14 | Wednesday | 117.58 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-04-15 | Thursday | 117.10 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-04-16 | Friday | 116.64 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-04-17 | Saturday | 116.20 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-04-18 | Sunday | 115.79 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-04-19 | Monday | 115.36 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-04-20 | Tuesday | 114.92 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-04-21 | Wednesday | 114.48 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-04-22 | Thursday | 114.03 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-04-23 | Friday | 113.58 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-04-24 | Saturday | 113.11 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-04-25 | Sunday | 112.64 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-04-26 | Monday | 112.15 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-04-27 | Tuesday | 111.65 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-04-28 | Wednesday | 111.14 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-04-29 | Thursday | 110.61 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-04-30 | Friday | 110.06 |
## +----+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Forecasting Covid 19 infection cases in Chelyabinsk"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +----+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +====+============+=================+====================+
## | 1 | 2021-04-10 | Saturday | 141.00 |
## +----+------------+-----------------+--------------------+
## | 2 | 2021-04-11 | Sunday | 140.38 |
## +----+------------+-----------------+--------------------+
## | 3 | 2021-04-12 | Monday | 139.69 |
## +----+------------+-----------------+--------------------+
## | 4 | 2021-04-13 | Tuesday | 138.94 |
## +----+------------+-----------------+--------------------+
## | 5 | 2021-04-14 | Wednesday | 138.13 |
## +----+------------+-----------------+--------------------+
## | 6 | 2021-04-15 | Thursday | 137.26 |
## +----+------------+-----------------+--------------------+
## | 7 | 2021-04-16 | Friday | 136.33 |
## +----+------------+-----------------+--------------------+
## | 8 | 2021-04-17 | Saturday | 135.34 |
## +----+------------+-----------------+--------------------+
## | 9 | 2021-04-18 | Sunday | 134.30 |
## +----+------------+-----------------+--------------------+
## | 10 | 2021-04-19 | Monday | 133.21 |
## +----+------------+-----------------+--------------------+
## | 11 | 2021-04-20 | Tuesday | 132.06 |
## +----+------------+-----------------+--------------------+
## | 12 | 2021-04-21 | Wednesday | 130.87 |
## +----+------------+-----------------+--------------------+
## | 13 | 2021-04-22 | Thursday | 129.63 |
## +----+------------+-----------------+--------------------+
## | 14 | 2021-04-23 | Friday | 128.34 |
## +----+------------+-----------------+--------------------+
## | 15 | 2021-04-24 | Saturday | 127.01 |
## +----+------------+-----------------+--------------------+
## | 16 | 2021-04-25 | Sunday | 125.64 |
## +----+------------+-----------------+--------------------+
## | 17 | 2021-04-26 | Monday | 124.23 |
## +----+------------+-----------------+--------------------+
## | 18 | 2021-04-27 | Tuesday | 122.78 |
## +----+------------+-----------------+--------------------+
## | 19 | 2021-04-28 | Wednesday | 121.31 |
## +----+------------+-----------------+--------------------+
## | 20 | 2021-04-29 | Thursday | 119.79 |
## +----+------------+-----------------+--------------------+
## | 21 | 2021-04-30 | Friday | 118.25 |
## +----+------------+-----------------+--------------------+
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,SIR.Model=MAPE_Mean_SIR,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-----------+------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | SIR.Model | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+===========+============+======+
## | 1 | Chelyabinsk | 0.64 | 1.713 | 1.873 | 0.85 | 2.951 | 14.663 | NNAR Model | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-----------+------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_SIR)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model" ,"SIR Model")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>Forecasting Covid 19 infection cases in Chelyabinsk
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 Covid 19 infection cases in Chelyabinsk