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
Full_original_data <- read_excel("data2.xlsx", sheet = "Northwestern federal") # path of your data ( time series data)
## New names:
## * region -> region...2
## * infection -> infection...3
## * `daily infection` -> `daily infection...4`
## * region -> region...5
## * infection -> infection...6
## * ...
original_data<-Full_original_data$`total daily`
y_lab <- "Daily Covid 19 Infection cases in Northwestern federal district" # input name of data
Actual_date_interval <- c("2020/03/12","2021/03/22")
Forecast_date_interval <- c("2021/03/23","2021/03/29")
validation_data_days <-4
Number_Neural<-5 # Number of Neural For model NNAR Model
NNAR_Model<- TRUE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Northwestern federal"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 581.2 857.0 2002.6 2775.0 7079.0
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.924066
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.15282
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 2043.616
#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
}
## Series: data_series
## Model: NNAR(8,5)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 8-5-1 network with 51 weights
## options were - linear output units
##
## sigma^2 estimated as 9096
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
}
# 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 4 days by using NNAR Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 4 days in NNAR Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
paste(MAPE_Mean_All,"%")
## [1] "4.641 % MAPE 4 days Daily Covid 19 Infection cases in Northwestern federal district %"
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 4 days in NNAR Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-19 | Friday | 1663.00 | 1689.54 | 1.596 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-20 | Saturday | 1653.00 | 1695.81 | 2.59 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-21 | Sunday | 1607.00 | 1708.20 | 6.297 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-22 | Monday | 1586.00 | 1714.15 | 8.08 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-03-23 | Tuesday | 1717.99 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 1728.10 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 1747.08 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 1768.44 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 1786.21 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 1806.57 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 1824.66 |
## +---+------------+-----------------+---------------------+
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 0.7533464 124.9531 68.68039 -Inf Inf 0.9385401 -0.001229123
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 0.976, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.9589182
## Beta: 0.06262585
## Damping Parameter: 0.976447
##
## Seed States:
## [,1]
## [1,] 20.31854450
## [2,] 0.01214592
##
## Sigma: 124.9531
## AIC: 5803.815
#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 4 days by using bats Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.998 % MAPE 4 days Daily Covid 19 Infection cases in Northwestern federal district %"
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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-19 | Friday | 1663.00 | 1647.98 | 0.903 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-20 | Saturday | 1653.00 | 1633.13 | 1.202 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-21 | Sunday | 1607.00 | 1618.62 | 0.723 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-22 | Monday | 1586.00 | 1604.45 | 1.164 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-03-23 | Tuesday | 1590.62 | 1200.68 | 994.25 | 1200.68 | 994.25 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1577.11 | 1138.75 | 906.70 | 1138.75 | 906.70 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1563.93 | 1078.31 | 821.24 | 1078.31 | 821.24 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1551.05 | 1018.97 | 737.31 | 1018.97 | 737.31 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1538.47 | 960.49 | 654.53 | 960.49 | 654.53 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1526.20 | 902.71 | 572.66 | 902.71 | 572.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1514.21 | 845.50 | 491.51 | 845.50 | 491.51 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 -1.012165 124.275 72.26282 NaN Inf 0.9874952 -0.002467678
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.9550866
## Beta: 0.06843071
## Damping Parameter: 1
## Gamma-1 Values: -0.0007177312
## Gamma-2 Values: -0.0003557686
##
## Seed States:
## [,1]
## [1,] 22.9502546
## [2,] -0.5704764
## [3,] 11.7074486
## [4,] -0.5884078
## [5,] -18.9730196
## [6,] -4.7630109
##
## Sigma: 124.275
## AIC: 5809.766
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 4 days by using TBATS Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 4 days in TBATS Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "3.976 % MAPE 4 days Daily Covid 19 Infection cases in Northwestern federal district %"
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 4 days in TBATS Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-19 | Friday | 1663.00 | 1621.66 | 2.486 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-20 | Saturday | 1653.00 | 1569.89 | 5.028 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-21 | Sunday | 1607.00 | 1540.06 | 4.165 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-22 | Monday | 1586.00 | 1518.98 | 4.226 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2021-03-23 | Tuesday | 1511.74 | 1168.92 | 987.44 | 1854.55 | 2036.03 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1505.58 | 1130.71 | 932.27 | 1880.46 | 2078.90 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1463.64 | 1059.34 | 845.31 | 1867.95 | 2081.98 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1411.87 | 980.23 | 751.74 | 1843.50 | 2071.99 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1382.05 | 924.72 | 682.63 | 1839.37 | 2081.46 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1360.96 | 879.32 | 624.35 | 1842.61 | 2097.58 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1353.72 | 848.95 | 581.74 | 1858.48 | 2125.69 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
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 -8.92819 128.0633 72.88554 -Inf Inf 0.9960048 0.1800532
# 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= 0.4892
##
## Smoothing parameters:
## alpha = 0.8087
## beta = 0.0454
##
## Initial states:
## l = -0.056
## b = 0.5005
##
## sigma: 2.6925
##
## AIC AICc BIC
## 2944.703 2944.867 2964.298
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -8.92819 128.0633 72.88554 -Inf Inf 0.9960048 0.1800532
# 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 4 days by using holt Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 4 days in holt Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
paste(MAPE_Mean_All.Holt,"%")
## [1] "1.711 % MAPE 4 days Daily Covid 19 Infection cases in Northwestern federal district %"
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 4 days in holt Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-19 | Friday | 1663.00 | 1634.68 | 1.703 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-20 | Saturday | 1653.00 | 1610.98 | 2.542 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-21 | Sunday | 1607.00 | 1587.45 | 1.217 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-22 | Monday | 1586.00 | 1564.10 | 1.381 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-03-23 | Tuesday | 1540.93 | 1248.71 | 1106.69 | 1864.57 | 2048.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1517.93 | 1196.75 | 1042.47 | 1878.16 | 2084.72 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1495.11 | 1146.43 | 980.92 | 1891.15 | 2120.05 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1472.46 | 1097.48 | 921.67 | 1903.82 | 2155.09 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1450.00 | 1049.74 | 864.47 | 1916.36 | 2190.14 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1427.71 | 1003.12 | 809.18 | 1928.92 | 2225.43 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1405.59 | 957.52 | 755.68 | 1941.59 | 2261.13 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
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 ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 = 3.6638, 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) = -0.25903, 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 = -1.1928, Lag order = 7, p-value = 0.9068
## 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 ==> Daily Covid 19 Infection cases in Northwestern federal district"
kpss.test(diff1_x1) # applay kpss test after taking first differences
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 0.48953, Truncation lag parameter = 5, p-value = 0.04403
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) = -385.48, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -4.4193, Lag order = 7, p-value = 0.01
## 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 Daily Covid 19 Infection cases in Northwestern federal district"
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 = 0.0092135, 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) = -469.31, 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 = -10.601, 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) : 4876.914
## ARIMA(0,2,1) : 4634.84
## ARIMA(0,2,2) : 4636.326
## ARIMA(0,2,3) : 4637.931
## ARIMA(0,2,4) : 4635.451
## ARIMA(0,2,5) : 4636.149
## ARIMA(1,2,0) : 4753.69
## ARIMA(1,2,1) : 4636.287
## ARIMA(1,2,2) : 4637.659
## ARIMA(1,2,3) : 4639.071
## ARIMA(1,2,4) : 4636.33
## ARIMA(2,2,0) : 4730.129
## ARIMA(2,2,1) : 4637.832
## ARIMA(2,2,2) : 4639.289
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 4713.196
## ARIMA(3,2,1) : 4636.21
## ARIMA(3,2,2) : 4636.368
## ARIMA(4,2,0) : 4685.469
## ARIMA(4,2,1) : 4634.692
## ARIMA(5,2,0) : 4674.422
##
##
##
## Best model: ARIMA(4,2,1)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(4,2,1)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## -0.0758 0.0058 -0.1251 -0.1057 -0.8989
## s.e. 0.0581 0.0564 0.0553 0.0554 0.0294
##
## sigma^2 estimated as 15726: log likelihood=-2311.23
## AIC=4634.46 AICc=4634.69 BIC=4657.94
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 4 2 1
strtoi(bestmodel[3])
## [1] 1
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## -0.0758 0.0058 -0.1251 -0.1057 -0.8989
## s.e. 0.0581 0.0564 0.0553 0.0554 0.0294
##
## sigma^2 estimated as 15513: log likelihood = -2311.23, aic = 4634.46
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Daily Covid 19 Infection cases in Northwestern federal district"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.6619162 124.2178 69.42682 -Inf Inf 0.9487403 -0.000929102
x1_model1$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(4,2,1)
## Q* = 16.714, df = 5, p-value = 0.005074
##
## 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 ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 = 134.21, 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 = 3928.5, 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 4 days by using bats Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.656 % MAPE 4 days Daily Covid 19 Infection cases in Northwestern federal district %"
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 4 days in bats Model for ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-19 | Friday | 1663.00 | 1644.57 | 1.108 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-20 | Saturday | 1653.00 | 1628.08 | 1.507 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-21 | Sunday | 1607.00 | 1606.92 | 0.005 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-22 | Monday | 1586.00 | 1586.08 | 0.005 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2021-03-23 | Tuesday | 1567.19 | 1185.01 | 982.69 | 1949.36 | 2151.68 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1548.42 | 1122.39 | 896.87 | 1974.45 | 2199.98 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1530.12 | 1058.53 | 808.89 | 2001.70 | 2251.34 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1511.50 | 991.95 | 716.92 | 2031.04 | 2306.07 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1492.68 | 923.93 | 622.85 | 2061.44 | 2362.52 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1473.81 | 855.14 | 527.64 | 2092.48 | 2419.98 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1454.93 | 785.66 | 431.36 | 2124.21 | 2478.50 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
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] "0.656 % MAPE 4 days Daily Covid 19 Infection cases in Northwestern federal district"
# 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)
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 ==> Daily Covid 19 Infection cases in Northwestern federal district"
best_recommended_model
## [1] 0.656
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")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Daily Covid 19 Infection cases in Northwestern federal district"
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$lower,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_bats | lower.80. | lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-03-23 | Tuesday | 1590.62 | 1200.68 | 994.25 | 1200.68 | 994.25 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1577.11 | 1138.75 | 906.70 | 1138.75 | 906.70 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1563.93 | 1078.31 | 821.24 | 1078.31 | 821.24 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1551.05 | 1018.97 | 737.31 | 1018.97 | 737.31 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1538.47 | 960.49 | 654.53 | 960.49 | 654.53 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1526.20 | 902.71 | 572.66 | 902.71 | 572.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1514.21 | 845.50 | 491.51 | 845.50 | 491.51 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Daily Covid 19 Infection cases in Northwestern federal district"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$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 | 2021-03-23 | Tuesday | 1511.74 | 1168.92 | 987.44 | 1854.55 | 2036.03 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1505.58 | 1130.71 | 932.27 | 1880.46 | 2078.90 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1463.64 | 1059.34 | 845.31 | 1867.95 | 2081.98 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1411.87 | 980.23 | 751.74 | 1843.50 | 2071.99 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1382.05 | 924.72 | 682.63 | 1839.37 | 2081.46 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1360.96 | 879.32 | 624.35 | 1842.61 | 2097.58 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1353.72 | 848.95 | 581.74 | 1858.48 | 2125.69 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-23 | Tuesday | 1540.93 | 1248.71 | 1106.69 | 1864.57 | 2048.66 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1517.93 | 1196.75 | 1042.47 | 1878.16 | 2084.72 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1495.11 | 1146.43 | 980.92 | 1891.15 | 2120.05 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1472.46 | 1097.48 | 921.67 | 1903.82 | 2155.09 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1450.00 | 1049.74 | 864.47 | 1916.36 | 2190.14 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1427.71 | 1003.12 | 809.18 | 1928.92 | 2225.43 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1405.59 | 957.52 | 755.68 | 1941.59 | 2261.13 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-23 | Tuesday | 1567.19 | 1185.01 | 982.69 | 1949.36 | 2151.68 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-03-24 | Wednesday | 1548.42 | 1122.39 | 896.87 | 1974.45 | 2199.98 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-03-25 | Thursday | 1530.12 | 1058.53 | 808.89 | 2001.70 | 2251.34 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-03-26 | Friday | 1511.50 | 991.95 | 716.92 | 2031.04 | 2306.07 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-03-27 | Saturday | 1492.68 | 923.93 | 622.85 | 2061.44 | 2362.52 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-03-28 | Sunday | 1473.81 | 855.14 | 527.64 | 2092.48 | 2419.98 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-03-29 | Monday | 1454.93 | 785.66 | 431.36 | 2124.21 | 2478.50 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Daily Covid 19 Infection cases in Northwestern federal district"
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 | 2021-03-23 | Tuesday | 1717.99 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-03-24 | Wednesday | 1728.10 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-03-25 | Thursday | 1747.08 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-03-26 | Friday | 1768.44 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-03-27 | Saturday | 1786.21 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-03-28 | Sunday | 1806.57 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-03-29 | Monday | 1824.66 |
## +---+------------+-----------------+---------------------+
result<-c(x1,x2,x3,x4,x5)
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,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+----------------------+------------+------------+-------------+------------+-------------+-------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Best.Model | Freq |
## +===+======================+============+============+=============+============+=============+=============+======+
## | 1 | Northwestern federal | 4.641 | 0.998 | 3.976 | 1.711 | 0.656 | ARIMA 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)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.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, and ARIMA Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend, and ARIMA Model ==>Daily Covid 19 Infection cases in Northwestern federal district
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Daily Covid 19 Infection cases in Northwestern federal district