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$India
y_lab <- "Cumulative Covid 19 Infection cases in India" # input name of data
Actual_date_interval <- c("2020/01/03","2021/01/10")
Forecast_date_interval <- c("2021/01/11","2021/01/17")
validation_data_days <-7
Number_Neural<-5 # Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
Population <-1387369463 # population in india for SIR Model
country.name <- "India"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 3547 731041 3148878 6888527 10450284
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 1.924422
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.7700359
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 3817709
#processing on data (input data)
rows <- NROW(original_data) # calculate number of rows in time series (number of days)
training_data<-original_data[1:(rows-validation_data_days)] # Training data
testing_data<-original_data[(rows-validation_data_days+1):rows] #testing data
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD)) #calculate number of days that you want to forecasting
validation_dates<-tail(AD,validation_data_days) # select validation_dates
validation_data_by_name<-weekdays(validation_dates) # put names of validation dates
forecasting_data_by_name<-weekdays(FD) # put names of Forecasting dates
#NNAR Model
if(NNAR_Model==TRUE){
data_series<-ts(training_data)
model_NNAR<-nnetar(data_series, size = Number_Neural)
saveRDS(model_NNAR, file = "model_NNAR.RDS")
my_model <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
if(NNAR_Model==FALSE){
data_series<-ts(training_data)
#model_NNAR<-nnetar(data_series, size = Number_Numeral)
model_NNAR <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
## Series: data_series
## Model: NNAR(1,5)
## Call: nnetar(y = data_series, size = 5)
##
## Average of 20 networks, each of which is
## a 1-5-1 network with 16 weights
## options were - linear output units
##
## sigma^2 estimated as 14171295
# Testing Data Evaluation
forecasting_NNAR <- forecast(model_NNAR, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_NNAR$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using NNAR Model for ==> Cumulative Covid 19 Infection cases in India"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Mean_All_NNAR<-round(mean(MAPE_Per_Day),3)
MAPE_NNAR<-paste(round(MAPE_Per_Day,3),"%")
MAPE_NNAR_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in NNAR Model for ==> Cumulative Covid 19 Infection cases in India"
paste(MAPE_Mean_All,"%")
## [1] "0.043 % MAPE 7 days Cumulative Covid 19 Infection cases in India %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in NNAR Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in NNAR Model for ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(date_NNAR=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_NNAR=validation_forecast,MAPE_NNAR_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_NNAR | validation_data_by_name | actual_data | forecasting_NNAR | MAPE_NNAR_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-01-04 | Monday | 10340469.00 | 10342515.87 | 0.02 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 10356844.00 | 10360655.76 | 0.037 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 10374932.00 | 10378389.29 | 0.033 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 10395278.00 | 10395721.22 | 0.004 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 10413417.00 | 10412656.43 | 0.007 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 10413417.00 | 10429199.92 | 0.152 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 10450284.00 | 10445356.81 | 0.047 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 10461132.34 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 10476531.83 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 10491560.70 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 10506224.46 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 10520528.70 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 10534479.08 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 10548081.31 |
## +---+------------+-----------------+---------------------+
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 86.56065 3208.077 1816.781 NaN Inf 0.0644076 -0.02768263
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.379331
## Beta: 0.5984324
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -24.982765
## [2,] 2.154116
##
## Sigma: 3208.077
## AIC: 8101.163
#ploting BATS Model
plot(model_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "))
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> Cumulative Covid 19 Infection cases in India"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in India"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.073 % MAPE 7 days Cumulative Covid 19 Infection cases in India %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_bats | validation_data_by_name | actual_data | forecasting_bats | MAPE_bats_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-01-04 | Monday | 10340469.00 | 10342602.37 | 0.021 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 10356844.00 | 10361615.39 | 0.046 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 10374932.00 | 10380628.40 | 0.055 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 10395278.00 | 10399641.41 | 0.042 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 10413417.00 | 10418654.42 | 0.05 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 10413417.00 | 10437667.43 | 0.233 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 10450284.00 | 10456680.44 | 0.061 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10475693.45 | 10432440.67 | 10409544.03 | 10432440.67 | 10409544.03 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10494706.47 | 10444570.55 | 10418030.21 | 10444570.55 | 10418030.21 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10513719.48 | 10456385.14 | 10426034.17 | 10456385.14 | 10426034.17 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10532732.49 | 10467896.07 | 10433573.75 | 10467896.07 | 10433573.75 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10551745.50 | 10479114.11 | 10440665.38 | 10479114.11 | 10440665.38 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10570758.51 | 10490049.12 | 10447324.14 | 10490049.12 | 10447324.14 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10589771.52 | 10500710.13 | 10453563.88 | 10500710.13 | 10453563.88 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
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 87.03885 3185.779 1884.273 NaN Inf 0.0668003 -0.03100345
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.387155
## Beta: 0.6003708
## Damping Parameter: 1
## Gamma-1 Values: -0.003017072
## Gamma-2 Values: 0.002311937
##
## Seed States:
## [,1]
## [1,] -8.306940
## [2,] -8.246748
## [3,] -209.710848
## [4,] -69.297703
## [5,] -68.536786
## [6,] 80.298188
##
## Sigma: 3185.779
## AIC: 8108.044
plot(model_TBATS,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
# Testing Data Evaluation
forecasting_tbats <- predict(model_TBATS, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_tbats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using TBATS Model for ==> Cumulative Covid 19 Infection cases in India"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in TBATS Model for ==> Cumulative Covid 19 Infection cases in India"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.082 % MAPE 7 days Cumulative Covid 19 Infection cases in India %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in TBATS Model for ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | | date_TBATS | validation_data_by_name | actual_data | forecasting_TBATS | MAPE_TBATS_Model |
## +===+============+=========================+=============+===================+==================+
## | 1 | 2021-01-04 | Monday | 10340469.00 | 10343250.48 | 0.027 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-01-05 | Tuesday | 10356844.00 | 10362372.16 | 0.053 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-01-06 | Wednesday | 10374932.00 | 10381400.63 | 0.062 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-01-07 | Thursday | 10395278.00 | 10401014.60 | 0.055 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-01-08 | Friday | 10413417.00 | 10419780.20 | 0.061 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-01-09 | Saturday | 10413417.00 | 10438553.22 | 0.241 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-01-10 | Sunday | 10450284.00 | 10458267.80 | 0.076 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10477389.49 | 10461985.87 | 10453831.69 | 10492793.10 | 10500947.28 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10496417.96 | 10480040.88 | 10471371.37 | 10512795.04 | 10521464.55 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10516031.92 | 10498736.07 | 10489580.20 | 10533327.77 | 10542483.64 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10534797.52 | 10516629.37 | 10507011.73 | 10552965.68 | 10562583.32 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10553570.54 | 10534581.99 | 10524530.06 | 10572559.09 | 10582611.02 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10573285.13 | 10553517.05 | 10543052.46 | 10593053.20 | 10603517.79 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10592406.81 | 10571887.77 | 10561025.65 | 10612925.85 | 10623787.98 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
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 -1484.96 4658.704 2534.105 NaN Inf 0.08983782 0.6358872
# 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= 0.2971
##
## Smoothing parameters:
## alpha = 0.9097
## beta = 0.2077
##
## Initial states:
## l = -3.3681
## b = 0.0018
##
## sigma: 0.4004
##
## AIC AICc BIC
## 1501.374 1501.540 1520.901
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -1484.96 4658.704 2534.105 NaN Inf 0.08983782 0.6358872
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt Model for ==> Cumulative Covid 19 Infection cases in India"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> Cumulative Covid 19 Infection cases in India"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.118 % MAPE 7 days Cumulative Covid 19 Infection cases in India %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)), type = "rest")
##
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | | date_holt | validation_data_by_name | actual_data | forecasting_holt | MAPE_holt_Model |
## +===+============+=========================+=============+==================+=================+
## | 1 | 2021-01-04 | Monday | 10340469.00 | 10344178.25 | 0.036 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 10356844.00 | 10364195.89 | 0.071 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 10374932.00 | 10384240.75 | 0.09 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 10395278.00 | 10404312.84 | 0.087 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 10413417.00 | 10424412.18 | 0.106 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 10413417.00 | 10444538.80 | 0.299 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 10450284.00 | 10464692.71 | 0.138 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10484873.95 | 10272834.03 | 10161815.96 | 10699971.40 | 10815083.43 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10505082.52 | 10264862.86 | 10139274.20 | 10749226.27 | 10880069.17 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10525318.46 | 10255867.83 | 10115210.28 | 10799706.44 | 10946974.98 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10545581.78 | 10245876.36 | 10089670.56 | 10851396.18 | 11015781.77 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10565872.50 | 10234916.04 | 10062701.67 | 10904279.62 | 11086470.27 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10586190.64 | 10223013.91 | 10034349.37 | 10958341.46 | 11159022.12 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10606536.24 | 10210196.11 | 10004658.05 | 11013567.36 | 11233420.49 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Cumulative Covid 19 Infection cases in India"
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 = 5.4104, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -1.3086, Truncation lag parameter = 5, p-value
## = 0.9824
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -8.1613, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Cumulative Covid 19 Infection cases in India"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 3.887, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = 0.19125, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.60168, Lag order = 7, p-value = 0.977
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab ,main = "2nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking Second differences in",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking Second differences in Cumulative Covid 19 Infection cases in India"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.58181, Truncation lag parameter = 5, p-value = 0.02429
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) = -268.05, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -3.5242, Lag order = 7, p-value = 0.0405
## 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) : 6984.838
## ARIMA(0,2,1) : 6986.09
## ARIMA(0,2,2) : 6937.797
## ARIMA(0,2,3) : 6937.621
## ARIMA(0,2,4) : 6939.359
## ARIMA(0,2,5) : 6925.974
## ARIMA(1,2,0) : 6986.599
## ARIMA(1,2,1) : 6970.3
## ARIMA(1,2,2) : 6936.606
## ARIMA(1,2,3) : 6935.194
## ARIMA(1,2,4) : 6937.193
## ARIMA(2,2,0) : 6946.158
## ARIMA(2,2,1) : 6945.256
## ARIMA(2,2,2) : 6937.019
## ARIMA(2,2,3) : 6937.225
## ARIMA(3,2,0) : 6948.202
## ARIMA(3,2,1) : 6945.656
## ARIMA(3,2,2) : 6935.153
## ARIMA(4,2,0) : 6941.324
## ARIMA(4,2,1) : 6931.411
## ARIMA(5,2,0) : 6898.366
##
##
##
## Best model: ARIMA(5,2,0)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(5,2,0)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5
## -0.0899 -0.3847 -0.1381 -0.1677 -0.3390
## s.e. 0.0491 0.0485 0.0519 0.0483 0.0489
##
## sigma^2 estimated as 9243714: log likelihood=-3443.07
## AIC=6898.13 AICc=6898.37 BIC=6921.53
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 5 2 0
strtoi(bestmodel[3])
## [1] 0
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5
## -0.0899 -0.3847 -0.1381 -0.1677 -0.3390
## s.e. 0.0491 0.0485 0.0519 0.0483 0.0489
##
## sigma^2 estimated as 9117088: log likelihood = -3443.07, aic = 6898.13
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in India"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 107.9783 3011.213 1797.98 0.5578941 2.58824 0.06374108 -0.02985419
x1_model1$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(5,2,0)
## Q* = 224.52, df = 5, p-value < 2.2e-16
##
## 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 ==> Cumulative Covid 19 Infection cases in India"
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 = 450.83, 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 = 294.01, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> Cumulative Covid 19 Infection cases in India"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in India"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.049 % MAPE 7 days Cumulative Covid 19 Infection cases in India %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)), type = "rest")
##
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | | date_auto.arima | validation_data_by_name | actual_data | forecasting_auto.arima | MAPE_auto.arima_Model |
## +===+=================+=========================+=============+========================+=======================+
## | 1 | 2021-01-04 | Monday | 10340469.00 | 10341228.57 | 0.007 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-01-05 | Tuesday | 10356844.00 | 10358921.37 | 0.02 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-01-06 | Wednesday | 10374932.00 | 10377817.54 | 0.028 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-01-07 | Thursday | 10395278.00 | 10397041.83 | 0.017 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-01-08 | Friday | 10413417.00 | 10416173.38 | 0.026 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-01-09 | Saturday | 10413417.00 | 10435258.54 | 0.21 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-01-10 | Sunday | 10450284.00 | 10453990.96 | 0.035 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+===========================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10472322.82 | 10437975.59 | 10419793.26 | 10506670.05 | 10524852.38 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10490737.12 | 10451234.94 | 10430323.75 | 10530239.29 | 10551150.48 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10509386.00 | 10464448.72 | 10440660.36 | 10554323.29 | 10578111.65 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10528112.26 | 10477405.44 | 10450562.86 | 10578819.09 | 10605661.67 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10546916.68 | 10490235.75 | 10460230.68 | 10603597.61 | 10633602.68 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10565773.88 | 10503044.81 | 10469838.05 | 10628502.94 | 10661709.70 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10584518.30 | 10515591.48 | 10479103.83 | 10653445.11 | 10689932.76 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
plot(forecasting_auto_arima)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph4<-autoplot(forecasting_auto_arima,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph4
MAPE_Mean_All.ARIMA
## [1] "0.049 % MAPE 7 days Cumulative Covid 19 Infection cases in India"
# SIR Model
#install.packages("dplyr")
library(deSolve)
first<-rows-13
secondr<-rows-7
vector_SIR<-original_data[first:secondr]
Infected <- c(vector_SIR)
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.1215115 0.1184629
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR<-data.frame(out)
validation_forecast<-result_SIR$I
MAPE_Mean_SIR<-round(mean(abs(((testing_data-validation_forecast)/testing_data)*100)),3)
## forecasting by SIR model
Infected <- c(tail(original_data,validation_data_days))
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.1240022 0.1211474
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 10340469.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 10359861.12 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 10378107.90 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 10395202.19 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 10411137.33 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 10425907.19 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 10439506.18 |
## +---+------------+-----------------+--------------------+
# Table for MAPE For counry
best_recommended_model <- min(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_SIR)
paste("System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> Cumulative Covid 19 Infection cases in India"
best_recommended_model
## [1] 0.043
x1<-if(best_recommended_model >= MAPE_Mean_All.bats_Model) {paste("BATS Model")}
x2<-if(best_recommended_model >= MAPE_Mean_All.TBATS_Model) {paste("TBATS Model")}
x3<-if(best_recommended_model >= MAPE_Mean_All.Holt_Model) {paste("Holt Model")}
x4<-if(best_recommended_model >= MAPE_Mean_All.ARIMA_Model) {paste("ARIMA Model")}
x5<-if(best_recommended_model >= MAPE_Mean_All_NNAR) {paste("NNAR Model")}
x6<-if(best_recommended_model >= MAPE_Mean_SIR) {paste("SIR Model")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days),lower=tail(forecasting_bats$lower,N_forecasting_days),Upper=tail(forecasting_bats$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10475693.45 | 10432440.67 | 10409544.03 | 10432440.67 | 10409544.03 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10494706.47 | 10444570.55 | 10418030.21 | 10444570.55 | 10418030.21 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10513719.48 | 10456385.14 | 10426034.17 | 10456385.14 | 10426034.17 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10532732.49 | 10467896.07 | 10433573.75 | 10467896.07 | 10433573.75 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10551745.50 | 10479114.11 | 10440665.38 | 10479114.11 | 10440665.38 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10570758.51 | 10490049.12 | 10447324.14 | 10490049.12 | 10447324.14 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10589771.52 | 10500710.13 | 10453563.88 | 10500710.13 | 10453563.88 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days),Lower=tail(forecasting_tbats$lower,N_forecasting_days),Upper=tail(forecasting_tbats$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10477389.49 | 10461985.87 | 10453831.69 | 10492793.10 | 10500947.28 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10496417.96 | 10480040.88 | 10471371.37 | 10512795.04 | 10521464.55 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10516031.92 | 10498736.07 | 10489580.20 | 10533327.77 | 10542483.64 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10534797.52 | 10516629.37 | 10507011.73 | 10552965.68 | 10562583.32 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10553570.54 | 10534581.99 | 10524530.06 | 10572559.09 | 10582611.02 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10573285.13 | 10553517.05 | 10543052.46 | 10593053.20 | 10603517.79 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10592406.81 | 10571887.77 | 10561025.65 | 10612925.85 | 10623787.98 |
## +---+------------+-----------------+----------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10484873.95 | 10272834.03 | 10161815.96 | 10699971.40 | 10815083.43 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10505082.52 | 10264862.86 | 10139274.20 | 10749226.27 | 10880069.17 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10525318.46 | 10255867.83 | 10115210.28 | 10799706.44 | 10946974.98 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10545581.78 | 10245876.36 | 10089670.56 | 10851396.18 | 11015781.77 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10565872.50 | 10234916.04 | 10062701.67 | 10904279.62 | 11086470.27 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10586190.64 | 10223013.91 | 10034349.37 | 10958341.46 | 11159022.12 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10606536.24 | 10210196.11 | 10004658.05 | 11013567.36 | 11233420.49 |
## +---+------------+-----------------+---------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days),Lower=tail(forecasting_auto_arima$lower,N_forecasting_days),Upper=tail(forecasting_auto_arima$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | | FD | forecating_date | forecasting_by_auto.arima | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+===========================+=============+=============+=============+=============+
## | 1 | 2021-01-11 | Monday | 10472322.82 | 10437975.59 | 10419793.26 | 10506670.05 | 10524852.38 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 2 | 2021-01-12 | Tuesday | 10490737.12 | 10451234.94 | 10430323.75 | 10530239.29 | 10551150.48 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 3 | 2021-01-13 | Wednesday | 10509386.00 | 10464448.72 | 10440660.36 | 10554323.29 | 10578111.65 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 4 | 2021-01-14 | Thursday | 10528112.26 | 10477405.44 | 10450562.86 | 10578819.09 | 10605661.67 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 5 | 2021-01-15 | Friday | 10546916.68 | 10490235.75 | 10460230.68 | 10603597.61 | 10633602.68 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 6 | 2021-01-16 | Saturday | 10565773.88 | 10503044.81 | 10469838.05 | 10628502.94 | 10661709.70 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
## | 7 | 2021-01-17 | Sunday | 10584518.30 | 10515591.48 | 10479103.83 | 10653445.11 | 10689932.76 |
## +---+------------+-----------------+---------------------------+-------------+-------------+-------------+-------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 10461132.34 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 10476531.83 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 10491560.70 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 10506224.46 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 10520528.70 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 10534479.08 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 10548081.31 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Cumulative Covid 19 Infection cases in India"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 10340469.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 10359861.12 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 10378107.90 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 10395202.19 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 10411137.33 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 10425907.19 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 10439506.18 |
## +---+------------+-----------------+--------------------+
result<-c(x1,x2,x3,x4,x5,x6)
table.error<-data.frame(country.name,NNAR.model=MAPE_Mean_All_NNAR, BATS.Model=MAPE_Mean_All.bats_Model,TBATS.Model=MAPE_Mean_All.TBATS_Model,Holt.Model=MAPE_Mean_All.Holt_Model,ARIMA.Model=MAPE_Mean_All.ARIMA_Model,SIR.Model=MAPE_Mean_SIR,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-----------+------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | SIR.Model | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+===========+============+======+
## | 1 | India | 0.043 | 0.073 | 0.082 | 0.118 | 0.049 | 1.205 | NNAR Model | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-----------+------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_SIR)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model" ,"SIR Model")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>Cumulative Covid 19 Infection cases in India
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Cumulative Covid 19 Infection cases in India