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$Germany
y_lab <- "Cumulative Covid 19 Infection cases in Germany" # input name of data
Actual_date_interval <- c("2020/01/03","2021/01/10")
Forecast_date_interval <- c("2021/01/11","2021/01/17")
validation_data_days <-7
Number_Neural<-5 # Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
Population <-83929471 # population in Germany for SIR Model
country.name <- "Germany"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 92633 197143 354902 313531 1908527
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 5.664267
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.90401
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 458368.3
#processing on data (input data)
rows <- NROW(original_data) # calculate number of rows in time series (number of days)
training_data<-original_data[1:(rows-validation_data_days)] # Training data
testing_data<-original_data[(rows-validation_data_days+1):rows] #testing data
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD)) #calculate number of days that you want to forecasting
validation_dates<-tail(AD,validation_data_days) # select validation_dates
validation_data_by_name<-weekdays(validation_dates) # put names of validation dates
forecasting_data_by_name<-weekdays(FD) # put names of Forecasting dates
#NNAR Model
if(NNAR_Model==TRUE){
data_series<-ts(training_data)
model_NNAR<-nnetar(data_series, size = Number_Neural)
saveRDS(model_NNAR, file = "model_NNAR.RDS")
my_model <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
if(NNAR_Model==FALSE){
data_series<-ts(training_data)
#model_NNAR<-nnetar(data_series, size = Number_Numeral)
model_NNAR <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
## Series: data_series
## Model: NNAR(1,5)
## Call: nnetar(y = data_series, size = 5)
##
## Average of 20 networks, each of which is
## a 1-5-1 network with 16 weights
## options were - linear output units
##
## sigma^2 estimated as 6489050
# 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 7 days by using NNAR Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 7 days in NNAR Model for ==> Cumulative Covid 19 Infection cases in Germany"
paste(MAPE_Mean_All,"%")
## [1] "1.933 % MAPE 7 days Cumulative Covid 19 Infection cases in Germany %"
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 7 days in NNAR Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-04 | Monday | 1775513.00 | 1777355.75 | 0.104 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 1787410.00 | 1787820.72 | 0.023 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 1808647.00 | 1797129.98 | 0.637 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 1835038.00 | 1805363.30 | 1.617 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 1866887.00 | 1812606.92 | 2.908 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 1891581.00 | 1818949.87 | 3.84 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 1908527.00 | 1824480.86 | 4.404 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-01-11 | Monday | 1829285.94 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 1833446.75 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 1837039.38 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 1840133.66 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 1842792.96 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 1845074.14 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 1847027.79 |
## +---+------------+-----------------+---------------------+
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 83.72172 1717.317 832.4402 NaN Inf 0.1725542 0.07843559
# Print Model Parameters
model_bats
## BATS(1, {0,3}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.09386863
## Beta: 0.1344958
## Damping Parameter: 0.999919
## MA coefficients: 1.61462 1.338717 0.489254
##
## Seed States:
## [,1]
## [1,] 329.1030
## [2,] -13.8473
## [3,] 0.0000
## [4,] 0.0000
## [5,] 0.0000
##
## Sigma: 1717.317
## AIC: 7656.48
#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 7 days by using bats Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in Germany"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.656 % MAPE 7 days Cumulative Covid 19 Infection cases in Germany %"
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 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-04 | Monday | 1775513.00 | 1780419.83 | 0.276 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 1787410.00 | 1796635.60 | 0.516 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 1808647.00 | 1813282.75 | 0.256 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 1835038.00 | 1831483.35 | 0.194 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 1866887.00 | 1849680.52 | 0.922 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 1891581.00 | 1867876.22 | 1.253 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 1908527.00 | 1886070.46 | 1.177 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-01-11 | Monday | 1904263.22 | 1888969.77 | 1880873.91 | 1888969.77 | 1880873.91 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1922454.53 | 1904328.11 | 1894732.57 | 1904328.11 | 1894732.57 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1940644.36 | 1919418.29 | 1908181.88 | 1919418.29 | 1908181.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1958832.73 | 1934270.99 | 1921268.78 | 1934270.99 | 1921268.78 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 1977019.64 | 1948908.84 | 1934027.88 | 1948908.84 | 1934027.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 1995205.08 | 1963349.01 | 1946485.43 | 1963349.01 | 1946485.43 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2013389.05 | 1977604.91 | 1958661.93 | 1977604.91 | 1958661.93 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 137.3776 2072.678 1073.51 NaN Inf 0.2225249 0.1906558
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.516078
## Beta: 0.3422423
## Damping Parameter: 1
## Gamma-1 Values: 0.0004359755
## Gamma-2 Values: -0.0007471495
##
## Seed States:
## [,1]
## [1,] 351.632919
## [2,] -25.444090
## [3,] -396.493065
## [4,] -3.116959
## [5,] 26.798621
## [6,] 5.326801
##
## Sigma: 2072.678
## AIC: 7792.53
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 7 days by using TBATS Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 7 days in TBATS Model for ==> Cumulative Covid 19 Infection cases in Germany"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.711 % MAPE 7 days Cumulative Covid 19 Infection cases in Germany %"
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 7 days in TBATS Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-04 | Monday | 1775513.00 | 1780008.35 | 0.253 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-01-05 | Tuesday | 1787410.00 | 1797664.61 | 0.574 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-01-06 | Wednesday | 1808647.00 | 1815092.00 | 0.356 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-01-07 | Thursday | 1835038.00 | 1832068.74 | 0.162 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-01-08 | Friday | 1866887.00 | 1848909.29 | 0.963 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-01-09 | Saturday | 1891581.00 | 1865965.08 | 1.354 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-01-10 | Sunday | 1908527.00 | 1883385.90 | 1.317 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2021-01-11 | Monday | 1901042.16 | 1890049.81 | 1884230.82 | 1912034.50 | 1917853.50 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1918469.55 | 1906759.62 | 1900560.76 | 1930179.48 | 1936378.34 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1935446.29 | 1923060.27 | 1916503.52 | 1947832.30 | 1954389.06 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1952286.84 | 1939260.00 | 1932364.01 | 1965313.69 | 1972209.68 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 1969342.63 | 1955703.13 | 1948482.81 | 1982982.13 | 1990202.44 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 1986763.45 | 1972536.99 | 1965005.96 | 2000989.90 | 2008520.93 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2004419.71 | 1989630.38 | 1981801.39 | 2019209.03 | 2027038.03 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -66.08626 2664.473 1275.882 Inf Inf 0.264474 0.4954787
# 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= 0.4296
##
## Smoothing parameters:
## alpha = 0.9998
## beta = 0.3947
##
## Initial states:
## l = -2.2429
## b = -0.6587
##
## sigma: 1.7745
##
## AIC AICc BIC
## 2594.201 2594.367 2613.728
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -66.08626 2664.473 1275.882 Inf Inf 0.264474 0.4954787
# 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 7 days by using holt Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 7 days in holt Model for ==> Cumulative Covid 19 Infection cases in Germany"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.816 % MAPE 7 days Cumulative Covid 19 Infection cases in Germany %"
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 7 days in holt Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-04 | Monday | 1775513.00 | 1781553.74 | 0.34 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 1787410.00 | 1797520.47 | 0.566 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 1808647.00 | 1813568.50 | 0.272 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 1835038.00 | 1829697.94 | 0.291 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 1866887.00 | 1845908.88 | 1.124 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 1891581.00 | 1862201.43 | 1.553 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 1908527.00 | 1878575.69 | 1.569 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-01-11 | Monday | 1895031.77 | 1833257.13 | 1801027.52 | 1957976.78 | 1991773.46 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1911569.75 | 1839994.94 | 1802734.97 | 1984706.56 | 2024057.98 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1928189.74 | 1846314.83 | 1803791.33 | 2012096.94 | 2057341.57 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1944891.84 | 1852231.15 | 1804221.36 | 2040141.09 | 2091616.81 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 1961676.15 | 1857756.90 | 1804047.76 | 2068833.58 | 2126878.42 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 1978542.78 | 1862903.88 | 1803291.43 | 2098170.20 | 2163123.00 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 1995491.81 | 1867682.88 | 1801971.70 | 2128147.78 | 2200348.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Cumulative Covid 19 Infection cases in Germany"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 4.0291, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
## Warning in pp.test(data_series): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = 5.6552, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -5.4001, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Cumulative Covid 19 Infection cases in Germany"
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 = 3.5045, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -15.576, Truncation lag parameter = 5, p-value
## = 0.2382
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -1.2813, Lag order = 7, p-value = 0.8803
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking Second differences in",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking Second differences in Cumulative Covid 19 Infection cases in Germany"
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 = 0.071117, 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) = -129.29, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
## Warning in adf.test(diff2_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -4.7825, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
####Fitting an ARIMA Model
#1. Using auto arima function
model1 <- auto.arima(data_series,stepwise=FALSE, approximation=FALSE, trace=T, test = c("kpss", "adf", "pp")) #applaying auto arima
##
## ARIMA(0,2,0) : 6687.334
## ARIMA(0,2,1) : 6646.072
## ARIMA(0,2,2) : 6620.676
## ARIMA(0,2,3) : 6549.704
## ARIMA(0,2,4) : 6550.56
## ARIMA(0,2,5) : 6490.061
## ARIMA(1,2,0) : 6659.295
## ARIMA(1,2,1) : 6648.081
## ARIMA(1,2,2) : 6587.087
## ARIMA(1,2,3) : 6551.142
## ARIMA(1,2,4) : 6551.571
## ARIMA(2,2,0) : 6612.434
## ARIMA(2,2,1) : 6494.638
## ARIMA(2,2,2) : 6334.205
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 6523.465
## ARIMA(3,2,1) : 6444.182
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 6456.728
## ARIMA(4,2,1) : 6414.775
## ARIMA(5,2,0) : 6363.189
##
##
##
## Best model: ARIMA(2,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2042 -0.9773 -1.4038 0.8626
## s.e. 0.0141 0.0127 0.0294 0.0352
##
## sigma^2 estimated as 1952621: log likelihood=-3162.02
## AIC=6334.04 AICc=6334.2 BIC=6353.54
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.2042 -0.9773 -1.4038 0.8626
## s.e. 0.0141 0.0127 0.0294 0.0352
##
## sigma^2 estimated as 1931223: log likelihood = -3162.02, aic = 6334.04
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in Germany"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 87.35174 1385.893 633.5932 1.006649 2.266608 0.1313358 -0.1212334
x1_model1$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(2,2,2)
## Q* = 54.413, df = 6, p-value = 6.089e-10
##
## Model df: 4. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Cumulative Covid 19 Infection cases in Germany"
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 = 413.64, 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 = 3468.9, 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 7 days by using bats Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in Germany"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.623 % MAPE 7 days Cumulative Covid 19 Infection cases in Germany %"
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 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-04 | Monday | 1775513.00 | 1779842.26 | 0.244 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-01-05 | Tuesday | 1787410.00 | 1801541.43 | 0.791 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-01-06 | Wednesday | 1808647.00 | 1828526.17 | 1.099 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-01-07 | Thursday | 1835038.00 | 1854523.74 | 1.062 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-01-08 | Friday | 1866887.00 | 1874167.10 | 0.39 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-01-09 | Saturday | 1891581.00 | 1887123.42 | 0.236 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-01-10 | Sunday | 1908527.00 | 1898237.09 | 0.539 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2021-01-11 | Monday | 1913666.97 | 1897884.97 | 1889530.48 | 1929448.98 | 1937803.46 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1936095.22 | 1917114.27 | 1907066.35 | 1955076.18 | 1965124.09 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1962732.77 | 1940651.60 | 1928962.53 | 1984813.95 | 1996503.02 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1987599.75 | 1962611.85 | 1949384.06 | 2012587.66 | 2025815.45 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2006220.94 | 1978373.36 | 1963631.74 | 2034068.53 | 2048810.15 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2019051.29 | 1988138.30 | 1971773.96 | 2049964.27 | 2066328.61 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2031012.20 | 1996645.06 | 1978452.20 | 2065379.33 | 2083572.19 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.623 % MAPE 7 days Cumulative Covid 19 Infection cases in Germany"
# SIR Model
#install.packages("dplyr")
library(deSolve)
first<-rows-13
secondr<-rows-7
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$message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.2031526 0.1852281
# 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$I
MAPE_Mean_SIR<-round(mean(abs(((testing_data-validation_forecast)/testing_data)*100)),3)
## forecasting by SIR model
Infected <- c(tail(original_data,validation_data_days))
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.01229837 0.00000000
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 1775513.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 1797013.57 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 1818768.74 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 1840781.38 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 1863054.03 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 1885590.10 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 1908392.43 |
## +---+------------+-----------------+--------------------+
# 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 ==> Cumulative Covid 19 Infection cases in Germany"
best_recommended_model
## [1] 0.623
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 ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-11 | Monday | 1904263.22 | 1888969.77 | 1880873.91 | 1888969.77 | 1880873.91 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1922454.53 | 1904328.11 | 1894732.57 | 1904328.11 | 1894732.57 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1940644.36 | 1919418.29 | 1908181.88 | 1919418.29 | 1908181.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1958832.73 | 1934270.99 | 1921268.78 | 1934270.99 | 1921268.78 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 1977019.64 | 1948908.84 | 1934027.88 | 1948908.84 | 1934027.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 1995205.08 | 1963349.01 | 1946485.43 | 1963349.01 | 1946485.43 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2013389.05 | 1977604.91 | 1958661.93 | 1977604.91 | 1958661.93 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-11 | Monday | 1901042.16 | 1890049.81 | 1884230.82 | 1912034.50 | 1917853.50 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1918469.55 | 1906759.62 | 1900560.76 | 1930179.48 | 1936378.34 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1935446.29 | 1923060.27 | 1916503.52 | 1947832.30 | 1954389.06 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1952286.84 | 1939260.00 | 1932364.01 | 1965313.69 | 1972209.68 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 1969342.63 | 1955703.13 | 1948482.81 | 1982982.13 | 1990202.44 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 1986763.45 | 1972536.99 | 1965005.96 | 2000989.90 | 2008520.93 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2004419.71 | 1989630.38 | 1981801.39 | 2019209.03 | 2027038.03 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-11 | Monday | 1895031.77 | 1833257.13 | 1801027.52 | 1957976.78 | 1991773.46 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1911569.75 | 1839994.94 | 1802734.97 | 1984706.56 | 2024057.98 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1928189.74 | 1846314.83 | 1803791.33 | 2012096.94 | 2057341.57 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1944891.84 | 1852231.15 | 1804221.36 | 2040141.09 | 2091616.81 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 1961676.15 | 1857756.90 | 1804047.76 | 2068833.58 | 2126878.42 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 1978542.78 | 1862903.88 | 1803291.43 | 2098170.20 | 2163123.00 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 1995491.81 | 1867682.88 | 1801971.70 | 2128147.78 | 2200348.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in Germany"
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 | 2021-01-11 | Monday | 1913666.97 | 1897884.97 | 1889530.48 | 1929448.98 | 1937803.46 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 1936095.22 | 1917114.27 | 1907066.35 | 1955076.18 | 1965124.09 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 1962732.77 | 1940651.60 | 1928962.53 | 1984813.95 | 1996503.02 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 1987599.75 | 1962611.85 | 1949384.06 | 2012587.66 | 2025815.45 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2006220.94 | 1978373.36 | 1963631.74 | 2034068.53 | 2048810.15 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2019051.29 | 1988138.30 | 1971773.96 | 2049964.27 | 2066328.61 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2031012.20 | 1996645.06 | 1978452.20 | 2065379.33 | 2083572.19 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in Germany"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 1829285.94 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 1833446.75 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 1837039.38 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 1840133.66 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 1842792.96 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 1845074.14 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 1847027.79 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Cumulative Covid 19 Infection cases in Germany"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 1775513.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 1797013.57 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 1818768.74 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 1840781.38 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 1863054.03 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 1885590.10 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 1908392.43 |
## +---+------------+-----------------+--------------------+
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 | Germany | 1.933 | 0.656 | 0.711 | 0.816 | 0.623 | 6.808 | ARIMA Model | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-----------+-------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,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 ==>Cumulative Covid 19 Infection cases in Germany
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Cumulative Covid 19 Infection cases in Germany