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$England
y_lab <- "Cumulative Covid 19 Infection cases in The United Kingdom" # 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 <-68078368 # population in England for SIR Model
country.name <- "The United Kingdom"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 54165 288032 528772 557434 3017413
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 5.188567
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.742938
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 684530.8
#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 6740431
# 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 The United Kingdom"
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 The United Kingdom"
paste(MAPE_Mean_All,"%")
## [1] "0.789 % MAPE 7 days Cumulative Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom"
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 | 2654783.00 | 2656886.40 | 0.079 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2713567.00 | 2713478.68 | 0.003 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2774483.00 | 2768329.75 | 0.222 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2836805.00 | 2820174.94 | 0.586 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2889423.00 | 2867886.22 | 0.745 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2957476.00 | 2910618.91 | 1.584 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 3017413.00 | 2947900.65 | 2.304 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2979642.83 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 3006084.48 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 3027697.21 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 3045082.53 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 3058883.89 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 3069723.58 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 3078164.82 |
## +---+------------+-----------------+---------------------+
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 114.5686 1969.839 895.0024 NaN Inf 0.1259988 -0.02881263
# Print Model Parameters
model_bats
## BATS(1, {1,1}, 0.996, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.4573979
## Beta: 0.04588305
## Damping Parameter: 0.995972
## AR coefficients: 0.990099
## MA coefficients: 0.312657
##
## Seed States:
## [,1]
## [1,] 26.28688
## [2,] 31.23649
## [3,] 0.00000
## [4,] 0.00000
##
## Sigma: 1969.839
## AIC: 7753.177
#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 The United Kingdom"
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 The United Kingdom"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.454 % MAPE 7 days Cumulative Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom"
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 | 2654783.00 | 2658925.27 | 0.156 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2713567.00 | 2719204.68 | 0.208 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2774483.00 | 2781162.63 | 0.241 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2836805.00 | 2844773.33 | 0.281 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2889423.00 | 2910011.29 | 0.713 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2957476.00 | 2976851.31 | 0.655 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 3017413.00 | 3045268.47 | 0.923 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 3115238.13 | 3085457.59 | 3069692.72 | 3085457.59 | 3069692.72 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3186735.96 | 3151168.29 | 3132339.90 | 3151168.29 | 3132339.90 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3259737.86 | 3217875.99 | 3195715.65 | 3217875.99 | 3195715.65 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3334220.04 | 3285550.44 | 3259786.31 | 3285550.44 | 3259786.31 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3410158.96 | 3354161.99 | 3324518.98 | 3354161.99 | 3324518.98 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3487531.37 | 3423681.56 | 3389881.51 | 3423681.56 | 3389881.51 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3566314.27 | 3494080.59 | 3455842.40 | 3494080.59 | 3455842.40 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 217.574 2035.066 1017.958 NaN Inf 0.1433086 -0.009596333
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.110404
## Beta: 0.7066523
## Damping Parameter: 1
## Gamma-1 Values: 0.0008801099
## Gamma-2 Values: -0.001787153
##
## Seed States:
## [,1]
## [1,] 56.85541
## [2,] 24.62076
## [3,] 49.91159
## [4,] 110.65960
## [5,] -239.39399
## [6,] -118.06086
##
## Sigma: 2035.066
## AIC: 7779.088
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 The United Kingdom"
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 The United Kingdom"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.319 % MAPE 7 days Cumulative Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom"
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 | 2654783.00 | 2656498.17 | 0.065 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-01-05 | Tuesday | 2713567.00 | 2712969.98 | 0.022 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-01-06 | Wednesday | 2774483.00 | 2769479.34 | 0.18 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-01-07 | Thursday | 2836805.00 | 2826047.58 | 0.379 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-01-08 | Friday | 2889423.00 | 2882806.19 | 0.229 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-01-09 | Saturday | 2957476.00 | 2939117.86 | 0.621 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-01-10 | Sunday | 3017413.00 | 2995201.63 | 0.736 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 3051673.44 | 3043557.51 | 3039261.20 | 3059789.37 | 3064085.69 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3108182.80 | 3099559.66 | 3094994.85 | 3116805.94 | 3121370.75 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3164751.04 | 3155648.92 | 3150830.54 | 3173853.16 | 3178671.53 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3221509.64 | 3211953.06 | 3206894.12 | 3231066.23 | 3236125.17 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3277821.32 | 3267826.71 | 3262535.88 | 3287815.94 | 3293106.77 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3333905.08 | 3323489.55 | 3317975.90 | 3344320.62 | 3349834.27 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3390376.90 | 3379558.86 | 3373832.14 | 3401194.94 | 3406921.66 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 85.94693 2017.146 915.629 Inf Inf 0.1289026 0.05307677
# 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= 0.3892
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.7276
##
## Initial states:
## l = -2.3039
## b = -0.3774
##
## sigma: 0.6143
##
## AIC AICc BIC
## 1815.571 1815.738 1835.098
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 85.94693 2017.146 915.629 Inf Inf 0.1289026 0.05307677
# 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 The United Kingdom"
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 The United Kingdom"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.08 % MAPE 7 days Cumulative Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom"
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 | 2654783.00 | 2657423.45 | 0.099 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2713567.00 | 2715827.82 | 0.083 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2774483.00 | 2775009.52 | 0.019 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2836805.00 | 2834972.27 | 0.065 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2889423.00 | 2895719.79 | 0.218 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2957476.00 | 2957255.75 | 0.007 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 3017413.00 | 3019583.86 | 0.072 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 3082707.77 | 3003182.03 | 2961596.49 | 3163506.60 | 3206796.76 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3146631.13 | 3052200.89 | 3002922.22 | 3242824.55 | 3294464.04 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3211357.60 | 3100978.88 | 3043499.82 | 3324103.26 | 3384751.55 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3276890.80 | 3149530.90 | 3083355.05 | 3407347.66 | 3477670.18 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3343234.36 | 3197868.90 | 3122509.25 | 3492565.79 | 3573235.68 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3410391.86 | 3246002.50 | 3160980.24 | 3579768.19 | 3671467.71 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3478366.92 | 3293939.46 | 3198783.04 | 3668967.41 | 3772389.12 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 The United Kingdom"
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 = 4.4287, 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) = 6.0668, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = 1.7351, Lag order = 7, p-value = 0.99
## 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 The United Kingdom"
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 = 3.6524, 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) = 5.6508, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = 2.1134, Lag order = 7, p-value = 0.99
## 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 The United Kingdom"
kpss.test(diff2_x1) # applay kpss test after taking Second differences
##
## KPSS Test for Level Stationarity
##
## data: diff2_x1
## KPSS Level = 0.72221, Truncation lag parameter = 5, p-value = 0.01153
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) = -362.72, 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 = -3.7891, Lag order = 7, p-value = 0.01982
## 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) : 6609.382
## ARIMA(0,2,1) : 6600.259
## ARIMA(0,2,2) : 6598.279
## ARIMA(0,2,3) : 6600.295
## ARIMA(0,2,4) : 6601.255
## ARIMA(0,2,5) : 6599.026
## ARIMA(1,2,0) : 6602.73
## ARIMA(1,2,1) : 6599.1
## ARIMA(1,2,2) : 6596.312
## ARIMA(1,2,3) : 6597.503
## ARIMA(1,2,4) : 6598.946
## ARIMA(2,2,0) : 6599.441
## ARIMA(2,2,1) : 6600.478
## ARIMA(2,2,2) : 6597.233
## ARIMA(2,2,3) : 6599.298
## ARIMA(3,2,0) : 6601.374
## ARIMA(3,2,1) : 6602.533
## ARIMA(3,2,2) : 6599.296
## ARIMA(4,2,0) : 6598.948
## ARIMA(4,2,1) : 6600.821
## ARIMA(5,2,0) : 6600.422
##
##
##
## Best model: ARIMA(1,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,2)
##
## Coefficients:
## ar1 ma1 ma2
## -0.8252 0.6543 -0.2412
## s.e. 0.0890 0.0998 0.0565
##
## sigma^2 estimated as 4072343: log likelihood=-3294.1
## AIC=6596.2 AICc=6596.31 BIC=6611.8
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1 ma2
## -0.8252 0.6543 -0.2412
## s.e. 0.0890 0.0998 0.0565
##
## sigma^2 estimated as 4038872: log likelihood = -3294.1, aic = 6596.2
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in The United Kingdom"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 200.204 2004.211 937.5939 0.6121025 2.243849 0.1319949
## ACF1
## Training set 0.0004357398
x1_model1$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(1,2,2)
## Q* = 28.793, df = 7, p-value = 0.0001578
##
## Model df: 3. 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 The United Kingdom"
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 = 215.91, 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 = 2433.8, 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 The United Kingdom"
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 The United Kingdom"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.272 % MAPE 7 days Cumulative Covid 19 Infection cases in The United Kingdom %"
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 The United Kingdom"
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 | 2654783.00 | 2657058.81 | 0.086 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-01-05 | Tuesday | 2713567.00 | 2713629.99 | 0.002 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-01-06 | Wednesday | 2774483.00 | 2770774.34 | 0.134 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-01-07 | Thursday | 2836805.00 | 2827445.74 | 0.33 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-01-08 | Friday | 2889423.00 | 2884507.40 | 0.17 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-01-09 | Saturday | 2957476.00 | 2941247.03 | 0.549 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-01-10 | Sunday | 3017413.00 | 2998252.38 | 0.635 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 3055038.47 | 3024882.19 | 3008918.41 | 3085194.76 | 3101158.53 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3112005.49 | 3076580.47 | 3057827.60 | 3147430.50 | 3166183.38 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3168823.21 | 3127837.58 | 3106141.10 | 3209808.84 | 3231505.32 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3225764.13 | 3178969.27 | 3154197.57 | 3272558.98 | 3297330.68 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3282603.39 | 3229738.03 | 3201752.80 | 3335468.75 | 3363453.98 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3339526.53 | 3280358.19 | 3249036.37 | 3398694.87 | 3430016.69 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3396380.46 | 3330670.53 | 3295885.79 | 3462090.39 | 3496875.13 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.272 % MAPE 7 days Cumulative Covid 19 Infection cases in The United Kingdom"
# 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
## 0.02177408 0.00000000
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR<-data.frame(out)
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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.10232895 0.07586272
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 2654783.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 2714591.07 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2774637.47 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2834858.67 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2895188.45 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2955557.99 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 3015896.03 |
## +---+------------+-----------------+--------------------+
# 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 The United Kingdom"
best_recommended_model
## [1] 0.08
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 The United Kingdom"
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 | 3115238.13 | 3085457.59 | 3069692.72 | 3085457.59 | 3069692.72 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3186735.96 | 3151168.29 | 3132339.90 | 3151168.29 | 3132339.90 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3259737.86 | 3217875.99 | 3195715.65 | 3217875.99 | 3195715.65 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3334220.04 | 3285550.44 | 3259786.31 | 3285550.44 | 3259786.31 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3410158.96 | 3354161.99 | 3324518.98 | 3354161.99 | 3324518.98 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3487531.37 | 3423681.56 | 3389881.51 | 3423681.56 | 3389881.51 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3566314.27 | 3494080.59 | 3455842.40 | 3494080.59 | 3455842.40 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in The United Kingdom"
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 | 3051673.44 | 3043557.51 | 3039261.20 | 3059789.37 | 3064085.69 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3108182.80 | 3099559.66 | 3094994.85 | 3116805.94 | 3121370.75 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3164751.04 | 3155648.92 | 3150830.54 | 3173853.16 | 3178671.53 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3221509.64 | 3211953.06 | 3206894.12 | 3231066.23 | 3236125.17 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3277821.32 | 3267826.71 | 3262535.88 | 3287815.94 | 3293106.77 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3333905.08 | 3323489.55 | 3317975.90 | 3344320.62 | 3349834.27 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3390376.90 | 3379558.86 | 3373832.14 | 3401194.94 | 3406921.66 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 The United Kingdom"
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 | 3082707.77 | 3003182.03 | 2961596.49 | 3163506.60 | 3206796.76 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3146631.13 | 3052200.89 | 3002922.22 | 3242824.55 | 3294464.04 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3211357.60 | 3100978.88 | 3043499.82 | 3324103.26 | 3384751.55 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3276890.80 | 3149530.90 | 3083355.05 | 3407347.66 | 3477670.18 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3343234.36 | 3197868.90 | 3122509.25 | 3492565.79 | 3573235.68 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3410391.86 | 3246002.50 | 3160980.24 | 3579768.19 | 3671467.71 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3478366.92 | 3293939.46 | 3198783.04 | 3668967.41 | 3772389.12 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in The United Kingdom"
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 | 3055038.47 | 3024882.19 | 3008918.41 | 3085194.76 | 3101158.53 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 3112005.49 | 3076580.47 | 3057827.60 | 3147430.50 | 3166183.38 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 3168823.21 | 3127837.58 | 3106141.10 | 3209808.84 | 3231505.32 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 3225764.13 | 3178969.27 | 3154197.57 | 3272558.98 | 3297330.68 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 3282603.39 | 3229738.03 | 3201752.80 | 3335468.75 | 3363453.98 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 3339526.53 | 3280358.19 | 3249036.37 | 3398694.87 | 3430016.69 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 3396380.46 | 3330670.53 | 3295885.79 | 3462090.39 | 3496875.13 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in The United Kingdom"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 2979642.83 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 3006084.48 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 3027697.21 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 3045082.53 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 3058883.89 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 3069723.58 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 3078164.82 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Cumulative Covid 19 Infection cases in The United Kingdom"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 2654783.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 2714591.07 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2774637.47 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2834858.67 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2895188.45 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2955557.99 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 3015896.03 |
## +---+------------+-----------------+--------------------+
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 | The United Kingdom | 0.789 | 0.454 | 0.319 | 0.08 | 0.272 | 13.949 | Holt 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 The United Kingdom
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 The United Kingdom