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$Italy
y_lab <- "Cumulative Covid 19 Infection cases in Italy" # 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 <-60414330 # population in Italy for SIR Model
country.name <- " Italy"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 125711 241888 457198 337284 2257866
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 4.777717
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.771383
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 603166.9
#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 5708643
# 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 Italy"
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 Italy"
paste(MAPE_Mean_All,"%")
## [1] "0.255 % MAPE 7 days Cumulative Covid 19 Infection cases in Italy %"
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 Italy"
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 | 2155446.00 | 2155865.80 | 0.019 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2166244.00 | 2170525.91 | 0.198 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2181619.00 | 2185175.06 | 0.163 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2201945.00 | 2199805.12 | 0.097 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2220361.00 | 2214406.09 | 0.268 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2237890.00 | 2228966.08 | 0.399 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2257866.00 | 2243471.31 | 0.638 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2257906.24 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 2272253.56 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 2286494.35 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 2300608.25 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 2314573.60 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 2328367.73 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 2341967.18 |
## +---+------------+-----------------+---------------------+
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 60.9349 1784.906 839.5508 NaN Inf 0.1434863 0.04844067
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.339002
## Beta: 0.6492352
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] 168.38809
## [2,] -82.15652
##
## Sigma: 1784.906
## AIC: 7670.815
#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 Italy"
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 Italy"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.32 % MAPE 7 days Cumulative Covid 19 Infection cases in Italy %"
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 Italy"
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 | 2155446.00 | 2153044.02 | 0.111 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2166244.00 | 2167480.79 | 0.057 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2181619.00 | 2181917.55 | 0.014 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2201945.00 | 2196354.31 | 0.254 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2220361.00 | 2210791.07 | 0.431 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2237890.00 | 2225227.83 | 0.566 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2257866.00 | 2239664.60 | 0.806 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2254101.36 | 2228914.09 | 2215580.75 | 2228914.09 | 2215580.75 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2268538.12 | 2239251.42 | 2223747.98 | 2239251.42 | 2223747.98 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2282974.88 | 2249394.92 | 2231618.76 | 2249394.92 | 2231618.76 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2297411.64 | 2259352.23 | 2239204.79 | 2259352.23 | 2239204.79 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2311848.41 | 2269130.29 | 2246516.69 | 2269130.29 | 2246516.69 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2326285.17 | 2278735.41 | 2253564.09 | 2278735.41 | 2253564.09 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2340721.93 | 2288173.32 | 2260355.77 | 2288173.32 | 2260355.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 60.96513 1759.393 917.3066 NaN Inf 0.1567755 0.04966612
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.33628
## Beta: 0.6568774
## Damping Parameter: 1
## Gamma-1 Values: -0.0029447
## Gamma-2 Values: 0.003549961
##
## Seed States:
## [,1]
## [1,] 202.39482
## [2,] -93.28488
## [3,] 41.82608
## [4,] -37.01090
## [5,] -257.52990
## [6,] 12.14850
##
## Sigma: 1759.393
## AIC: 7672.248
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 Italy"
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 Italy"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.29 % MAPE 7 days Cumulative Covid 19 Infection cases in Italy %"
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 Italy"
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 | 2155446.00 | 2153486.94 | 0.091 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-01-05 | Tuesday | 2166244.00 | 2167937.18 | 0.078 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-01-06 | Wednesday | 2181619.00 | 2182454.63 | 0.038 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-01-07 | Thursday | 2201945.00 | 2197621.58 | 0.196 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-01-08 | Friday | 2220361.00 | 2212159.79 | 0.369 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-01-09 | Saturday | 2237890.00 | 2226354.06 | 0.515 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-01-10 | Sunday | 2257866.00 | 2241109.88 | 0.742 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2255560.12 | 2247342.73 | 2242992.71 | 2263777.51 | 2268127.53 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2270077.57 | 2261343.50 | 2256719.96 | 2278811.64 | 2283435.17 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2285244.52 | 2276022.68 | 2271140.92 | 2294466.37 | 2299348.12 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2299782.73 | 2290097.10 | 2284969.84 | 2309468.35 | 2314595.61 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2313977.00 | 2303857.23 | 2298500.14 | 2324096.78 | 2329453.87 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2328732.82 | 2318200.45 | 2312624.95 | 2339265.19 | 2344840.69 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2343183.06 | 2332251.27 | 2326464.32 | 2354114.86 | 2359901.80 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -100.8329 2017.843 914.1722 NaN Inf 0.1562398 0.3694451
# 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= 0.3809
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.5856
##
## Initial states:
## l = -3.1591
## b = 0.3205
##
## sigma: 0.6711
##
## AIC AICc BIC
## 1880.499 1880.665 1900.026
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -100.8329 2017.843 914.1722 NaN Inf 0.1562398 0.3694451
# 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 Italy"
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 Italy"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.158 % MAPE 7 days Cumulative Covid 19 Infection cases in Italy %"
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 Italy"
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 | 2155446.00 | 2156999.87 | 0.072 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 2166244.00 | 2172869.73 | 0.306 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 2181619.00 | 2188811.67 | 0.33 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2201945.00 | 2204825.82 | 0.131 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2220361.00 | 2220912.30 | 0.025 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2237890.00 | 2237071.24 | 0.037 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2257866.00 | 2253302.76 | 0.202 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2269606.99 | 2200530.50 | 2164497.28 | 2340010.03 | 2377819.46 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2285984.04 | 2205079.30 | 2162979.31 | 2368701.20 | 2413227.95 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2302434.06 | 2209058.65 | 2160594.14 | 2398214.34 | 2449898.85 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2318957.16 | 2212492.36 | 2157382.32 | 2428536.69 | 2487817.20 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2335553.46 | 2215401.52 | 2153380.22 | 2459658.34 | 2526972.39 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2352223.10 | 2217804.98 | 2148620.76 | 2491571.64 | 2567357.37 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2368966.19 | 2219719.75 | 2143134.06 | 2524270.86 | 2608968.09 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 Italy"
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 = 3.8664, 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) = 3.1096, 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 smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -5.5415, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main = "1nd differenced series")
##Testing the stationary of the first differenced series
paste ("tests For Check Stationarity in series after taking first differences in ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series after taking first differences in ==> Cumulative Covid 19 Infection cases in Italy"
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 = 2.9313, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -5.8652, Truncation lag parameter = 5, p-value
## = 0.7819
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -2.3133, Lag order = 7, p-value = 0.4447
## 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 Italy"
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 = 0.11586, 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) = -198.96, 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 = -3.4824, Lag order = 7, p-value = 0.04452
## 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) : 6527.572
## ARIMA(0,2,1) : 6523.196
## ARIMA(0,2,2) : 6509.715
## ARIMA(0,2,3) : 6492.953
## ARIMA(0,2,4) : 6469.381
## ARIMA(0,2,5) : 6403.571
## ARIMA(1,2,0) : 6524.777
## ARIMA(1,2,1) : 6500.282
## ARIMA(1,2,2) : 6501.938
## ARIMA(1,2,3) : 6494.888
## ARIMA(1,2,4) : 6467.509
## ARIMA(2,2,0) : 6516.502
## ARIMA(2,2,1) : 6483.043
## ARIMA(2,2,2) : 6361.089
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 6483.294
## ARIMA(3,2,1) : 6456.023
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 6434.546
## ARIMA(4,2,1) : 6432.609
## ARIMA(5,2,0) : 6429.015
##
##
##
## Best model: ARIMA(2,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.3043 -0.9357 -1.5869 0.9607
## s.e. 0.0250 0.0244 0.0215 0.0234
##
## sigma^2 estimated as 2099963: log likelihood=-3175.46
## AIC=6360.92 AICc=6361.09 BIC=6380.42
#Make changes in the source of auto arima to run the best model
arima.string <- function (object, padding = FALSE)
{
order <- object$arma[c(1, 6, 2, 3, 7, 4, 5)]
m <- order[7]
result <- paste("ARIMA(", order[1], ",", order[2], ",",
order[3], ")", sep = "")
if (m > 1 && sum(order[4:6]) > 0) {
result <- paste(result, "(", order[4], ",", order[5],
",", order[6], ")[", m, "]", sep = "")
}
if (padding && m > 1 && sum(order[4:6]) == 0) {
result <- paste(result, " ", sep = "")
if (m <= 9) {
result <- paste(result, " ", sep = "")
}
else if (m <= 99) {
result <- paste(result, " ", sep = "")
}
else {
result <- paste(result, " ", sep = "")
}
}
if (!is.null(object$xreg)) {
if (NCOL(object$xreg) == 1 && is.element("drift", names(object$coef))) {
result <- paste(result, "with drift ")
}
else {
result <- paste("Regression with", result, "errors")
}
}
else {
if (is.element("constant", names(object$coef)) || is.element("intercept",
names(object$coef))) {
result <- paste(result, "with non-zero mean")
}
else if (order[2] == 0 && order[5] == 0) {
result <- paste(result, "with zero mean ")
}
else {
result <- paste(result, " ")
}
}
if (!padding) {
result <- gsub("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.3043 -0.9357 -1.5869 0.9607
## s.e. 0.0250 0.0244 0.0215 0.0234
##
## sigma^2 estimated as 2076950: log likelihood = -3175.46, aic = 6360.92
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in Italy"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 70.53378 1437.23 693.7591 0.9984558 2.400332 0.1185693 0.07236444
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,2,2)
## Q* = 135.97, df = 6, p-value < 2.2e-16
##
## Model df: 4. 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 Italy"
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 = 666.82, 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 = 985.04, 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 Italy"
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 Italy"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.406 % MAPE 7 days Cumulative Covid 19 Infection cases in Italy %"
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 Italy"
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 | 2155446.00 | 2148434.82 | 0.325 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-01-05 | Tuesday | 2166244.00 | 2156483.88 | 0.451 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-01-06 | Wednesday | 2181619.00 | 2169892.02 | 0.538 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-01-07 | Thursday | 2201945.00 | 2189527.29 | 0.564 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-01-08 | Friday | 2220361.00 | 2212270.33 | 0.364 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-01-09 | Saturday | 2237890.00 | 2233240.42 | 0.208 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-01-10 | Sunday | 2257866.00 | 2248990.19 | 0.393 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2259589.95 | 2244228.84 | 2236097.15 | 2274951.07 | 2283082.75 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2268356.98 | 2249709.93 | 2239838.77 | 2287004.03 | 2296875.19 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2279552.20 | 2257581.51 | 2245950.93 | 2301522.89 | 2313153.48 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2295629.36 | 2270478.85 | 2257164.98 | 2320779.87 | 2334093.74 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2315802.09 | 2287598.94 | 2272669.10 | 2344005.24 | 2358935.08 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2336748.87 | 2305459.37 | 2288895.71 | 2368038.37 | 2384602.03 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2354873.18 | 2320267.86 | 2301948.91 | 2389478.50 | 2407797.46 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.406 % MAPE 7 days Cumulative Covid 19 Infection cases in Italy"
# 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
## 0.009129539 0.001619862
# 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.015846195 0.007803401
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 2155446.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 2171614.22 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2187884.68 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2204257.75 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2220733.75 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2237313.04 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 2253995.95 |
## +---+------------+-----------------+--------------------+
# 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 Italy"
best_recommended_model
## [1] 0.158
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 Italy"
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 | 2254101.36 | 2228914.09 | 2215580.75 | 2228914.09 | 2215580.75 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2268538.12 | 2239251.42 | 2223747.98 | 2239251.42 | 2223747.98 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2282974.88 | 2249394.92 | 2231618.76 | 2249394.92 | 2231618.76 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2297411.64 | 2259352.23 | 2239204.79 | 2259352.23 | 2239204.79 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2311848.41 | 2269130.29 | 2246516.69 | 2269130.29 | 2246516.69 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2326285.17 | 2278735.41 | 2253564.09 | 2278735.41 | 2253564.09 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2340721.93 | 2288173.32 | 2260355.77 | 2288173.32 | 2260355.77 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in Italy"
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 | 2255560.12 | 2247342.73 | 2242992.71 | 2263777.51 | 2268127.53 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2270077.57 | 2261343.50 | 2256719.96 | 2278811.64 | 2283435.17 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2285244.52 | 2276022.68 | 2271140.92 | 2294466.37 | 2299348.12 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2299782.73 | 2290097.10 | 2284969.84 | 2309468.35 | 2314595.61 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2313977.00 | 2303857.23 | 2298500.14 | 2324096.78 | 2329453.87 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2328732.82 | 2318200.45 | 2312624.95 | 2339265.19 | 2344840.69 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2343183.06 | 2332251.27 | 2326464.32 | 2354114.86 | 2359901.80 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 Italy"
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 | 2269606.99 | 2200530.50 | 2164497.28 | 2340010.03 | 2377819.46 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2285984.04 | 2205079.30 | 2162979.31 | 2368701.20 | 2413227.95 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2302434.06 | 2209058.65 | 2160594.14 | 2398214.34 | 2449898.85 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2318957.16 | 2212492.36 | 2157382.32 | 2428536.69 | 2487817.20 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2335553.46 | 2215401.52 | 2153380.22 | 2459658.34 | 2526972.39 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2352223.10 | 2217804.98 | 2148620.76 | 2491571.64 | 2567357.37 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2368966.19 | 2219719.75 | 2143134.06 | 2524270.86 | 2608968.09 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in Italy"
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 | 2259589.95 | 2244228.84 | 2236097.15 | 2274951.07 | 2283082.75 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2268356.98 | 2249709.93 | 2239838.77 | 2287004.03 | 2296875.19 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2279552.20 | 2257581.51 | 2245950.93 | 2301522.89 | 2313153.48 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2295629.36 | 2270478.85 | 2257164.98 | 2320779.87 | 2334093.74 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2315802.09 | 2287598.94 | 2272669.10 | 2344005.24 | 2358935.08 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2336748.87 | 2305459.37 | 2288895.71 | 2368038.37 | 2384602.03 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2354873.18 | 2320267.86 | 2301948.91 | 2389478.50 | 2407797.46 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 2257906.24 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 2272253.56 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 2286494.35 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 2300608.25 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 2314573.60 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 2328367.73 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 2341967.18 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Cumulative Covid 19 Infection cases in Italy"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 2155446.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 2171614.22 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2187884.68 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2204257.75 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2220733.75 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2237313.04 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 2253995.95 |
## +---+------------+-----------------+--------------------+
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 | Italy | 0.255 | 0.32 | 0.29 | 0.158 | 0.406 | 5.012 | 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 Italy
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 Italy