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$France
y_lab <- "Cumulative Covid 19 Infection cases in France" # 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 <-65351079 # population in France for SIR Model
country.name <- "France"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 68220 159739 579272 640047 2721692
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 3.540325
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.463495
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 828412.2
#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 22771402
# 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 France"
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 France"
paste(MAPE_Mean_All,"%")
## [1] "0.309 % MAPE 7 days Cumulative Covid 19 Infection cases in France %"
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 France"
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 | 2611616.00 | 2614861.23 | 0.124 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2615185.00 | 2631375.44 | 0.619 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2635551.00 | 2648769.93 | 0.502 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2660740.00 | 2667160.22 | 0.241 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2682250.00 | 2686680.24 | 0.165 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2701658.00 | 2707486.17 | 0.216 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2721692.00 | 2729761.37 | 0.296 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2753722.53 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 2779627.51 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 2807785.35 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 2838569.10 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 2872432.36 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 2909930.59 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 2951748.49 |
## +---+------------+-----------------+---------------------+
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 95.50453 5053.442 2328.272 NaN Inf 0.3276473 -0.005556488
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.289331
## Beta: 0.3378169
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 94.22191
## [2,] 17.07528
##
## Sigma: 5053.442
## AIC: 8434.691
#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 France"
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 France"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.737 % MAPE 7 days Cumulative Covid 19 Infection cases in France %"
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 France"
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 | 2611616.00 | 2606845.42 | 0.183 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2615185.00 | 2618703.03 | 0.135 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2635551.00 | 2630560.64 | 0.189 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2660740.00 | 2642418.25 | 0.689 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2682250.00 | 2654275.86 | 1.043 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2701658.00 | 2666133.47 | 1.315 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2721692.00 | 2677991.08 | 1.606 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2689848.69 | 2642698.81 | 2617739.17 | 2642698.81 | 2617739.17 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2701706.31 | 2647934.07 | 2619468.77 | 2647934.07 | 2619468.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2713563.92 | 2652919.87 | 2620816.85 | 2652919.87 | 2620816.85 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2725421.53 | 2657661.47 | 2621791.46 | 2657661.47 | 2621791.46 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2737279.14 | 2662164.55 | 2622401.29 | 2662164.55 | 2622401.29 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2749136.75 | 2666434.87 | 2622655.15 | 2666434.87 | 2622655.15 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2760994.36 | 2670478.09 | 2622561.67 | 2670478.09 | 2622561.67 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 96.41653 5002.77 2448.114 NaN Inf 0.3445122 -0.009355887
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.297666
## Beta: 0.340283
## Damping Parameter: 1
## Gamma-1 Values: -0.002418955
## Gamma-2 Values: 0.002956272
##
## Seed States:
## [,1]
## [1,] 195.27949
## [2,] -20.89611
## [3,] -151.22193
## [4,] -10.81590
## [5,] -660.19708
## [6,] -213.01129
##
## Sigma: 5002.77
## AIC: 8439.294
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 France"
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 France"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.711 % MAPE 7 days Cumulative Covid 19 Infection cases in France %"
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 France"
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 | 2611616.00 | 2606384.70 | 0.2 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-01-05 | Tuesday | 2615185.00 | 2619337.96 | 0.159 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-01-06 | Wednesday | 2635551.00 | 2631660.24 | 0.148 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-01-07 | Thursday | 2660740.00 | 2643524.59 | 0.647 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-01-08 | Friday | 2682250.00 | 2656212.25 | 0.971 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-01-09 | Saturday | 2701658.00 | 2667454.55 | 1.266 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-01-10 | Sunday | 2721692.00 | 2678504.53 | 1.587 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2691457.79 | 2668687.16 | 2656633.11 | 2714228.43 | 2726282.47 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2703780.07 | 2679579.71 | 2666768.81 | 2727980.43 | 2740791.33 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2715644.43 | 2690094.22 | 2676568.76 | 2741194.63 | 2754720.09 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2728332.08 | 2701498.55 | 2687293.74 | 2755165.61 | 2769370.43 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2739574.38 | 2711535.99 | 2696693.36 | 2767612.78 | 2782455.41 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2750624.37 | 2721439.42 | 2705989.84 | 2779809.32 | 2795258.90 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2763577.63 | 2733283.71 | 2717247.08 | 2793871.54 | 2809908.17 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -252.3653 5403.496 2460.661 NaN Inf 0.3462779 0.2550632
# 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= 0.3406
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.3248
##
## Initial states:
## l = -3.0438
## b = 0.0957
##
## sigma: 0.7122
##
## AIC AICc BIC
## 1924.132 1924.299 1943.659
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -252.3653 5403.496 2460.661 NaN Inf 0.3462779 0.2550632
# 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 France"
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 France"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.504 % MAPE 7 days Cumulative Covid 19 Infection cases in France %"
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 France"
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 | 2611616.00 | 2612119.95 | 0.019 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2615185.00 | 2625154.24 | 0.381 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2635551.00 | 2638231.33 | 0.102 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2660740.00 | 2651351.32 | 0.353 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2682250.00 | 2664514.25 | 0.661 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2701658.00 | 2677720.20 | 0.886 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2721692.00 | 2690969.23 | 1.129 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2704261.42 | 2603715.73 | 2551502.69 | 2807334.25 | 2862931.03 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2717596.84 | 2602081.94 | 2542264.93 | 2836443.04 | 2900720.55 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2730975.54 | 2599825.97 | 2532113.07 | 2866414.31 | 2939870.30 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2744397.59 | 2596970.32 | 2521086.63 | 2897239.49 | 2980373.15 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2757863.08 | 2593536.16 | 2509223.10 | 2928911.42 | 3022224.21 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2771372.05 | 2589543.38 | 2496557.93 | 2961424.30 | 3065420.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2784924.59 | 2585010.59 | 2483124.67 | 2994773.68 | 3109962.26 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 France"
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 = 4.253, 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) = 1.1659, 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 = -2.3947, Lag order = 7, p-value = 0.4104
## 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 France"
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 = 3.023, 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 smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -45.141, 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 = -1.8077, Lag order = 7, p-value = 0.6581
## 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 France"
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 = 0.049254, 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) = -319.01, 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 = -7.6004, 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) : 7340.466
## ARIMA(0,2,1) : 7301.808
## ARIMA(0,2,2) : 7269.693
## ARIMA(0,2,3) : 7271.583
## ARIMA(0,2,4) : 7273.378
## ARIMA(0,2,5) : 7252.943
## ARIMA(1,2,0) : 7327.788
## ARIMA(1,2,1) : 7276.775
## ARIMA(1,2,2) : 7271.582
## ARIMA(1,2,3) : 7272.55
## ARIMA(1,2,4) : 7273.879
## ARIMA(2,2,0) : 7306.726
## ARIMA(2,2,1) : 7269.251
## ARIMA(2,2,2) : 7272.886
## ARIMA(2,2,3) : 7274.432
## ARIMA(3,2,0) : 7297.035
## ARIMA(3,2,1) : 7267.362
## ARIMA(3,2,2) : 7246.132
## ARIMA(4,2,0) : 7263.527
## ARIMA(4,2,1) : 7254.384
## ARIMA(5,2,0) : 7259.495
##
##
##
## Best model: ARIMA(3,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(3,2,2)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.9506 -0.5996 -0.2395 -1.3615 0.8860
## s.e. 0.0629 0.0671 0.0575 0.0412 0.0357
##
## sigma^2 estimated as 23903096: log likelihood=-3616.95
## AIC=7245.9 AICc=7246.13 BIC=7269.3
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 3 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.9506 -0.5996 -0.2395 -1.3615 0.8860
## s.e. 0.0629 0.0671 0.0575 0.0412 0.0357
##
## sigma^2 estimated as 23575657: log likelihood = -3616.95, aic = 7245.9
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in France"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 55.0802 4842.229 2142.61 0.7576608 2.40337 0.30152 -0.04451188
x1_model1$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(3,2,2)
## Q* = 54.127, df = 5, p-value = 1.973e-10
##
## 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 France"
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 = 446.04, 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 = 4202.3, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using bats Model for ==> Cumulative Covid 19 Infection cases in France"
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 France"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.55 % MAPE 7 days Cumulative Covid 19 Infection cases in France %"
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 France"
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 | 2611616.00 | 2605783.80 | 0.223 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-01-05 | Tuesday | 2615185.00 | 2616028.06 | 0.032 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-01-06 | Wednesday | 2635551.00 | 2631546.98 | 0.152 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-01-07 | Thursday | 2660740.00 | 2649164.72 | 0.435 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-01-08 | Friday | 2682250.00 | 2664755.82 | 0.652 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-01-09 | Saturday | 2701658.00 | 2675898.85 | 0.953 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-01-10 | Sunday | 2721692.00 | 2683526.21 | 1.402 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2690964.03 | 2635743.99 | 2606512.27 | 2746184.07 | 2775415.79 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2701394.83 | 2635862.25 | 2601171.39 | 2766927.41 | 2801618.26 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2715626.24 | 2639631.74 | 2599402.69 | 2791620.73 | 2831849.79 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2731721.24 | 2645243.05 | 2599464.26 | 2818199.42 | 2863978.21 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2746592.15 | 2649419.00 | 2597978.64 | 2843765.30 | 2895205.66 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2758271.95 | 2649871.97 | 2592488.49 | 2866671.93 | 2924055.41 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2767206.03 | 2646828.39 | 2583104.32 | 2887583.66 | 2951307.73 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.55 % MAPE 7 days Cumulative Covid 19 Infection cases in France"
# 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
## 0.01574447 0.00957691
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR<-data.frame(out)
validation_forecast<-result_SIR$I
MAPE_Mean_SIR<-round(mean(abs(((testing_data-validation_forecast)/testing_data)*100)),3)
## forecasting by SIR model
Infected <- c(tail(original_data,validation_data_days))
Day <- 1:(length(Infected))
N <- Population # population of the us
SIR <- function(time, state, parameters) {
par <- as.list(c(state, parameters))
with(par, {
dS <- -beta/N * I * S
dI <- beta/N * I * S - gamma * I
dR <- gamma * I
list(c(dS, dI, dR))
})
}
init <- c(S = N-Infected[1], I = Infected[1], R = 0)
RSS <- function(parameters) {
names(parameters) <- c("beta", "gamma")
out <- ode(y = init, times = Day, func = SIR, parms = parameters)
fit <- out[ , 3]
sum((Infected - fit)^2)
}
# optimize with some sensible conditions
Opt <- optim(c(0.5, 0.5), RSS, method = "L-BFGS-B",
lower = c(0, 0), upper = c(10, 10))
Opt$message
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
Opt_par <- setNames(Opt$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.011226678 0.004171974
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 2611616.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 2628919.22 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2646324.20 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2663831.38 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2681441.17 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2699153.99 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 2716970.28 |
## +---+------------+-----------------+--------------------+
# 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 France"
best_recommended_model
## [1] 0.309
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 France"
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 | 2689848.69 | 2642698.81 | 2617739.17 | 2642698.81 | 2617739.17 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2701706.31 | 2647934.07 | 2619468.77 | 2647934.07 | 2619468.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2713563.92 | 2652919.87 | 2620816.85 | 2652919.87 | 2620816.85 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2725421.53 | 2657661.47 | 2621791.46 | 2657661.47 | 2621791.46 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2737279.14 | 2662164.55 | 2622401.29 | 2662164.55 | 2622401.29 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2749136.75 | 2666434.87 | 2622655.15 | 2666434.87 | 2622655.15 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2760994.36 | 2670478.09 | 2622561.67 | 2670478.09 | 2622561.67 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in France"
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 | 2691457.79 | 2668687.16 | 2656633.11 | 2714228.43 | 2726282.47 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2703780.07 | 2679579.71 | 2666768.81 | 2727980.43 | 2740791.33 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2715644.43 | 2690094.22 | 2676568.76 | 2741194.63 | 2754720.09 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2728332.08 | 2701498.55 | 2687293.74 | 2755165.61 | 2769370.43 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2739574.38 | 2711535.99 | 2696693.36 | 2767612.78 | 2782455.41 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2750624.37 | 2721439.42 | 2705989.84 | 2779809.32 | 2795258.90 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2763577.63 | 2733283.71 | 2717247.08 | 2793871.54 | 2809908.17 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 France"
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 | 2704261.42 | 2603715.73 | 2551502.69 | 2807334.25 | 2862931.03 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2717596.84 | 2602081.94 | 2542264.93 | 2836443.04 | 2900720.55 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2730975.54 | 2599825.97 | 2532113.07 | 2866414.31 | 2939870.30 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2744397.59 | 2596970.32 | 2521086.63 | 2897239.49 | 2980373.15 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2757863.08 | 2593536.16 | 2509223.10 | 2928911.42 | 3022224.21 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2771372.05 | 2589543.38 | 2496557.93 | 2961424.30 | 3065420.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2784924.59 | 2585010.59 | 2483124.67 | 2994773.68 | 3109962.26 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in France"
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 | 2690964.03 | 2635743.99 | 2606512.27 | 2746184.07 | 2775415.79 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2701394.83 | 2635862.25 | 2601171.39 | 2766927.41 | 2801618.26 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2715626.24 | 2639631.74 | 2599402.69 | 2791620.73 | 2831849.79 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2731721.24 | 2645243.05 | 2599464.26 | 2818199.42 | 2863978.21 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2746592.15 | 2649419.00 | 2597978.64 | 2843765.30 | 2895205.66 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2758271.95 | 2649871.97 | 2592488.49 | 2866671.93 | 2924055.41 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2767206.03 | 2646828.39 | 2583104.32 | 2887583.66 | 2951307.73 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in France"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 2753722.53 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 2779627.51 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 2807785.35 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 2838569.10 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 2872432.36 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 2909930.59 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 2951748.49 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Cumulative Covid 19 Infection cases in France"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 2611616.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 2628919.22 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2646324.20 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2663831.38 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2681441.17 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2699153.99 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 2716970.28 |
## +---+------------+-----------------+--------------------+
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 | France | 0.309 | 0.737 | 0.711 | 0.504 | 0.55 | 3.848 | 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 France
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 France