South ural state university, Chelyabinsk, Russian federation
#Import library
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
library(tseries)
require(tseries) # need to install tseries tj test Stationarity in time series
library(forecast) # install library forecast
library(ascii) # for make tables
##Global vriable##
Full_original_data <- read_excel("data.xlsx") # path of your data ( time series data)
original_data<-Full_original_data$cases # select colum from your data
y_lab <- "(Daily Covid 19 Infection cases in Chelyabinsk)" # input name of data
Actual_date_interval <- c("2020/03/12","2021/07/31") # put actual range date of your data
Forecast_date_interval <- c("2021/08/01","2021/08/07") #put forecasting date range
validation_data_days <-7 # Number of testing data(#testing last 10 days)10
Number_Neural<-15# Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new NNAR model (TRUE/FALSE)
frequency<-"days" # type of you data( daily-weekly-month-years)
country.name <- "Chelyabinsk" # name of area or country or cases
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 85 122 145 214 338
# calculate Cofficient of kurtosis
# calculate Cofficient of skewness
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data),skewness=skewness(original_data),Standard.deviation =sd(original_data))
## kurtosis skewness Standard.deviation
## 1 2.193685 0.488203 91.90665
#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(2,15)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 2-15-1 network with 61 weights
## options were - linear output units
##
## sigma^2 estimated as 81.77
# 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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_All,"%")
## [1] "4.543 % MAPE 7 days (Daily Covid 19 Infection cases in Chelyabinsk) %"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 | 2021-07-25 | Sunday | 315.00 | 315.28 | 0.09 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 316.07 | 1.535 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 315.26 | 2.698 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 313.53 | 4.703 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 311.38 | 5.927 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 309.17 | 7.71 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 307.11 | 9.14 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-08-01 | Sunday | 305.30 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-08-02 | Monday | 303.80 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-08-03 | Tuesday | 302.59 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-08-04 | Wednesday | 301.66 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-08-05 | Thursday | 300.96 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-08-06 | Friday | 300.46 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-08-07 | Saturday | 300.12 |
## +---+------------+-----------------+---------------------+
plot(forecasting_NNAR,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph1<-autoplot(forecasting_NNAR,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph1+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(forecasting_NNAR$mean, series="NNAR Model",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
#################
## 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 0.4279646 9.700088 5.296793 NaN Inf 0.9583393 -0.0006436153
# Print Model Parameters
model_bats
## BATS(1, {4,5}, 0.955, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.19281
## Beta: 0.1334899
## Damping Parameter: 0.95535
## AR coefficients: -0.75151 -0.07387 -0.058625 -0.540428
## MA coefficients: 0.279061 -0.234796 -0.099764 0.346198 -0.24875
##
## Seed States:
## [,1]
## [1,] -6.5739305
## [2,] 0.3030306
## [3,] 0.0000000
## [4,] 0.0000000
## [5,] 0.0000000
## [6,] 0.0000000
## [7,] 0.0000000
## [8,] 0.0000000
## [9,] 0.0000000
## [10,] 0.0000000
## [11,] 0.0000000
##
## Sigma: 9.700088
## AIC: 5425.439
#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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_All.bats,"%")
## [1] "2.028 % MAPE 7 days (Daily Covid 19 Infection cases in Chelyabinsk) %"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 | 2021-07-25 | Sunday | 315.00 | 314.12 | 0.28 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 316.78 | 1.315 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 318.48 | 1.704 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 320.86 | 2.475 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 322.97 | 2.425 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 325.12 | 2.95 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 327.70 | 3.047 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-08-01 | Sunday | 329.36 | 299.23 | 283.28 | 299.23 | 283.28 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 331.59 | 299.18 | 282.02 | 299.18 | 282.02 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 333.20 | 298.49 | 280.12 | 298.49 | 280.12 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 334.84 | 297.76 | 278.13 | 297.76 | 278.13 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 336.76 | 297.60 | 276.87 | 297.60 | 276.87 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 338.01 | 296.48 | 274.50 | 296.48 | 274.50 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 339.90 | 296.20 | 273.07 | 296.20 | 273.07 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
plot(forecasting_bats)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph2<-autoplot(forecasting_bats,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph2+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(forecasting_bats$mean, series="BATS Model",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
###############
## TBATS Model#
###############
# Data Modeling
data_series<-ts(training_data)
model_TBATS<-forecast:::fitSpecificTBATS(data_series,use.box.cox=FALSE, use.beta=TRUE, seasonal.periods=c(6),use.damping=FALSE,k.vector=c(2))
accuracy(model_TBATS) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.2301264 10.10564 5.55011 NaN Inf 1.004172 0.003646674
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.7796876
## Beta: 0.0344705
## Damping Parameter: 1
## Gamma-1 Values: -0.001547862
## Gamma-2 Values: 0.001337259
##
## Seed States:
## [,1]
## [1,] -6.7533183
## [2,] 0.3487651
## [3,] 1.0349772
## [4,] -0.4017906
## [5,] 0.1867790
## [6,] 0.6643893
##
## Sigma: 10.10564
## AIC: 5440.398
plot(model_TBATS,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
# Testing Data Evaluation
forecasting_tbats <- predict(model_TBATS, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_tbats$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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.584 % MAPE 7 days (Daily Covid 19 Infection cases in Chelyabinsk) %"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 | 2021-07-25 | Sunday | 315.00 | 313.62 | 0.438 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 317.30 | 1.152 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 323.18 | 0.253 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 327.00 | 0.607 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 332.27 | 0.384 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 337.71 | 0.81 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 339.51 | 0.447 % |
## +---+------------+-------------------------+-------------+-------------------+------------------+
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 | 2021-08-01 | Sunday | 343.19 | 313.69 | 298.08 | 372.69 | 388.30 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 349.07 | 317.95 | 301.47 | 380.20 | 396.67 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 352.89 | 320.22 | 302.93 | 385.57 | 402.86 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 358.16 | 324.01 | 305.94 | 392.31 | 410.39 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 363.60 | 328.06 | 309.24 | 399.15 | 417.97 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 365.40 | 328.52 | 309.00 | 402.28 | 421.80 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 369.08 | 330.91 | 310.71 | 407.25 | 427.45 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
plot(forecasting_tbats)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph3<-autoplot(forecasting_tbats,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph3+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(forecasting_tbats$mean, series="TBATS Model",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
#######################
## 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 0.2230251 10.18832 5.402464 -Inf Inf 0.977458 0.003585629
# Print Model Parameters
summary(model_holt$model)
## Holt's method
##
## Call:
## holt(y = data_series, h = N_forecasting_days + validation_data_days,
##
## Call:
## lambda = "auto")
##
## Box-Cox transformation: lambda= 1
##
## Smoothing parameters:
## alpha = 0.7766
## beta = 0.0342
##
## Initial states:
## l = -1.5417
## b = 0.5614
##
## sigma: 10.2287
##
## AIC AICc BIC
## 5438.490 5438.611 5459.563
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.2230251 10.18832 5.402464 -Inf Inf 0.977458 0.003585629
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$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's Linear trend Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using holt's Linear trend Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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's Linear trend Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt's Linear trend Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.501 % MAPE 7 days (Daily Covid 19 Infection cases in Chelyabinsk) %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt's Linear trend Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt's Linear trend Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 | 2021-07-25 | Sunday | 315.00 | 315.90 | 0.287 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 320.28 | 0.225 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 324.65 | 0.201 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 329.03 | 0.008 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 333.40 | 0.726 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 337.78 | 0.829 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 342.15 | 1.228 % |
## +---+------------+-------------------------+-------------+------------------+-----------------+
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$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_holt | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+=====================+===========+===========+===========+===========+
## | 1 | 2021-08-01 | Sunday | 346.53 | 312.16 | 293.96 | 380.89 | 399.09 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 350.90 | 313.88 | 294.28 | 387.92 | 407.52 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 355.27 | 315.62 | 294.62 | 394.93 | 415.93 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 359.65 | 317.37 | 294.98 | 401.93 | 424.32 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 364.02 | 319.12 | 295.35 | 408.93 | 432.70 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 368.40 | 320.88 | 295.72 | 415.92 | 441.08 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 372.77 | 322.63 | 296.08 | 422.92 | 449.46 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
plot(forecasting_holt)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph4<-autoplot(forecasting_holt,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph4+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(forecasting_holt$mean, series="Holt's Linear Trend Model",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
##################
#Auto arima model#
##################
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 = 2.5989, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -3.0132, Truncation lag parameter = 5, p-value
## = 0.9336
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -1.3447, Lag order = 7, p-value = 0.8557
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 1
#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 Chelyabinsk)"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value greater than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 0.21315, Truncation lag parameter = 5, p-value = 0.1
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) = -587.94, 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 = -6.3002, 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 Chelyabinsk)"
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 = 0.0063281, 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) = -675.61, 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 = -15.468, 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(0,1,0) : 3760.2
## ARIMA(0,1,0) with drift : 3760.427
## ARIMA(0,1,1) : 3748.96
## ARIMA(0,1,1) with drift : 3748.412
## ARIMA(0,1,2) : 3748.922
## ARIMA(0,1,2) with drift : 3748.711
## ARIMA(0,1,3) : 3748.395
## ARIMA(0,1,3) with drift : 3747.91
## ARIMA(0,1,4) : 3749.388
## ARIMA(0,1,4) with drift : 3748.808
## ARIMA(0,1,5) : 3737.529
## ARIMA(0,1,5) with drift : 3737.239
## ARIMA(1,1,0) : 3747.519
## ARIMA(1,1,0) with drift : 3747.024
## ARIMA(1,1,1) : 3748.832
## ARIMA(1,1,1) with drift : 3748.455
## ARIMA(1,1,2) : 3750.324
## ARIMA(1,1,2) with drift : 3750.112
## ARIMA(1,1,3) : 3750.267
## ARIMA(1,1,3) with drift : 3749.763
## ARIMA(1,1,4) : 3744.125
## ARIMA(1,1,4) with drift : 3743.516
## ARIMA(2,1,0) : 3748.577
## ARIMA(2,1,0) with drift : 3748.288
## ARIMA(2,1,1) : 3750.61
## ARIMA(2,1,1) with drift : 3750.328
## ARIMA(2,1,2) : 3719.943
## ARIMA(2,1,2) with drift : 3719.84
## ARIMA(2,1,3) : 3738.997
## ARIMA(2,1,3) with drift : 3738.402
## ARIMA(3,1,0) : 3750.61
## ARIMA(3,1,0) with drift : 3750.32
## ARIMA(3,1,1) : 3752.4
## ARIMA(3,1,1) with drift : 3751.96
## ARIMA(3,1,2) : Inf
## ARIMA(3,1,2) with drift : Inf
## ARIMA(4,1,0) : 3744.318
## ARIMA(4,1,0) with drift : 3743.36
## ARIMA(4,1,1) : 3738.131
## ARIMA(4,1,1) with drift : 3737.347
## ARIMA(5,1,0) : 3735.152
## ARIMA(5,1,0) with drift : 3734.942
##
##
##
## Best model: ARIMA(2,1,2) with drift
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,1,2) with drift
##
## Coefficients:
## ar1 ar2 ma1 ma2 drift
## -1.6380 -0.9635 1.5557 0.8952 0.6240
## s.e. 0.0196 0.0186 0.0313 0.0342 0.4259
##
## sigma^2 estimated as 99.58: log likelihood=-1853.83
## AIC=3719.67 AICc=3719.84 BIC=3744.94
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 1 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## -1.6379 -0.9636 1.5562 0.8959
## s.e. 0.0197 0.0185 0.0311 0.0340
##
## sigma^2 estimated as 99: log likelihood = -1854.91, aic = 3719.82
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.6507405 9.940167 5.570409 NaN Inf 1.007844 -0.02903287
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,1,2)
## Q* = 21.049, df = 6, p-value = 0.001798
##
## Model df: 4. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 = 333.26, df = 20, p-value < 2.2e-16
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 3824.7, 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
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "4.744 % MAPE 7 days (Daily Covid 19 Infection cases in Chelyabinsk) %"
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 ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 | 2021-07-25 | Sunday | 315.00 | 311.63 | 1.069 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 312.13 | 2.764 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 311.67 | 3.805 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 311.94 | 5.185 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 311.94 | 5.759 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 311.68 | 6.961 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 312.10 | 7.662 % |
## +---+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2021-08-01 | Sunday | 311.66 | 276.93 | 258.55 | 346.38 | 364.77 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 311.98 | 275.22 | 255.75 | 348.75 | 368.21 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 311.88 | 273.18 | 252.69 | 350.59 | 371.08 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 311.73 | 271.04 | 249.50 | 352.43 | 373.97 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 312.07 | 269.71 | 247.28 | 354.44 | 376.86 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 311.66 | 267.46 | 244.06 | 355.86 | 379.26 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 312.01 | 266.20 | 241.96 | 357.81 | 382.06 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
plot(forecasting_auto_arima)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph5<-autoplot(forecasting_auto_arima,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph5+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(forecasting_auto_arima$mean, series="auto.arima Model",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
#########################################################################################
# Returns local linear forecasts and prediction intervals using cubic smoothing splines.#
# Testing Data Evaluation #
#########################################################################################
forecasting_splinef <- splinef(original_data,h=N_forecasting_days+validation_data_days)
summary(forecasting_splinef)
##
## Forecast method: Cubic Smoothing Spline
##
## Model Information:
## $beta
## [1] 13.03238
##
## $call
## splinef(y = original_data, h = N_forecasting_days + validation_data_days)
##
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.03719775 11.15907 5.537464 -Inf Inf 1.00645 0.2139956
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 508 342.2448 327.8995 356.5901 320.3055 364.1840
## 509 345.8382 328.2202 363.4563 318.8937 372.7827
## 510 349.4317 327.5488 371.3146 315.9647 382.8987
## 511 353.0251 326.1017 379.9486 311.8493 394.2010
## 512 356.6186 323.9845 389.2526 306.7091 406.5281
## 513 360.2120 321.3190 399.1050 300.7303 419.6937
## 514 363.8055 318.1655 409.4455 294.0051 433.6058
## 515 367.3989 314.5669 420.2309 286.5994 448.1984
## 516 370.9924 310.5555 431.4292 278.5621 463.4226
## 517 374.5858 306.1552 443.0164 269.9303 479.2414
## 518 378.1793 301.4053 454.9532 260.7636 495.5949
## 519 381.7727 296.3160 467.2295 251.0779 512.4675
## 520 385.3662 290.8962 479.8361 240.8868 529.8455
## 521 388.9596 285.1600 492.7593 230.2117 547.7075
validation_forecast<-head(forecasting_splinef$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 cubic smoothing splines Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using cubic smoothing splines Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
MAPE_Mean_All.splinef_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.splinef<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_splinef<-paste(round(MAPE_Per_Day,3),"%")
MAPE_splinef_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in cubic smoothing splines Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in cubic smoothing splines Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_All.splinef,"%")
## [1] "7.777 % MAPE 7 days (Daily Covid 19 Infection cases in Chelyabinsk) %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in cubic smoothing splines Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in cubic smoothing splines Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(date_splinef=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_splinef=validation_forecast,MAPE_splinef_Model)), type = "rest")
##
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | | date_splinef | validation_data_by_name | actual_data | Series.1 | MAPE_splinef_Model |
## +===+==============+=========================+=============+==========+====================+
## | 1 | 2021-07-25 | Sunday | 315.00 | 342.24 | 8.649 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 345.84 | 7.738 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 349.43 | 7.849 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 353.03 | 7.302 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 356.62 | 7.74 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 360.21 | 7.526 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 363.81 | 7.635 % |
## +---+--------------+-------------------------+-------------+----------+--------------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_splinef=tail(forecasting_splinef$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | Series.1 | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+==========+===========+===========+===========+===========+
## | 1 | 2021-08-01 | Sunday | 367.40 | 312.16 | 293.96 | 380.89 | 399.09 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 370.99 | 313.88 | 294.28 | 387.92 | 407.52 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 374.59 | 315.62 | 294.62 | 394.93 | 415.93 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 378.18 | 317.37 | 294.98 | 401.93 | 424.32 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 381.77 | 319.12 | 295.35 | 408.93 | 432.70 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 385.37 | 320.88 | 295.72 | 415.92 | 441.08 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 388.96 | 322.63 | 296.08 | 422.92 | 449.46 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
plot(forecasting_splinef)
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) )
lines(x1_test, col='red',lwd=2)
graph6<-autoplot(forecasting_splinef,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab)
graph6+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(forecasting_splinef$mean, series="cubic smoothing splines Model",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
######################
#Ensembling (Average)#
######################
re_NNAR<-forecasting_NNAR$mean
re_BATS<-forecasting_bats$mean
re_TBATS<-forecasting_tbats$mean
re_holt<-forecasting_holt$mean
re_autoarima<-forecasting_auto_arima$mean
splinef_model<-data.frame(forecasting_splinef)
splinef<-splinef_model$Point.Forecast
result_df<-data.frame(re_NNAR,re_BATS,re_TBATS,re_holt,re_autoarima,splinef)
average_models<-rowMeans(result_df)
# Testing Data Evaluation
Ensembling_average1<-head(average_models,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-Ensembling_average1)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using Ensembling (Average) for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using Ensembling (Average) for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
MAPE_Mean_EnsemblingAverage<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_Ensembling<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Ensembling<-paste(round(MAPE_Per_Day,3),"%")
MAPE_Ensembling_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in Ensembling Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in Ensembling Model for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_EnsemblingAverage,"%")
## [1] "0.912 %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in Ensembling (Average) for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in Ensembling (Average) for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(date_Ensembling=validation_dates,validation_data_by_name,actual_data=testing_data,Ensembling=Ensembling_average1,MAPE_Ensembling)), type = "rest")
##
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | | date_Ensembling | validation_data_by_name | actual_data | Ensembling | MAPE_Ensembling |
## +===+=================+=========================+=============+============+=================+
## | 1 | 2021-07-25 | Sunday | 315.00 | 318.80 | 1.206 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 321.40 | 0.124 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 323.78 | 0.068 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 325.90 | 0.943 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 328.10 | 0.877 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 330.28 | 1.409 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 332.06 | 1.756 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,Ensembling_Average=tail(average_models,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+--------------------+
## | | FD | forecating_date | Ensembling_Average |
## +===+============+=================+====================+
## | 1 | 2021-08-01 | Sunday | 333.91 |
## +---+------------+-----------------+--------------------+
## | 2 | 2021-08-02 | Monday | 336.39 |
## +---+------------+-----------------+--------------------+
## | 3 | 2021-08-03 | Tuesday | 338.40 |
## +---+------------+-----------------+--------------------+
## | 4 | 2021-08-04 | Wednesday | 340.70 |
## +---+------------+-----------------+--------------------+
## | 5 | 2021-08-05 | Thursday | 343.20 |
## +---+------------+-----------------+--------------------+
## | 6 | 2021-08-06 | Friday | 344.88 |
## +---+------------+-----------------+--------------------+
## | 7 | 2021-08-07 | Saturday | 347.14 |
## +---+------------+-----------------+--------------------+
#############################
#Ensembling (weight average)#
#############################
weight.model<-0.90# priotizer the weights ( weight average)
re_NNAR<-forecasting_NNAR$mean
re_BATS<-forecasting_bats$mean
re_TBATS<-forecasting_tbats$mean
re_holt<-forecasting_holt$mean
re_autoarima<-forecasting_auto_arima$mean
re_splinef<-c(forecasting_splinef$mean)
re_bestmodel<-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_All.splinef_Model)
y1<-if(re_bestmodel >= MAPE_Mean_All.bats_Model) {re_BATS*weight.model
} else {
(re_BATS*(1-weight.model))/5
}
y2<-if(re_bestmodel >= MAPE_Mean_All.TBATS_Model) {re_TBATS*weight.model
} else {
(re_TBATS*(1-weight.model))/5
}
y3<-if(re_bestmodel >= MAPE_Mean_All.Holt_Model) {re_holt*weight.model
} else {
(re_holt*(1-weight.model))/5
}
y4<-if(re_bestmodel >= MAPE_Mean_All.ARIMA_Model) {re_autoarima*weight.model
} else {
(re_autoarima*(1-weight.model))/5
}
y5<-if(re_bestmodel >= MAPE_Mean_All_NNAR) {re_NNAR*weight.model
} else {
(re_NNAR*(1-weight.model))/5
}
y6<-if(re_bestmodel >= MAPE_Mean_All.splinef_Model) {re_splinef*weight.model
} else {
(splinef*(1-weight.model))/5
}
Ensembling.weight<-(y1+y2+y3+y4+y5+y6)
# Testing Data Evaluation
validation_forecast2<-head(Ensembling.weight,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast2)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using Ensembling (weight average) for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 days by using Ensembling (weight average) for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
MAPE_Mean_EnsemblingAverage1<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_Ensembling<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_Ensembling<-paste(round(MAPE_Per_Day,3),"%")
MAPE_Ensembling_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in Ensembling weight average for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in Ensembling weight average for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
paste(MAPE_Mean_EnsemblingAverage1,"%")
## [1] "0.403 %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in Ensembling weight average for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in Ensembling weight average for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(date_Ensembling=validation_dates,validation_data_by_name,actual_data=testing_data,Ensembling=validation_forecast2,MAPE_Ensembling)), type = "rest")
##
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | | date_Ensembling | validation_data_by_name | actual_data | Ensembling | MAPE_Ensembling |
## +===+=================+=========================+=============+============+=================+
## | 1 | 2021-07-25 | Sunday | 315.00 | 316.25 | 0.397 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 2 | 2021-07-26 | Monday | 321.00 | 320.41 | 0.183 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 3 | 2021-07-27 | Tuesday | 324.00 | 324.55 | 0.169 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 4 | 2021-07-28 | Wednesday | 329.00 | 328.65 | 0.106 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 5 | 2021-07-29 | Thursday | 331.00 | 332.77 | 0.533 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 6 | 2021-07-30 | Friday | 335.00 | 336.88 | 0.56 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
## | 7 | 2021-07-31 | Saturday | 338.00 | 340.94 | 0.87 % |
## +---+-----------------+-------------------------+-------------+------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_Ensembling=tail(Ensembling.weight,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------------+
## | | FD | forecating_date | forecasting_by_Ensembling |
## +===+============+=================+===========================+
## | 1 | 2021-08-01 | Sunday | 345.01 |
## +---+------------+-----------------+---------------------------+
## | 2 | 2021-08-02 | Monday | 349.16 |
## +---+------------+-----------------+---------------------------+
## | 3 | 2021-08-03 | Tuesday | 353.25 |
## +---+------------+-----------------+---------------------------+
## | 4 | 2021-08-04 | Wednesday | 357.38 |
## +---+------------+-----------------+---------------------------+
## | 5 | 2021-08-05 | Thursday | 361.52 |
## +---+------------+-----------------+---------------------------+
## | 6 | 2021-08-06 | Friday | 365.58 |
## +---+------------+-----------------+---------------------------+
## | 7 | 2021-08-07 | Saturday | 369.70 |
## +---+------------+-----------------+---------------------------+
graph8<-autoplot(Ensembling.weight,xlab = paste ("Time in", frequency ,y_lab,"by using Ensembling weight average" , sep=" "), ylab=y_lab)
graph8+scale_y_continuous(labels = scales::comma)+
forecast::autolayer(Ensembling.weight, series="Ensembling weight average",size = 0.7) +
guides(colour=guide_legend(title="Forecasts"),fill = "black")+
theme(legend.position="bottom")+
theme(legend.background = element_rect(fill="white",
size=0.7, linetype="solid",
colour ="gray"))
# 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_All.splinef_Model,MAPE_Mean_EnsemblingAverage,MAPE_Mean_EnsemblingAverage1)
paste("System Choose Least Error ==> ( MAPE %) of Forecasting by using NNAR model, BATS Model, TBATS Model, Holt's Linear Model , autoarima Model, cubic smoothing splines Model, Ensembling (Average), and Ensembling weight average , for ==> ", y_lab , sep=" ")
## [1] "System Choose Least Error ==> ( MAPE %) of Forecasting by using NNAR model, BATS Model, TBATS Model, Holt's Linear Model , autoarima Model, cubic smoothing splines Model, Ensembling (Average), and Ensembling weight average , for ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
best_recommended_model
## [1] 0.403
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_All.splinef_Model) {paste("cubic smoothing splines")}
x7<-if(best_recommended_model >= MAPE_Mean_EnsemblingAverage) {paste("Ensembling (Average)")}
x8<-if(best_recommended_model >= MAPE_Mean_EnsemblingAverage1) {paste("Ensembling weight average")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_NNAR=tail(forecasting_NNAR$mean,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+---------------------+
## | | FD | forecating_date | forecasting_by_NNAR |
## +===+============+=================+=====================+
## | 1 | 2021-08-01 | Sunday | 305.30 |
## +---+------------+-----------------+---------------------+
## | 2 | 2021-08-02 | Monday | 303.80 |
## +---+------------+-----------------+---------------------+
## | 3 | 2021-08-03 | Tuesday | 302.59 |
## +---+------------+-----------------+---------------------+
## | 4 | 2021-08-04 | Wednesday | 301.66 |
## +---+------------+-----------------+---------------------+
## | 5 | 2021-08-05 | Thursday | 300.96 |
## +---+------------+-----------------+---------------------+
## | 6 | 2021-08-06 | Friday | 300.46 |
## +---+------------+-----------------+---------------------+
## | 7 | 2021-08-07 | Saturday | 300.12 |
## +---+------------+-----------------+---------------------+
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$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 | 2021-08-01 | Sunday | 329.36 | 299.23 | 283.28 | 299.23 | 283.28 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 331.59 | 299.18 | 282.02 | 299.18 | 282.02 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 333.20 | 298.49 | 280.12 | 298.49 | 280.12 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 334.84 | 297.76 | 278.13 | 297.76 | 278.13 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 336.76 | 297.60 | 276.87 | 297.60 | 276.87 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 338.01 | 296.48 | 274.50 | 296.48 | 274.50 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 339.90 | 296.20 | 273.07 | 296.20 | 273.07 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | forecasting_by_TBATS | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+======================+===========+===========+===========+===========+
## | 1 | 2021-08-01 | Sunday | 343.19 | 313.69 | 298.08 | 372.69 | 388.30 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 349.07 | 317.95 | 301.47 | 380.20 | 396.67 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 352.89 | 320.22 | 302.93 | 385.57 | 402.86 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 358.16 | 324.01 | 305.94 | 392.31 | 410.39 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 363.60 | 328.06 | 309.24 | 399.15 | 417.97 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 365.40 | 328.52 | 309.00 | 402.28 | 421.80 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 369.08 | 330.91 | 310.71 | 407.25 | 427.45 |
## +---+------------+-----------------+----------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$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 | 2021-08-01 | Sunday | 346.53 | 312.16 | 293.96 | 380.89 | 399.09 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 350.90 | 313.88 | 294.28 | 387.92 | 407.52 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 355.27 | 315.62 | 294.62 | 394.93 | 415.93 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 359.65 | 317.37 | 294.98 | 401.93 | 424.32 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 364.02 | 319.12 | 295.35 | 408.93 | 432.70 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 368.40 | 320.88 | 295.72 | 415.92 | 441.08 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 372.77 | 322.63 | 296.08 | 422.92 | 449.46 |
## +---+------------+-----------------+---------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
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 | 2021-08-01 | Sunday | 311.66 | 276.93 | 258.55 | 346.38 | 364.77 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 311.98 | 275.22 | 255.75 | 348.75 | 368.21 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 311.88 | 273.18 | 252.69 | 350.59 | 371.08 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 311.73 | 271.04 | 249.50 | 352.43 | 373.97 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 312.07 | 269.71 | 247.28 | 354.44 | 376.86 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 311.66 | 267.46 | 244.06 | 355.86 | 379.26 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 312.01 | 266.20 | 241.96 | 357.81 | 382.06 |
## +---+------------+-----------------+---------------------------+-----------+-----------+-----------+-----------+
paste("Forecasting by using cubic smoothing splines Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using cubic smoothing splines Model ==> (Daily Covid 19 Infection cases in Chelyabinsk)"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_splinef=tail(forecasting_splinef$mean,N_forecasting_days),Lower=tail(forecasting_splinef$lower,N_forecasting_days),Upper=tail(forecasting_splinef$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | | FD | forecating_date | Series.1 | Lower.Series.1 | Lower.Series.2 | Upper.Series.1 | Upper.Series.2 |
## +===+============+=================+==========+================+================+================+================+
## | 1 | 2021-08-01 | Sunday | 367.40 | 314.57 | 286.60 | 420.23 | 448.20 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | 2 | 2021-08-02 | Monday | 370.99 | 310.56 | 278.56 | 431.43 | 463.42 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | 3 | 2021-08-03 | Tuesday | 374.59 | 306.16 | 269.93 | 443.02 | 479.24 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | 4 | 2021-08-04 | Wednesday | 378.18 | 301.41 | 260.76 | 454.95 | 495.59 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | 5 | 2021-08-05 | Thursday | 381.77 | 296.32 | 251.08 | 467.23 | 512.47 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | 6 | 2021-08-06 | Friday | 385.37 | 290.90 | 240.89 | 479.84 | 529.85 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
## | 7 | 2021-08-07 | Saturday | 388.96 | 285.16 | 230.21 | 492.76 | 547.71 |
## +---+------------+-----------------+----------+----------------+----------------+----------------+----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_splinef=tail(forecasting_splinef$mean,N_forecasting_days),Lower=tail(forecasting_holt$lower,N_forecasting_days),Upper=tail(forecasting_holt$upper,N_forecasting_days))), type = "rest")
##
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | | FD | forecating_date | Series.1 | Lower.80. | Lower.95. | Upper.80. | Upper.95. |
## +===+============+=================+==========+===========+===========+===========+===========+
## | 1 | 2021-08-01 | Sunday | 367.40 | 312.16 | 293.96 | 380.89 | 399.09 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 2 | 2021-08-02 | Monday | 370.99 | 313.88 | 294.28 | 387.92 | 407.52 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 3 | 2021-08-03 | Tuesday | 374.59 | 315.62 | 294.62 | 394.93 | 415.93 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 4 | 2021-08-04 | Wednesday | 378.18 | 317.37 | 294.98 | 401.93 | 424.32 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 5 | 2021-08-05 | Thursday | 381.77 | 319.12 | 295.35 | 408.93 | 432.70 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 6 | 2021-08-06 | Friday | 385.37 | 320.88 | 295.72 | 415.92 | 441.08 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
## | 7 | 2021-08-07 | Saturday | 388.96 | 322.63 | 296.08 | 422.92 | 449.46 |
## +---+------------+-----------------+----------+-----------+-----------+-----------+-----------+
result<-c(x1,x2,x3,x4,x5,x6,x7,x8)
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,cubic_smoothing.splines=MAPE_Mean_All.splinef_Model,Ensembling_Average=MAPE_Mean_EnsemblingAverage,Ensembling_weight=MAPE_Mean_EnsemblingAverage1,Best.Model=result)
knitr::kable(table.error,caption = paste("Accuracy MAPE % daily Covid-19 infection cases for testing data last" , validation_data_days ,frequency, y_lab , sep=" "))
Accuracy MAPE % daily Covid-19 infection cases for testing data last 7 days (Daily Covid 19 Infection cases in Chelyabinsk)
| Chelyabinsk |
4.543 |
2.028 |
0.584 |
0.501 |
4.744 |
7.777 |
0.912 |
0.403 |
Ensembling weight average |
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_All.splinef_Model,MAPE_Mean_EnsemblingAverage,MAPE_Mean_EnsemblingAverage1)
Model<-c("NNAR model","BATS Model","TBATS Model","Holt Model","ARIMA Model","cubic smoothing splines","Ensembling (Average)","Ensembling weight")
channel_data<-data.frame(Model,MAPE.Value)
#comparison and visualization plot accuracy models.
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 NNAR, BATS, TBATS, Holt's Linear Trend, ARIMA, cubic smoothing splines, Ensembling (Average), and Ensembling weight ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using NNAR, BATS, TBATS, Holt's Linear Trend, ARIMA, cubic smoothing splines, Ensembling (Average), and Ensembling weight ==>(Daily Covid 19 Infection cases in Chelyabinsk)
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 Chelyabinsk)