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$cases
y_lab <- "Forecasting daily Covid 19 Infection cases in Russia" # input name of data
Actual_date_interval <- c("2020/03/01","2021/04/27")
Forecast_date_interval <- c("2021/04/28","2021/05/10")
validation_data_days <-7
frequency<-"day"
Number_Neural<-3 # Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Russia"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 4892 8457 9936 14494 29935
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.661596
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.7801642
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 8336.614
#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(22,3)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 22-3-1 network with 73 weights
## options were - linear output units
##
## sigma^2 estimated as 152541
# 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 ==> Forecasting 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 7 days in NNAR Model for ==> Forecasting daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All,"%")
## [1] "2.197 % MAPE 7 days Forecasting 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 7 days in NNAR Model for ==> Forecasting 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 | 2021-04-21 | Wednesday | 8271.00 | 8443.40 | 2.084 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-04-22 | Thursday | 8996.00 | 8748.80 | 2.748 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-04-23 | Friday | 8840.00 | 8915.26 | 0.851 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-04-24 | Saturday | 8828.00 | 8868.20 | 0.455 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-04-25 | Sunday | 8780.00 | 8655.80 | 1.415 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-04-26 | Monday | 8803.00 | 8325.20 | 5.428 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-04-27 | Tuesday | 8053.00 | 8246.27 | 2.4 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +====+============+=================+=====================+
## | 1 | 2021-04-28 | Wednesday | 8299.92 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-04-29 | Thursday | 8635.63 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-04-30 | Friday | 8806.76 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-01 | Saturday | 8749.86 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-02 | Sunday | 8561.98 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-03 | Monday | 8333.79 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-04 | Tuesday | 8236.28 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-05 | Wednesday | 8398.28 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-06 | Thursday | 8652.75 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-07 | Friday | 8782.95 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-08 | Saturday | 8781.40 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-09 | Sunday | 8547.32 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-10 | Monday | 8408.91 |
## +----+------------+-----------------+---------------------+
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 5.425765 543.3884 332.8554 NaN Inf 0.9468972 0.001566267
# Print Model Parameters
model_bats
## BATS(1, {2,2}, 0.973, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.333915
## Beta: 0.04059146
## Damping Parameter: 0.973412
## AR coefficients: 0.229466 -0.092601
## MA coefficients: 0.250213 0.125126
##
## Seed States:
## [,1]
## [1,] -15.108386
## [2,] 1.370856
## [3,] 0.000000
## [4,] 0.000000
## [5,] 0.000000
## [6,] 0.000000
##
## Sigma: 543.3884
## AIC: 8916.75
#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 ==> Forecasting 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 7 days in bats Model for ==> Forecasting daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.bats,"%")
## [1] "4.325 % MAPE 7 days Forecasting 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 7 days in bats Model for ==> Forecasting 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 | 2021-04-21 | Wednesday | 8271.00 | 8310.36 | 0.476 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-04-22 | Thursday | 8996.00 | 8389.51 | 6.742 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-04-23 | Friday | 8840.00 | 8413.99 | 4.819 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-04-24 | Saturday | 8828.00 | 8391.26 | 4.947 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-04-25 | Sunday | 8780.00 | 8363.31 | 4.746 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-04-26 | Monday | 8803.00 | 8339.09 | 5.27 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-04-27 | Tuesday | 8053.00 | 8316.73 | 3.275 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-04-28 | Wednesday | 8294.98 | 6658.61 | 5792.37 | 6658.61 | 5792.37 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 8273.69 | 6503.47 | 5566.37 | 6503.47 | 5566.37 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 8252.93 | 6345.28 | 5335.43 | 6345.28 | 5335.43 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 8232.74 | 6184.50 | 5100.22 | 6184.50 | 5100.22 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 8213.08 | 6021.48 | 4861.31 | 6021.48 | 4861.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 8193.95 | 5856.55 | 4619.20 | 5856.55 | 4619.20 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 8175.33 | 5689.98 | 4374.31 | 5689.98 | 4374.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 8157.20 | 5522.01 | 4127.03 | 5522.01 | 4127.03 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 8139.55 | 5352.86 | 3877.68 | 5352.86 | 3877.68 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 8122.38 | 5182.71 | 3626.55 | 5182.71 | 3626.55 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 8105.65 | 5011.73 | 3373.91 | 5011.73 | 3373.91 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 8089.38 | 4840.07 | 3120.00 | 4840.07 | 3120.00 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 8073.54 | 4667.87 | 2865.02 | 4667.87 | 2865.02 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 -2.842828 559.9235 351.6475 NaN Inf 1.000357 0.02729539
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.8356046
## Beta: 0.04412813
## Damping Parameter: 1
## Gamma-1 Values: -0.001669341
## Gamma-2 Values: 0.0006959933
##
## Seed States:
## [,1]
## [1,] -17.622545
## [2,] 2.426949
## [3,] 14.653302
## [4,] 8.845870
## [5,] 11.596632
## [6,] -19.484255
##
## Sigma: 559.9235
## AIC: 8939.167
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 ==> Forecasting 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 7 days in TBATS Model for ==> Forecasting daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "7.346 % MAPE 7 days Forecasting 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 7 days in TBATS Model for ==> Forecasting 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 | 2021-04-21 | Wednesday | 8271.00 | 8192.72 | 0.946 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-04-22 | Thursday | 8996.00 | 8123.97 | 9.694 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-04-23 | Friday | 8840.00 | 8076.88 | 8.633 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-04-24 | Saturday | 8828.00 | 7994.30 | 9.444 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-04-25 | Sunday | 8780.00 | 7913.96 | 9.864 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-04-26 | Monday | 8803.00 | 7894.18 | 10.324 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-04-27 | Tuesday | 8053.00 | 7850.50 | 2.515 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+======================+===========+===========+===========+===========+
## | 1 | 2021-04-28 | Wednesday | 7781.76 | 6052.38 | 5136.90 | 9511.14 | 10426.61 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 7734.66 | 5907.54 | 4940.31 | 9561.79 | 10529.01 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 7652.08 | 5732.18 | 4715.84 | 9571.98 | 10588.32 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 7571.75 | 5563.43 | 4500.30 | 9580.06 | 10643.20 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 7551.97 | 5459.81 | 4352.29 | 9644.13 | 10751.65 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 7508.29 | 5336.16 | 4186.31 | 9680.41 | 10830.27 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 7439.54 | 5190.45 | 3999.85 | 9688.63 | 10879.23 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 7392.45 | 5069.17 | 3839.30 | 9715.73 | 10945.60 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 7309.87 | 4914.70 | 3646.77 | 9705.04 | 10972.96 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 7229.53 | 4764.64 | 3459.80 | 9694.43 | 10999.27 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 7209.75 | 4677.73 | 3337.36 | 9741.78 | 11082.15 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 7166.07 | 4569.19 | 3194.49 | 9762.96 | 11137.66 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 7097.33 | 4437.30 | 3029.17 | 9757.35 | 11165.49 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 -13.15558 562.5031 348.4877 NaN Inf 0.9913674 0.06660971
# 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= 0.746
##
## Smoothing parameters:
## alpha = 0.7802
## beta = 0.0499
##
## Initial states:
## l = -1.4982
## b = -0.5798
##
## sigma: 49.9664
##
## AIC AICc BIC
## 6634.356 6634.484 6655.162
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -13.15558 562.5031 348.4877 NaN Inf 0.9913674 0.06660971
# 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 ==> Forecasting 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 7 days in holt Model for ==> Forecasting daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.Holt,"%")
## [1] "6.672 % MAPE 7 days Forecasting 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 7 days in holt Model for ==> Forecasting 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 | 2021-04-21 | Wednesday | 8271.00 | 8209.98 | 0.738 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-04-22 | Thursday | 8996.00 | 8161.51 | 9.276 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-04-23 | Friday | 8840.00 | 8113.12 | 8.223 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-04-24 | Saturday | 8828.00 | 8064.80 | 8.645 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-04-25 | Sunday | 8780.00 | 8016.55 | 8.695 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-04-26 | Monday | 8803.00 | 7968.37 | 9.481 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-04-27 | Tuesday | 8053.00 | 7920.27 | 1.648 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-04-28 | Wednesday | 7872.24 | 6178.39 | 5325.71 | 9664.57 | 10649.89 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 7824.29 | 5993.47 | 5076.83 | 9771.58 | 10845.28 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 7776.41 | 5809.45 | 4830.23 | 9879.49 | 11042.53 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 7728.61 | 5626.08 | 4585.59 | 9988.67 | 11242.19 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 7680.88 | 5443.17 | 4342.71 | 10099.37 | 11444.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 7633.22 | 5260.61 | 4101.52 | 10211.79 | 11650.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 7585.65 | 5078.34 | 3862.02 | 10326.09 | 11859.35 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 7538.14 | 4896.32 | 3624.26 | 10442.40 | 12072.00 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 7490.72 | 4714.57 | 3388.37 | 10560.81 | 12288.43 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 7443.37 | 4533.09 | 3154.51 | 10681.41 | 12508.77 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 7396.09 | 4351.92 | 2922.88 | 10804.26 | 12733.14 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 7348.89 | 4171.13 | 2693.74 | 10929.41 | 12961.63 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 7301.77 | 3990.77 | 2467.37 | 11056.91 | 13194.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Forecasting 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 = 4.5352, 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) = 0.18394, 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 = -0.998, Lag order = 7, p-value = 0.9389
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Forecasting 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 = 0.64647, Truncation lag parameter = 5, p-value = 0.01841
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) = -470.18, 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 = -3.7423, Lag order = 7, p-value = 0.02194
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking Second differences in",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking Second differences in Forecasting 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 = 0.0094299, 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) = -562.33, 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 = -16.477, 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) : 7684.697
## ARIMA(0,2,1) : 7331.85
## ARIMA(0,2,2) : 7325.309
## ARIMA(0,2,3) : 7309.704
## ARIMA(0,2,4) : 7304.85
## ARIMA(0,2,5) : 7306.527
## ARIMA(1,2,0) : 7548.798
## ARIMA(1,2,1) : 7327.849
## ARIMA(1,2,2) : 7307.703
## ARIMA(1,2,3) : 7306.695
## ARIMA(1,2,4) : 7306.001
## ARIMA(2,2,0) : 7490.251
## ARIMA(2,2,1) : 7322.133
## ARIMA(2,2,2) : 7305.236
## ARIMA(2,2,3) : 7245.569
## ARIMA(3,2,0) : 7452.382
## ARIMA(3,2,1) : 7315.035
## ARIMA(3,2,2) : 7301.474
## ARIMA(4,2,0) : 7442.284
## ARIMA(4,2,1) : 7308.683
## ARIMA(5,2,0) : 7378.812
##
##
##
## 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
## 1.233 -0.8270 -2.3919 2.2420 -0.8162
## s.e. 0.036 0.0336 0.0375 0.0646 0.0342
##
## sigma^2 estimated as 265440: log likelihood=-3616.69
## AIC=7245.39 AICc=7245.57 BIC=7270.33
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 3
strtoi(bestmodel[3])
## [1] 3
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## 1.233 -0.8270 -2.3919 2.2420 -0.8162
## s.e. 0.036 0.0336 0.0375 0.0646 0.0342
##
## sigma^2 estimated as 262628: log likelihood = -3616.69, aic = 7245.39
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting daily Covid 19 Infection cases in Russia"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -1.094356 511.3903 317.0862 NaN Inf 0.9020374 -0.08472288
x1_model1$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* = 36.107, df = 5, p-value = 9.043e-07
##
## Model df: 5. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Forecasting 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 = 450.07, 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 = 222.11, 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 ==> Forecasting 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 7 days in bats Model for ==> Forecasting daily Covid 19 Infection cases in Russia"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "3.149 % MAPE 7 days Forecasting 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 7 days in bats Model for ==> Forecasting 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 | 2021-04-21 | Wednesday | 8271.00 | 8391.18 | 1.453 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-04-22 | Thursday | 8996.00 | 8623.57 | 4.14 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-04-23 | Friday | 8840.00 | 8704.58 | 1.532 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-04-24 | Saturday | 8828.00 | 8594.66 | 2.643 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-04-25 | Sunday | 8780.00 | 8374.50 | 4.618 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-04-26 | Monday | 8803.00 | 8176.35 | 7.119 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-04-27 | Tuesday | 8053.00 | 8096.48 | 0.54 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +====+============+=================+===========================+===========+===========+===========+===========+
## | 1 | 2021-04-28 | Wednesday | 8144.27 | 6409.79 | 5491.62 | 9878.74 | 10796.92 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 8251.61 | 6327.88 | 5309.52 | 10175.34 | 11193.70 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 8326.82 | 6246.24 | 5144.84 | 10407.41 | 11508.81 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 8313.16 | 6095.16 | 4921.03 | 10531.15 | 11705.28 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 8216.48 | 5860.68 | 4613.59 | 10572.29 | 11819.38 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 8090.97 | 5580.54 | 4251.60 | 10601.40 | 11930.34 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 7998.54 | 5311.05 | 3888.39 | 10686.03 | 12108.70 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 7970.77 | 5091.16 | 3566.79 | 10850.37 | 12374.75 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 7995.34 | 4922.39 | 3295.67 | 11068.28 | 12695.00 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 8030.98 | 4773.51 | 3049.11 | 11288.44 | 13012.84 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 8036.98 | 4604.82 | 2787.95 | 11469.14 | 13286.01 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 7997.28 | 4394.07 | 2486.64 | 11600.50 | 13507.93 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 7925.75 | 4146.84 | 2146.40 | 11704.66 | 13705.10 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "3.149 % MAPE 7 days Forecasting 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 ==> Forecasting daily Covid 19 Infection cases in Russia"
best_recommended_model
## [1] 2.197
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 ==> Forecasting 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 | 2021-04-28 | Wednesday | 8294.98 | 6658.61 | 5792.37 | 6658.61 | 5792.37 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 8273.69 | 6503.47 | 5566.37 | 6503.47 | 5566.37 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 8252.93 | 6345.28 | 5335.43 | 6345.28 | 5335.43 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 8232.74 | 6184.50 | 5100.22 | 6184.50 | 5100.22 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 8213.08 | 6021.48 | 4861.31 | 6021.48 | 4861.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 8193.95 | 5856.55 | 4619.20 | 5856.55 | 4619.20 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 8175.33 | 5689.98 | 4374.31 | 5689.98 | 4374.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 8157.20 | 5522.01 | 4127.03 | 5522.01 | 4127.03 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 8139.55 | 5352.86 | 3877.68 | 5352.86 | 3877.68 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 8122.38 | 5182.71 | 3626.55 | 5182.71 | 3626.55 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 8105.65 | 5011.73 | 3373.91 | 5011.73 | 3373.91 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 8089.38 | 4840.07 | 3120.00 | 4840.07 | 3120.00 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 8073.54 | 4667.87 | 2865.02 | 4667.87 | 2865.02 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting 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 | 2021-04-28 | Wednesday | 7781.76 | 6052.38 | 5136.90 | 9511.14 | 10426.61 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 7734.66 | 5907.54 | 4940.31 | 9561.79 | 10529.01 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 7652.08 | 5732.18 | 4715.84 | 9571.98 | 10588.32 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 7571.75 | 5563.43 | 4500.30 | 9580.06 | 10643.20 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 7551.97 | 5459.81 | 4352.29 | 9644.13 | 10751.65 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 7508.29 | 5336.16 | 4186.31 | 9680.41 | 10830.27 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 7439.54 | 5190.45 | 3999.85 | 9688.63 | 10879.23 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 7392.45 | 5069.17 | 3839.30 | 9715.73 | 10945.60 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 7309.87 | 4914.70 | 3646.77 | 9705.04 | 10972.96 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 7229.53 | 4764.64 | 3459.80 | 9694.43 | 10999.27 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 7209.75 | 4677.73 | 3337.36 | 9741.78 | 11082.15 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 7166.07 | 4569.19 | 3194.49 | 9762.96 | 11137.66 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 7097.33 | 4437.30 | 3029.17 | 9757.35 | 11165.49 |
## +----+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Forecasting 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 | 2021-04-28 | Wednesday | 7872.24 | 6178.39 | 5325.71 | 9664.57 | 10649.89 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 7824.29 | 5993.47 | 5076.83 | 9771.58 | 10845.28 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 7776.41 | 5809.45 | 4830.23 | 9879.49 | 11042.53 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 7728.61 | 5626.08 | 4585.59 | 9988.67 | 11242.19 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 7680.88 | 5443.17 | 4342.71 | 10099.37 | 11444.67 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 7633.22 | 5260.61 | 4101.52 | 10211.79 | 11650.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 7585.65 | 5078.34 | 3862.02 | 10326.09 | 11859.35 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 7538.14 | 4896.32 | 3624.26 | 10442.40 | 12072.00 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 7490.72 | 4714.57 | 3388.37 | 10560.81 | 12288.43 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 7443.37 | 4533.09 | 3154.51 | 10681.41 | 12508.77 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 7396.09 | 4351.92 | 2922.88 | 10804.26 | 12733.14 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 7348.89 | 4171.13 | 2693.74 | 10929.41 | 12961.63 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 7301.77 | 3990.77 | 2467.37 | 11056.91 | 13194.31 |
## +----+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting 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 | 2021-04-28 | Wednesday | 8144.27 | 6409.79 | 5491.62 | 9878.74 | 10796.92 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-04-29 | Thursday | 8251.61 | 6327.88 | 5309.52 | 10175.34 | 11193.70 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-04-30 | Friday | 8326.82 | 6246.24 | 5144.84 | 10407.41 | 11508.81 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-05-01 | Saturday | 8313.16 | 6095.16 | 4921.03 | 10531.15 | 11705.28 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-05-02 | Sunday | 8216.48 | 5860.68 | 4613.59 | 10572.29 | 11819.38 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-05-03 | Monday | 8090.97 | 5580.54 | 4251.60 | 10601.40 | 11930.34 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-05-04 | Tuesday | 7998.54 | 5311.05 | 3888.39 | 10686.03 | 12108.70 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 8 | 2021-05-05 | Wednesday | 7970.77 | 5091.16 | 3566.79 | 10850.37 | 12374.75 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 9 | 2021-05-06 | Thursday | 7995.34 | 4922.39 | 3295.67 | 11068.28 | 12695.00 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 10 | 2021-05-07 | Friday | 8030.98 | 4773.51 | 3049.11 | 11288.44 | 13012.84 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 11 | 2021-05-08 | Saturday | 8036.98 | 4604.82 | 2787.95 | 11469.14 | 13286.01 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 12 | 2021-05-09 | Sunday | 7997.28 | 4394.07 | 2486.64 | 11600.50 | 13507.93 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 13 | 2021-05-10 | Monday | 7925.75 | 4146.84 | 2146.40 | 11704.66 | 13705.10 |
## +----+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting 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 | 2021-04-28 | Wednesday | 8299.92 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-04-29 | Thursday | 8635.63 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-04-30 | Friday | 8806.76 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-01 | Saturday | 8749.86 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-02 | Sunday | 8561.98 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-03 | Monday | 8333.79 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-04 | Tuesday | 8236.28 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-05 | Wednesday | 8398.28 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-06 | Thursday | 8652.75 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-07 | Friday | 8782.95 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-08 | Saturday | 8781.40 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-09 | Sunday | 8547.32 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-10 | Monday | 8408.91 |
## +----+------------+-----------------+---------------------+
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 | 2.197 | 4.325 | 7.346 | 6.672 | 3.149 | NNAR Model | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
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,ARIMA Model, and SIR Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>Forecasting 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 ==> Forecasting daily Covid 19 Infection cases in Russia