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$Spain
y_lab <- "Cumulative Covid 19 Infection cases in Spain" # 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 <-46764483 # population in Spain for SIR Model
country.name <- "Spain"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 146358 257960 564018 875247 2025560
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.781643
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.090816
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 616918.1
#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 9860905
# 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 Spain"
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 Spain"
paste(MAPE_Mean_All,"%")
## [1] "0.303 % MAPE 7 days Cumulative Covid 19 Infection cases in Spain %"
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 Spain"
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 | 1974823.00 | 1975918.49 | 0.055 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 1983011.00 | 1985666.95 | 0.134 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 1999362.00 | 1995564.14 | 0.19 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2019090.00 | 2005622.33 | 0.667 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2025560.00 | 2015854.32 | 0.479 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2025560.00 | 2026273.50 | 0.035 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2025560.00 | 2036893.89 | 0.56 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2047730.21 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 2058797.87 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 2070113.05 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 2081692.74 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 2093554.79 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 2105717.93 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 2118201.81 |
## +---+------------+-----------------+---------------------+
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 64.33216 1721.255 1021.583 NaN Inf 0.1901531 -0.004840924
# Print Model Parameters
model_bats
## BATS(1, {2,2}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.126776
## Beta: 0.183256
## Damping Parameter: 0.999998
## AR coefficients: 0.920605 -0.407193
## MA coefficients: 0.715634 -0.07047
##
## Seed States:
## [,1]
## [1,] 695.98285
## [2,] -71.17898
## [3,] 0.00000
## [4,] 0.00000
## [5,] 0.00000
## [6,] 0.00000
##
## Sigma: 1721.255
## AIC: 7662.161
#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 Spain"
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 Spain"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.725 % MAPE 7 days Cumulative Covid 19 Infection cases in Spain %"
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 Spain"
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 | 1974823.00 | 1977081.40 | 0.114 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 1983011.00 | 1991197.10 | 0.413 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 1999362.00 | 2006904.06 | 0.377 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2019090.00 | 2022698.03 | 0.179 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2025560.00 | 2037924.17 | 0.61 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2025560.00 | 2052592.10 | 1.335 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2025560.00 | 2066977.35 | 2.045 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2081329.65 | 2064167.27 | 2055082.05 | 2064167.27 | 2055082.05 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2095766.72 | 2075299.80 | 2064465.27 | 2075299.80 | 2064465.27 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2110295.22 | 2086291.09 | 2073584.07 | 2086291.09 | 2073584.07 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2124873.38 | 2097143.30 | 2082463.88 | 2097143.30 | 2082463.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2139460.00 | 2107828.81 | 2091084.27 | 2107828.81 | 2091084.27 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2154034.18 | 2118328.38 | 2099426.87 | 2118328.38 | 2099426.87 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2168593.46 | 2128640.50 | 2107490.68 | 2128640.50 | 2107490.68 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 76.99495 1896.6 1134.408 NaN Inf 0.2111539 0.04419437
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.720444
## Beta: 0.3850237
## Damping Parameter: 1
## Gamma-1 Values: -0.003286456
## Gamma-2 Values: 0.005744953
##
## Seed States:
## [,1]
## [1,] 750.14984
## [2,] -88.11144
## [3,] -251.23764
## [4,] -15.25863
## [5,] -126.99616
## [6,] -25.34281
##
## Sigma: 1896.6
## AIC: 7727.366
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 Spain"
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 Spain"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.31 % MAPE 7 days Cumulative Covid 19 Infection cases in Spain %"
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 Spain"
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 | 1974823.00 | 1977028.57 | 0.112 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-01-05 | Tuesday | 1983011.00 | 1987797.57 | 0.241 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-01-06 | Wednesday | 1999362.00 | 1998698.09 | 0.033 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-01-07 | Thursday | 2019090.00 | 2009786.09 | 0.461 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-01-08 | Friday | 2025560.00 | 2020204.97 | 0.264 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-01-09 | Saturday | 2025560.00 | 2030722.65 | 0.255 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-01-10 | Sunday | 2025560.00 | 2041777.93 | 0.801 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2052546.93 | 2041299.52 | 2035345.50 | 2063794.34 | 2069748.35 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2063447.45 | 2051469.57 | 2045128.86 | 2075425.33 | 2081766.03 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2074535.45 | 2061869.16 | 2055164.02 | 2087201.74 | 2093906.87 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2084954.33 | 2071633.66 | 2064582.11 | 2098275.01 | 2105326.55 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2095472.01 | 2081540.87 | 2074166.17 | 2109403.15 | 2116777.85 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2106527.29 | 2092015.82 | 2084333.91 | 2121038.75 | 2128720.66 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2117296.28 | 2102221.13 | 2094240.82 | 2132371.44 | 2140351.75 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -26.30459 2328.927 1282.801 NaN Inf 0.2387752 0.2026866
# 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= 0.6438
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.9999
##
## Initial states:
## l = -2.3353
## b = -0.7639
##
## sigma: 18.2188
##
## AIC AICc BIC
## 4303.647 4303.813 4323.174
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -26.30459 2328.927 1282.801 NaN Inf 0.2387752 0.2026866
# 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 Spain"
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 Spain"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.827 % MAPE 7 days Cumulative Covid 19 Infection cases in Spain %"
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 Spain"
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 | 1974823.00 | 1972437.18 | 0.121 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-01-05 | Tuesday | 1983011.00 | 1978573.64 | 0.224 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-01-06 | Wednesday | 1999362.00 | 1984716.89 | 0.732 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-01-07 | Thursday | 2019090.00 | 1990866.92 | 1.398 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-01-08 | Friday | 2025560.00 | 1997023.72 | 1.409 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-01-09 | Saturday | 2025560.00 | 2003187.30 | 1.105 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-01-10 | Sunday | 2025560.00 | 2009357.63 | 0.8 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2015534.72 | 1957159.03 | 1926504.90 | 2074518.92 | 2105987.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2021718.56 | 1952709.86 | 1916525.60 | 2091576.65 | 2128898.29 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2027909.14 | 1947694.48 | 1905700.03 | 2109270.23 | 2152799.84 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2034106.47 | 1942142.17 | 1894075.46 | 2127576.18 | 2177658.83 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2040310.52 | 1936078.59 | 1881693.65 | 2146474.63 | 2203447.05 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2046521.30 | 1929526.52 | 1868591.97 | 2165948.54 | 2230140.64 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2052738.80 | 1922506.40 | 1854804.21 | 2185983.22 | 2257719.25 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
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 Spain"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 5.1304, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
## Warning in pp.test(data_series): p-value greater than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = 0.73192, Truncation lag parameter = 5, p-value
## = 0.99
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -3.2906, Lag order = 7, p-value = 0.07281
## 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 Spain"
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 = 3.8554, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -30.559, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -2.4687, Lag order = 7, p-value = 0.3791
## 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 Spain"
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 = 0.059268, 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) = -153.36, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff2_x1) # applay adf test after taking Second differences
## Warning in adf.test(diff2_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff2_x1
## Dickey-Fuller = -5.2906, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
####Fitting an ARIMA Model
#1. Using auto arima function
model1 <- auto.arima(data_series,stepwise=FALSE, approximation=FALSE, trace=T, test = c("kpss", "adf", "pp")) #applaying auto arima
##
## ARIMA(0,2,0) : 6696.498
## ARIMA(0,2,1) : 6654.804
## ARIMA(0,2,2) : 6563.483
## ARIMA(0,2,3) : 6564.945
## ARIMA(0,2,4) : 6560.478
## ARIMA(0,2,5) : 6452.524
## ARIMA(1,2,0) : 6682.932
## ARIMA(1,2,1) : 6627.926
## ARIMA(1,2,2) : 6562.667
## ARIMA(1,2,3) : 6560.268
## ARIMA(1,2,4) : 6534.126
## ARIMA(2,2,0) : 6608.658
## ARIMA(2,2,1) : 6540.68
## ARIMA(2,2,2) : 6420.077
## ARIMA(2,2,3) : 6543.098
## ARIMA(3,2,0) : 6602.728
## ARIMA(3,2,1) : 6540.2
## ARIMA(3,2,2) : 6522.062
## ARIMA(4,2,0) : 6529.162
## ARIMA(4,2,1) : 6467.972
## ARIMA(5,2,0) : 6390.814
##
##
##
## Best model: ARIMA(5,2,0)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(5,2,0)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5
## -0.0829 -0.5867 -0.3799 -0.3480 -0.5770
## s.e. 0.0430 0.0395 0.0466 0.0395 0.0437
##
## sigma^2 estimated as 2284965: log likelihood=-3189.29
## AIC=6390.58 AICc=6390.81 BIC=6413.98
#Make changes in the source of auto arima to run the best model
arima.string <- function (object, padding = FALSE)
{
order <- object$arma[c(1, 6, 2, 3, 7, 4, 5)]
m <- order[7]
result <- paste("ARIMA(", order[1], ",", order[2], ",",
order[3], ")", sep = "")
if (m > 1 && sum(order[4:6]) > 0) {
result <- paste(result, "(", order[4], ",", order[5],
",", order[6], ")[", m, "]", sep = "")
}
if (padding && m > 1 && sum(order[4:6]) == 0) {
result <- paste(result, " ", sep = "")
if (m <= 9) {
result <- paste(result, " ", sep = "")
}
else if (m <= 99) {
result <- paste(result, " ", sep = "")
}
else {
result <- paste(result, " ", sep = "")
}
}
if (!is.null(object$xreg)) {
if (NCOL(object$xreg) == 1 && is.element("drift", names(object$coef))) {
result <- paste(result, "with drift ")
}
else {
result <- paste("Regression with", result, "errors")
}
}
else {
if (is.element("constant", names(object$coef)) || is.element("intercept",
names(object$coef))) {
result <- paste(result, "with non-zero mean")
}
else if (order[2] == 0 && order[5] == 0) {
result <- paste(result, "with zero mean ")
}
else {
result <- paste(result, " ")
}
}
if (!padding) {
result <- gsub("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 5 2 0
strtoi(bestmodel[3])
## [1] 0
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5
## -0.0829 -0.5867 -0.3799 -0.3480 -0.5770
## s.e. 0.0430 0.0395 0.0466 0.0395 0.0437
##
## sigma^2 estimated as 2253664: log likelihood = -3189.29, aic = 6390.58
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Cumulative Covid 19 Infection cases in Spain"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 87.43194 1497.125 916.4811 0.982646 2.534609 0.1705899 -0.115491
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(5,2,0)
## Q* = 250.02, df = 5, p-value < 2.2e-16
##
## Model df: 5. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Cumulative Covid 19 Infection cases in Spain"
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 = 351.81, 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 = 182.6, 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 Spain"
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 Spain"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.398 % MAPE 7 days Cumulative Covid 19 Infection cases in Spain %"
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 Spain"
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 | 1974823.00 | 1970440.26 | 0.222 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-01-05 | Tuesday | 1983011.00 | 1978330.51 | 0.236 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-01-06 | Wednesday | 1999362.00 | 1990986.19 | 0.419 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-01-07 | Thursday | 2019090.00 | 2007231.87 | 0.587 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-01-08 | Friday | 2025560.00 | 2022580.11 | 0.147 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-01-09 | Saturday | 2025560.00 | 2033926.96 | 0.413 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-01-10 | Sunday | 2025560.00 | 2040941.99 | 0.759 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2047005.44 | 2034134.91 | 2027321.66 | 2059875.97 | 2066689.22 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2055450.02 | 2040336.28 | 2032335.55 | 2070563.75 | 2078564.48 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2067811.40 | 2050423.93 | 2041219.56 | 2085198.87 | 2094403.23 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2082629.02 | 2063065.69 | 2052709.50 | 2102192.34 | 2112548.53 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2096871.28 | 2075290.79 | 2063866.77 | 2118451.77 | 2129875.79 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2107952.75 | 2084488.01 | 2072066.52 | 2131417.49 | 2143838.97 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2115963.68 | 2090512.52 | 2077039.49 | 2141414.83 | 2154887.86 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "0.398 % MAPE 7 days Cumulative Covid 19 Infection cases in Spain"
# 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
## 0.05060856 0.04182966
# 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$par, c("beta", "gamma"))
Opt_par
## beta gamma
## 0.1955389 0.1783149
# beta gamma
# 0.6512503 0.4920399
out <- ode(y = init, times = Day, func = SIR, parms = Opt_par)
plot(out)
plot(out, obs=data.frame(time=Day, I=Infected))
result_SIR <-data.frame(out)
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 1974823.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 1991069.72 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2004348.77 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2014604.50 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2021800.00 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2025917.32 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 2026957.45 |
## +---+------------+-----------------+--------------------+
# 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 Spain"
best_recommended_model
## [1] 0.303
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 Spain"
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 | 2081329.65 | 2064167.27 | 2055082.05 | 2064167.27 | 2055082.05 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2095766.72 | 2075299.80 | 2064465.27 | 2075299.80 | 2064465.27 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2110295.22 | 2086291.09 | 2073584.07 | 2086291.09 | 2073584.07 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2124873.38 | 2097143.30 | 2082463.88 | 2097143.30 | 2082463.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2139460.00 | 2107828.81 | 2091084.27 | 2107828.81 | 2091084.27 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2154034.18 | 2118328.38 | 2099426.87 | 2118328.38 | 2099426.87 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2168593.46 | 2128640.50 | 2107490.68 | 2128640.50 | 2107490.68 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Cumulative Covid 19 Infection cases in Spain"
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 | 2052546.93 | 2041299.52 | 2035345.50 | 2063794.34 | 2069748.35 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2063447.45 | 2051469.57 | 2045128.86 | 2075425.33 | 2081766.03 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2074535.45 | 2061869.16 | 2055164.02 | 2087201.74 | 2093906.87 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2084954.33 | 2071633.66 | 2064582.11 | 2098275.01 | 2105326.55 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2095472.01 | 2081540.87 | 2074166.17 | 2109403.15 | 2116777.85 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2106527.29 | 2092015.82 | 2084333.91 | 2121038.75 | 2128720.66 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2117296.28 | 2102221.13 | 2094240.82 | 2132371.44 | 2140351.75 |
## +---+------------+-----------------+----------------------+------------+------------+------------+------------+
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 Spain"
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 | 2015534.72 | 1957159.03 | 1926504.90 | 2074518.92 | 2105987.88 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2021718.56 | 1952709.86 | 1916525.60 | 2091576.65 | 2128898.29 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2027909.14 | 1947694.48 | 1905700.03 | 2109270.23 | 2152799.84 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2034106.47 | 1942142.17 | 1894075.46 | 2127576.18 | 2177658.83 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2040310.52 | 1936078.59 | 1881693.65 | 2146474.63 | 2203447.05 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2046521.30 | 1929526.52 | 1868591.97 | 2165948.54 | 2230140.64 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2052738.80 | 1922506.40 | 1854804.21 | 2185983.22 | 2257719.25 |
## +---+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Cumulative Covid 19 Infection cases in Spain"
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 | 2047005.44 | 2034134.91 | 2027321.66 | 2059875.97 | 2066689.22 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-01-12 | Tuesday | 2055450.02 | 2040336.28 | 2032335.55 | 2070563.75 | 2078564.48 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-01-13 | Wednesday | 2067811.40 | 2050423.93 | 2041219.56 | 2085198.87 | 2094403.23 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-01-14 | Thursday | 2082629.02 | 2063065.69 | 2052709.50 | 2102192.34 | 2112548.53 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-01-15 | Friday | 2096871.28 | 2075290.79 | 2063866.77 | 2118451.77 | 2129875.79 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-01-16 | Saturday | 2107952.75 | 2084488.01 | 2072066.52 | 2131417.49 | 2143838.97 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-01-17 | Sunday | 2115963.68 | 2090512.52 | 2077039.49 | 2141414.83 | 2154887.86 |
## +---+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Cumulative Covid 19 Infection cases in Spain"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-01-11 | Monday | 2047730.21 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-01-12 | Tuesday | 2058797.87 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-01-13 | Wednesday | 2070113.05 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-01-14 | Thursday | 2081692.74 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-01-15 | Friday | 2093554.79 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-01-16 | Saturday | 2105717.93 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-01-17 | Sunday | 2118201.81 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using SIR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using SIR Model ==> Cumulative Covid 19 Infection cases in Spain"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_SIR=result_SIR$I)), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | forecasting_by_SIR |
## +===+============+=================+====================+
## | 1 | 2021-01-11 | Monday | 1974823.00 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-01-12 | Tuesday | 1991069.72 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-01-13 | Wednesday | 2004348.77 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-01-14 | Thursday | 2014604.50 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-01-15 | Friday | 2021800.00 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-01-16 | Saturday | 2025917.32 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-01-17 | Sunday | 2026957.45 |
## +---+------------+-----------------+--------------------+
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 | Spain | 0.303 | 0.725 | 0.31 | 0.827 | 0.398 | 3.772 | NNAR Model | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-----------+------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_SIR)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model" ,"SIR Model")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and SIR Model ==>Cumulative Covid 19 Infection cases in Spain
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 Spain