South ural state university, Chelyabinsk, Russian federation
#Import
library(fpp2)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v ggplot2 3.3.2 v fma 2.4
## v forecast 8.13 v expsmooth 2.3
##
library(forecast)
library(ggplot2)
library("readxl")
library(moments)
library(forecast)
require(forecast)
require(tseries)
## Loading required package: tseries
require(markovchain)
## Loading required package: markovchain
## Package: markovchain
## Version: 0.8.5-3
## Date: 2020-12-03
## BugReport: https://github.com/spedygiorgio/markovchain/issues
require(data.table)
## Loading required package: data.table
library(Hmisc)
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(ascii)
library(pander)
##
## Attaching package: 'pander'
## The following object is masked from 'package:ascii':
##
## Pandoc
##Global vriable##
Full_original_data <- read_excel("data.xlsx", sheet = "Infection and deaths") # path of your data ( time series data)
original_data<-Full_original_data$New_cases
y_lab <- "Daily Covid 19 Infection cases in Russia" # input name of data
Actual_date_interval <- c("2020/03/01","2021/03/22")
Forecast_date_interval <- c("2021/03/23","2021/03/29")
validation_data_days <-8
Number_Neural<-5 # Number of Neural For model NNAR Model
NNAR_Model<- TRUE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Russia"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 4744 7972 10036 15916 29935
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.437764
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.7181981
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 8659.757
#processing on data (input data)
rows <- NROW(original_data) # calculate number of rows in time series (number of days)
training_data<-original_data[1:(rows-validation_data_days)] # Training data
testing_data<-original_data[(rows-validation_data_days+1):rows] #testing data
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD)) #calculate number of days that you want to forecasting
validation_dates<-tail(AD,validation_data_days) # select validation_dates
validation_data_by_name<-weekdays(validation_dates) # put names of validation dates
forecasting_data_by_name<-weekdays(FD) # put names of Forecasting dates
#NNAR Model
if(NNAR_Model==TRUE){
data_series<-ts(training_data)
model_NNAR<-nnetar(data_series, size = Number_Neural)
saveRDS(model_NNAR, file = "model_NNAR.RDS")
my_model <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
## Series: data_series
## Model: NNAR(22,5)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 22-5-1 network with 121 weights
## options were - linear output units
##
## sigma^2 estimated as 94195
if(NNAR_Model==FALSE){
data_series<-ts(training_data)
#model_NNAR<-nnetar(data_series, size = Number_Numeral)
model_NNAR <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
# Testing Data Evaluation
forecasting_NNAR <- forecast(model_NNAR, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_NNAR$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 8 days by using NNAR Model for ==> Daily Covid 19 Infection cases in Russia"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Mean_All_NNAR<-round(mean(MAPE_Per_Day),3)
MAPE_NNAR<-paste(round(MAPE_Per_Day,3),"%")
MAPE_NNAR_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 8 days in NNAR Model for ==> Daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "2.5 % MAPE 8 days Daily Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in NNAR Model for ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_NNAR=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_NNAR=validation_forecast,MAPE_NNAR_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_NNAR | validation_data_by_name | actual_data | forecasting_NNAR | MAPE_NNAR_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-03-15 | Monday | 9437.00 | 9423.52 | 0.143 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 9393.00 | 9127.82 | 2.823 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 8998.00 | 9001.65 | 0.041 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 9803.00 | 9060.78 | 7.571 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 9699.00 | 9348.10 | 3.618 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 9632.00 | 9467.15 | 1.711 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 9299.00 | 9203.69 | 1.025 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 9284.00 | 8999.15 | 3.068 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-03-23 | Tuesday | 8660.40 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 8642.20 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 8806.16 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 9007.49 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 9036.25 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 8863.50 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 8513.86 |
## +---+------------+-----------------+---------------------+
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 -14.7722 528.3535 326.3773 NaN Inf 0.920723 -0.07745486
# Print Model Parameters
model_bats
## BATS(1, {2,2}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.7984101
## Beta: 0.02769451
## Damping Parameter: 1
## AR coefficients: 1.23045 -0.980294
## MA coefficients: -1.177856 0.888411
##
## Seed States:
## [,1]
## [1,] -15.907984
## [2,] 1.487672
## [3,] 0.000000
## [4,] 0.000000
## [5,] 0.000000
## [6,] 0.000000
##
## Sigma: 528.3535
## AIC: 8160.706
#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 8 days by using bats Model for ==> Daily Covid 19 Infection cases in Russia"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 8 days in bats Model for ==> Daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.bats,"%")
## [1] "5.589 % MAPE 8 days Daily Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in bats Model for ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_bats | validation_data_by_name | actual_data | forecasting_bats | MAPE_bats_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-03-15 | Monday | 9437.00 | 9508.56 | 0.758 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 9393.00 | 9048.20 | 3.671 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 8998.00 | 8823.67 | 1.937 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 9803.00 | 8872.75 | 9.489 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 9699.00 | 9027.35 | 6.925 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 9632.00 | 9043.53 | 6.11 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 9299.00 | 8785.97 | 5.517 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 9284.00 | 8327.29 | 10.305 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 7889.46 | 6048.50 | 5073.95 | 6048.50 | 5073.95 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 7674.46 | 5701.31 | 4656.79 | 5701.31 | 4656.79 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 7713.20 | 5626.57 | 4521.97 | 5626.57 | 4521.97 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 7845.71 | 5657.61 | 4499.30 | 5657.61 | 4499.30 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 7844.86 | 5554.19 | 4341.58 | 5554.19 | 4341.58 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 7588.00 | 5182.46 | 3909.04 | 5182.46 | 3909.04 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 7146.86 | 4612.17 | 3270.39 | 4612.17 | 3270.39 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 -7.46483 571.2913 354.1412 NaN Inf 0.9990459 0.02685763
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.8388134
## Beta: 0.04406353
## Damping Parameter: 1
## Gamma-1 Values: -0.001991603
## Gamma-2 Values: 0.0008920926
##
## Seed States:
## [,1]
## [1,] -16.992283
## [2,] 2.089447
## [3,] 10.518133
## [4,] 3.549350
## [5,] 10.383125
## [6,] -20.110738
##
## Sigma: 571.2913
## AIC: 8224.995
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 8 days by using TBATS Model for ==> Daily Covid 19 Infection cases in Russia"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 8 days in TBATS Model for ==> Daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "4.29 % MAPE 8 days Daily Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in TBATS Model for ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | | date_TBATS | validation_data_by_name | actual_data | forecasting_TBATS | MAPE_TBATS_Model |
## +===+============+=========================+=============+===================+==================+
## | 1 | 2021-03-15 | Monday | 9437.00 | 9900.27 | 4.909 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-16 | Tuesday | 9393.00 | 9759.63 | 3.903 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-17 | Wednesday | 8998.00 | 9620.01 | 6.913 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-18 | Thursday | 9803.00 | 9493.97 | 3.152 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-19 | Friday | 9699.00 | 9322.40 | 3.883 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-20 | Saturday | 9632.00 | 9164.13 | 4.857 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-21 | Sunday | 9299.00 | 9050.36 | 2.674 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-03-22 | Monday | 9284.00 | 8909.72 | 4.031 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 8770.10 | 6902.57 | 5913.96 | 10637.63 | 11626.24 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 8644.06 | 6681.91 | 5643.21 | 10606.21 | 11644.91 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 8472.49 | 6420.17 | 5333.74 | 10524.82 | 11611.25 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 8314.22 | 6176.57 | 5044.97 | 10451.87 | 11583.47 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 8200.45 | 5981.53 | 4806.91 | 10419.36 | 11593.98 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 8059.81 | 5762.67 | 4546.64 | 10356.95 | 11572.98 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 7920.19 | 5547.69 | 4291.76 | 10292.69 | 11548.62 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 -22.23267 577.6336 354.3449 NaN Inf 0.9996207 0.1211244
# 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= 0.6308
##
## Smoothing parameters:
## alpha = 0.7123
## beta = 0.0545
##
## Initial states:
## l = -2.2852
## b = -0.0023
##
## sigma: 17.7594
##
## AIC AICc BIC
## 5177.334 5177.474 5197.734
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -22.23267 577.6336 354.3449 NaN Inf 0.9996207 0.1211244
# 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 8 days by using holt Model for ==> Daily Covid 19 Infection cases in Russia"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 8 days in holt Model for ==> Daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.Holt,"%")
## [1] "3.319 % MAPE 8 days Daily Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in holt Model for ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_holt | validation_data_by_name | actual_data | forecasting_holt | MAPE_holt_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-03-15 | Monday | 9437.00 | 9846.75 | 4.342 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-16 | Tuesday | 9393.00 | 9741.29 | 3.708 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-17 | Wednesday | 8998.00 | 9636.26 | 7.093 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-18 | Thursday | 9803.00 | 9531.65 | 2.768 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-19 | Friday | 9699.00 | 9427.45 | 2.8 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-20 | Saturday | 9632.00 | 9323.69 | 3.201 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-21 | Sunday | 9299.00 | 9220.34 | 0.846 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-03-22 | Monday | 9284.00 | 9117.42 | 1.794 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 9014.93 | 7180.92 | 6273.66 | 10998.53 | 12106.48 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 8912.87 | 6944.13 | 5977.01 | 11057.32 | 12260.27 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 8811.24 | 6708.55 | 5683.22 | 11118.31 | 12418.10 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 8710.04 | 6474.15 | 5392.29 | 11181.68 | 12580.27 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 8609.27 | 6240.93 | 5104.34 | 11247.55 | 12747.02 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 8508.93 | 6008.93 | 4819.51 | 11316.03 | 12918.54 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 8409.03 | 5778.23 | 4538.02 | 11387.20 | 13094.97 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Daily Covid 19 Infection cases in Russia"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 5.097, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
## Warning in pp.test(data_series): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = 0.28984, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -1.0808, Lag order = 7, p-value = 0.9253
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Daily Covid 19 Infection cases in Russia"
kpss.test(diff1_x1) # applay kpss test after taking first differences
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 0.54453, Truncation lag parameter = 5, p-value = 0.03164
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) = -435.62, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -3.606, Lag order = 7, p-value = 0.03237
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking Second differences in",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking Second differences in Daily Covid 19 Infection cases in Russia"
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 = 0.0088768, 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) = -516.44, 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 = -15.791, 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) : 7099.355
## ARIMA(0,2,1) : 6775.362
## ARIMA(0,2,2) : 6769.754
## ARIMA(0,2,3) : 6755.791
## ARIMA(0,2,4) : 6752.643
## ARIMA(0,2,5) : 6754.565
## ARIMA(1,2,0) : 6976.206
## ARIMA(1,2,1) : 6772.058
## ARIMA(1,2,2) : 6754.768
## ARIMA(1,2,3) : 6753.84
## ARIMA(1,2,4) : 6754.289
## ARIMA(2,2,0) : 6918.912
## ARIMA(2,2,1) : 6766.355
## ARIMA(2,2,2) : 6752.605
## ARIMA(2,2,3) : 6700.053
## ARIMA(3,2,0) : 6885.306
## ARIMA(3,2,1) : 6761.512
## ARIMA(3,2,2) : 6750.553
## ARIMA(4,2,0) : 6875.427
## ARIMA(4,2,1) : 6755.897
## ARIMA(5,2,0) : 6821.9
##
##
##
## Best model: ARIMA(2,2,3)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,3)
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## 1.2361 -0.8247 -2.3937 2.2429 -0.8153
## s.e. 0.0378 0.0361 0.0396 0.0679 0.0362
##
## sigma^2 estimated as 278963: log likelihood=-3343.93
## AIC=6699.86 AICc=6700.05 BIC=6724.31
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 3
strtoi(bestmodel[3])
## [1] 3
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## 1.2361 -0.8247 -2.3937 2.2429 -0.8153
## s.e. 0.0378 0.0361 0.0396 0.0679 0.0362
##
## sigma^2 estimated as 275757: log likelihood = -3343.93, aic = 6699.86
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Daily Covid 19 Infection cases in Russia"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -4.314945 523.9224 321.2708 NaN Inf 0.9063172 -0.07730037
x1_model1$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(2,2,3)
## Q* = 31.483, df = 5, p-value = 7.521e-06
##
## 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 ==> Daily Covid 19 Infection cases in Russia"
Box.test(x1_model1$residuals^2, lag=20, type="Ljung-Box") # Do test for resdulas by using Box-Ljung test , Ljung-Box test For Modelling
##
## Box-Ljung test
##
## data: x1_model1$residuals^2
## X-squared = 409.01, 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 = 189.61, 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 8 days by using bats Model for ==> Daily Covid 19 Infection cases in Russia"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 8 days in bats Model for ==> Daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "1.638 % MAPE 8 days Daily Covid 19 Infection cases in Russia %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 8 days in bats Model for ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)), type = "rest")
##
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | | date_auto.arima | validation_data_by_name | actual_data | forecasting_auto.arima | MAPE_auto.arima_Model |
## +===+=================+=========================+=============+========================+=======================+
## | 1 | 2021-03-15 | Monday | 9437.00 | 9488.02 | 0.541 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-16 | Tuesday | 9393.00 | 9172.85 | 2.344 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-17 | Wednesday | 8998.00 | 9210.00 | 2.356 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-18 | Thursday | 9803.00 | 9451.92 | 3.581 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-19 | Friday | 9699.00 | 9656.37 | 0.439 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-20 | Saturday | 9632.00 | 9645.65 | 0.142 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-21 | Sunday | 9299.00 | 9399.83 | 1.084 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-03-22 | Monday | 9284.00 | 9040.85 | 2.619 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+===========================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 8735.90 | 6759.87 | 5713.82 | 10711.94 | 11757.99 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 8591.05 | 6452.21 | 5319.98 | 10729.90 | 11862.13 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 8599.56 | 6317.97 | 5110.17 | 10881.14 | 12088.94 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 8665.58 | 6241.50 | 4958.27 | 11089.66 | 12372.90 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 8676.24 | 6093.29 | 4725.96 | 11259.19 | 12626.52 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 8571.02 | 5806.72 | 4343.39 | 11335.32 | 12798.66 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 8368.22 | 5406.87 | 3839.23 | 11329.56 | 12897.20 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "1.638 % MAPE 8 days Daily Covid 19 Infection cases in Russia"
# Table for MAPE For counry
best_recommended_model <- min(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
paste("System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> Daily Covid 19 Infection cases in Russia"
best_recommended_model
## [1] 1.638
x1<-if(best_recommended_model >= MAPE_Mean_All.bats_Model) {paste("BATS Model")}
x2<-if(best_recommended_model >= MAPE_Mean_All.TBATS_Model) {paste("TBATS Model")}
x3<-if(best_recommended_model >= MAPE_Mean_All.Holt_Model) {paste("Holt Model")}
x4<-if(best_recommended_model >= MAPE_Mean_All.ARIMA_Model) {paste("ARIMA Model")}
x5<-if(best_recommended_model >= MAPE_Mean_All_NNAR) {paste("NNAR Model")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 7889.46 | 6048.50 | 5073.95 | 6048.50 | 5073.95 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 7674.46 | 5701.31 | 4656.79 | 5701.31 | 4656.79 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 7713.20 | 5626.57 | 4521.97 | 5626.57 | 4521.97 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 7845.71 | 5657.61 | 4499.30 | 5657.61 | 4499.30 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 7844.86 | 5554.19 | 4341.58 | 5554.19 | 4341.58 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 7588.00 | 5182.46 | 3909.04 | 5182.46 | 3909.04 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 7146.86 | 4612.17 | 3270.39 | 4612.17 | 3270.39 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 8770.10 | 6902.57 | 5913.96 | 10637.63 | 11626.24 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 8644.06 | 6681.91 | 5643.21 | 10606.21 | 11644.91 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 8472.49 | 6420.17 | 5333.74 | 10524.82 | 11611.25 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 8314.22 | 6176.57 | 5044.97 | 10451.87 | 11583.47 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 8200.45 | 5981.53 | 4806.91 | 10419.36 | 11593.98 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 8059.81 | 5762.67 | 4546.64 | 10356.95 | 11572.98 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 7920.19 | 5547.69 | 4291.76 | 10292.69 | 11548.62 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 9014.93 | 7180.92 | 6273.66 | 10998.53 | 12106.48 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 8912.87 | 6944.13 | 5977.01 | 11057.32 | 12260.27 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 8811.24 | 6708.55 | 5683.22 | 11118.31 | 12418.10 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 8710.04 | 6474.15 | 5392.29 | 11181.68 | 12580.27 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 8609.27 | 6240.93 | 5104.34 | 11247.55 | 12747.02 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 8508.93 | 6008.93 | 4819.51 | 11316.03 | 12918.54 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 8409.03 | 5778.23 | 4538.02 | 11387.20 | 13094.97 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+===========================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 8735.90 | 6759.87 | 5713.82 | 10711.94 | 11757.99 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 8591.05 | 6452.21 | 5319.98 | 10729.90 | 11862.13 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 8599.56 | 6317.97 | 5110.17 | 10881.14 | 12088.94 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 8665.58 | 6241.50 | 4958.27 | 11089.66 | 12372.90 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 8676.24 | 6093.29 | 4725.96 | 11259.19 | 12626.52 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 8571.02 | 5806.72 | 4343.39 | 11335.32 | 12798.66 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 8368.22 | 5406.87 | 3839.23 | 11329.56 | 12897.20 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Daily Covid 19 Infection cases in Russia"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-03-23 | Tuesday | 8660.40 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 8642.20 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 8806.16 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 9007.49 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 9036.25 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 8863.50 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 8513.86 |
## +---+------------+-----------------+---------------------+
result<-c(x1,x2,x3,x4,x5)
table.error<-data.frame(country.name,NNAR.model=MAPE_Mean_All_NNAR, BATS.Model=MAPE_Mean_All.bats_Model,TBATS.Model=MAPE_Mean_All.TBATS_Model,Holt.Model=MAPE_Mean_All.Holt_Model,ARIMA.Model=MAPE_Mean_All.ARIMA_Model,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+=============+======+
## | 1 | Russia | 2.5 | 5.589 | 4.29 | 3.319 | 1.638 | 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)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend, and ARIMA Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend, and ARIMA Model ==>Daily Covid 19 Infection cases in Russia
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Daily Covid 19 Infection cases in Russia