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
library(ascii)
require(tseries) # need to install tseries tj test Stationarity in time series
library(forecast) # install library forecast
library(tseries)
##Global vriable##
Full_original_data <- read.csv("data.csv") # path of your data ( time series data)
original_data<-Full_original_data$cases #Cumulative #cases
y_lab <- "Forecasting cumulative Covid 19 Infection cases in Poland" # input name of data
Actual_date_interval <- c("2020/03/01","2021/05/08")
Forecast_date_interval <- c("2021/05/09","2021/05/30")
validation_data_days <-45
frequency<-"day"
Number_Neural<-3# Number of Neural For model NNAR Model
NNAR_Model<- FALSE #create new model (TRUE/FALSE)
frequency<-"days"
country.name <- "Poland"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 13928 69475 649461 1334098 2829196
# calculate standard deviation
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 2.874348
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 1.102134
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 874962.9
#processing on data (input data)
rows <- NROW(original_data) # calculate number of rows in time series (number of days)
training_data<-original_data[1:(rows-validation_data_days)] # Training data
testing_data<-original_data[(rows-validation_data_days+1):rows] #testing data
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD)) #calculate number of days that you want to forecasting
validation_dates<-tail(AD,validation_data_days) # select validation_dates
validation_data_by_name<-weekdays(validation_dates) # put names of validation dates
forecasting_data_by_name<-weekdays(FD) # put names of Forecasting dates
#NNAR Model
if(NNAR_Model==TRUE){
data_series<-ts(training_data)
model_NNAR<-nnetar(data_series, size = Number_Neural)
saveRDS(model_NNAR, file = "model_NNAR.RDS")
my_model <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
if(NNAR_Model==FALSE){
data_series<-ts(training_data)
#model_NNAR<-nnetar(data_series, size = Number_Numeral)
model_NNAR <- readRDS("model_NNAR.RDS")
accuracy(model_NNAR) # accuracy on training data #Print Model Parameters
model_NNAR
}
## Series: data_series
## Model: NNAR(1,3)
## Call: nnetar(y = data_series, size = Number_Neural)
##
## Average of 20 networks, each of which is
## a 1-3-1 network with 10 weights
## options were - linear output units
##
## sigma^2 estimated as 5925916
# 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 45 days by using NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
paste(MAPE_Mean_All,"%")
## [1] "2.897 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Poland %"
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 45 days in NNAR Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-03-25 | Thursday | 2154821.00 | 2146550.26 | 0.384 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 2189966.00 | 2173014.64 | 0.774 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 2221725.00 | 2199951.58 | 0.98 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 2250991.00 | 2227223.73 | 1.056 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 2267964.00 | 2254669.71 | 0.586 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 2288826.00 | 2282106.60 | 0.294 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 2321717.00 | 2309334.20 | 0.533 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 2356970.00 | 2336141.25 | 0.884 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 2387511.00 | 2362313.16 | 1.055 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 2415584.00 | 2387640.75 | 1.157 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 2438542.00 | 2411929.32 | 1.091 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 2448463.00 | 2435007.12 | 0.55 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 2456709.00 | 2456732.40 | 0.001 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 2471617.00 | 2476998.37 | 0.218 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 2499507.00 | 2495735.65 | 0.151 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 2528006.00 | 2512912.25 | 0.597 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 2552898.00 | 2528531.22 | 0.954 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 2574631.00 | 2542626.54 | 1.243 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 2586647.00 | 2555257.82 | 1.214 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 2599850.00 | 2566504.48 | 1.283 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 2621116.00 | 2576459.89 | 1.704 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 2642242.00 | 2585226.00 | 2.158 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 2660088.00 | 2592908.62 | 2.525 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 2675874.00 | 2599613.55 | 2.85 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 2688025.00 | 2605443.66 | 3.072 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 2695327.00 | 2610496.68 | 3.147 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 2704571.00 | 2614863.80 | 3.317 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 2718493.00 | 2618628.82 | 3.674 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 2731256.00 | 2621867.81 | 4.005 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 2742122.00 | 2624649.12 | 4.284 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 2751632.00 | 2627033.61 | 4.528 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 2758856.00 | 2629075.09 | 4.704 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 2762323.00 | 2630820.84 | 4.761 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 2768034.00 | 2632312.19 | 4.903 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 2776927.00 | 2633585.10 | 5.162 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 2785353.00 | 2634670.77 | 5.41 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 2792142.00 | 2635596.16 | 5.607 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 2798617.00 | 2636384.49 | 5.797 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 2803233.00 | 2637055.76 | 5.928 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 2805756.00 | 2637627.13 | 5.992 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 2808052.00 | 2638113.30 | 6.052 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 2811951.00 | 2638526.86 | 6.167 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 2818378.00 | 2638878.57 | 6.369 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 2824425.00 | 2639177.61 | 6.559 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 2829196.00 | 2639431.83 | 6.707 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-05-09 | Sunday | 2639647.91 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 2639831.56 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 2639987.61 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 2640120.22 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 2640232.89 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 2640328.61 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 2640409.92 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 2640479.00 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 2640537.68 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 2640587.53 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 2640629.86 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 2640665.83 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 2640696.37 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 2640722.32 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 2640744.35 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 2640763.06 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 2640778.96 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 2640792.46 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 2640803.92 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 2640813.66 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 2640821.93 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 2640828.96 |
## +----+------------+-----------------+---------------------+
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 153.4438 2543.205 1126.811 -Inf Inf 0.2369805 -0.004435005
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 1.127032
## Beta: 0.3404099
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -0.08133717
## [2,] 1.11499478
##
## Sigma: 2543.205
## AIC: 9745.859
#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 45 days by using bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
paste(MAPE_Mean_All.bats,"%")
## [1] "3.462 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Poland %"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-03-25 | Thursday | 2154821.00 | 2145514.70 | 0.432 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 2189966.00 | 2168864.31 | 0.964 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 2221725.00 | 2192213.93 | 1.328 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 2250991.00 | 2215563.54 | 1.574 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 2267964.00 | 2238913.16 | 1.281 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 2288826.00 | 2262262.77 | 1.161 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 2321717.00 | 2285612.39 | 1.555 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 2356970.00 | 2308962.00 | 2.037 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 2387511.00 | 2332311.62 | 2.312 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 2415584.00 | 2355661.23 | 2.481 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 2438542.00 | 2379010.85 | 2.441 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 2448463.00 | 2402360.46 | 1.883 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 2456709.00 | 2425710.08 | 1.262 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 2471617.00 | 2449059.69 | 0.913 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 2499507.00 | 2472409.31 | 1.084 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 2528006.00 | 2495758.92 | 1.276 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 2552898.00 | 2519108.53 | 1.324 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 2574631.00 | 2542458.15 | 1.25 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 2586647.00 | 2565807.76 | 0.806 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 2599850.00 | 2589157.38 | 0.411 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 2621116.00 | 2612506.99 | 0.328 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 2642242.00 | 2635856.61 | 0.242 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 2660088.00 | 2659206.22 | 0.033 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 2675874.00 | 2682555.84 | 0.25 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 2688025.00 | 2705905.45 | 0.665 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 2695327.00 | 2729255.07 | 1.259 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 2704571.00 | 2752604.68 | 1.776 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 2718493.00 | 2775954.30 | 2.114 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 2731256.00 | 2799303.91 | 2.491 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 2742122.00 | 2822653.53 | 2.937 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 2751632.00 | 2846003.14 | 3.43 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 2758856.00 | 2869352.75 | 4.005 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 2762323.00 | 2892702.37 | 4.72 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 2768034.00 | 2916051.98 | 5.347 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 2776927.00 | 2939401.60 | 5.851 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 2785353.00 | 2962751.21 | 6.369 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 2792142.00 | 2986100.83 | 6.947 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 2798617.00 | 3009450.44 | 7.533 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 2803233.00 | 3032800.06 | 8.189 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 2805756.00 | 3056149.67 | 8.924 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 2808052.00 | 3079499.29 | 9.667 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 2811951.00 | 3102848.90 | 10.345 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 2818378.00 | 3126198.52 | 10.922 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 2824425.00 | 3149548.13 | 11.511 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 2829196.00 | 3172897.75 | 12.148 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-05-09 | Sunday | 3196247.36 | 2977845.19 | 2862230.06 | 2977845.19 | 2862230.06 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3219596.97 | 2994446.75 | 2875259.42 | 2994446.75 | 2875259.42 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3242946.59 | 3010980.28 | 2888184.74 | 3010980.28 | 2888184.74 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3266296.20 | 3027446.46 | 2901007.04 | 3027446.46 | 2901007.04 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3289645.82 | 3043845.92 | 2913727.32 | 3043845.92 | 2913727.32 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3312995.43 | 3060179.31 | 2926346.54 | 3060179.31 | 2926346.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3336345.05 | 3076447.24 | 2938865.65 | 3076447.24 | 2938865.65 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3359694.66 | 3092650.31 | 2951285.57 | 3092650.31 | 2951285.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3383044.28 | 3108789.10 | 2963607.18 | 3108789.10 | 2963607.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3406393.89 | 3124864.17 | 2975831.34 | 3124864.17 | 2975831.34 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3429743.51 | 3140876.09 | 2987958.91 | 3140876.09 | 2987958.91 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3453093.12 | 3156825.38 | 2999990.71 | 3156825.38 | 2999990.71 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3476442.74 | 3172712.57 | 3011927.54 | 3172712.57 | 3011927.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3499792.35 | 3188538.18 | 3023770.18 | 3188538.18 | 3023770.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3523141.97 | 3204302.70 | 3035519.39 | 3204302.70 | 3035519.39 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3546491.58 | 3220006.62 | 3047175.92 | 3220006.62 | 3047175.92 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3569841.20 | 3235650.42 | 3058740.51 | 3235650.42 | 3058740.51 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3593190.81 | 3251234.56 | 3070213.85 | 3251234.56 | 3070213.85 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3616540.42 | 3266759.49 | 3081596.65 | 3266759.49 | 3081596.65 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 3639890.04 | 3282225.66 | 3092889.58 | 3282225.66 | 3092889.58 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 3663239.65 | 3297633.51 | 3104093.30 | 3297633.51 | 3104093.30 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 3686589.27 | 3312983.45 | 3115208.48 | 3312983.45 | 3115208.48 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
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 152.4499 2532.129 1217.418 NaN Inf 0.2560361 -0.005657954
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 1.127334
## Beta: 0.3413824
## Damping Parameter: 1
## Gamma-1 Values: -0.002897789
## Gamma-2 Values: -0.0002014399
##
## Seed States:
## [,1]
## [1,] 1.102094
## [2,] -3.900142
## [3,] -239.394132
## [4,] 23.871110
## [5,] 28.240407
## [6,] 41.565978
##
## Sigma: 2532.129
## AIC: 9753.957
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 45 days by using TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "3.43 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Poland %"
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 45 days in TBATS Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-03-25 | Thursday | 2154821.00 | 2145464.19 | 0.434 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 2 | 2021-03-26 | Friday | 2189966.00 | 2168466.81 | 0.982 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 3 | 2021-03-27 | Saturday | 2221725.00 | 2191530.39 | 1.359 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 4 | 2021-03-28 | Sunday | 2250991.00 | 2214745.59 | 1.61 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 5 | 2021-03-29 | Monday | 2267964.00 | 2238128.33 | 1.316 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 6 | 2021-03-30 | Tuesday | 2288826.00 | 2261689.41 | 1.186 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 7 | 2021-03-31 | Wednesday | 2321717.00 | 2285022.00 | 1.581 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 8 | 2021-04-01 | Thursday | 2356970.00 | 2308024.62 | 2.077 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 9 | 2021-04-02 | Friday | 2387511.00 | 2331088.20 | 2.363 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 10 | 2021-04-03 | Saturday | 2415584.00 | 2354303.40 | 2.537 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 11 | 2021-04-04 | Sunday | 2438542.00 | 2377686.13 | 2.496 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 12 | 2021-04-05 | Monday | 2448463.00 | 2401247.22 | 1.928 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 13 | 2021-04-06 | Tuesday | 2456709.00 | 2424579.81 | 1.308 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 14 | 2021-04-07 | Wednesday | 2471617.00 | 2447582.42 | 0.972 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 15 | 2021-04-08 | Thursday | 2499507.00 | 2470646.01 | 1.155 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 16 | 2021-04-09 | Friday | 2528006.00 | 2493861.21 | 1.351 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 17 | 2021-04-10 | Saturday | 2552898.00 | 2517243.94 | 1.397 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 18 | 2021-04-11 | Sunday | 2574631.00 | 2540805.03 | 1.314 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 19 | 2021-04-12 | Monday | 2586647.00 | 2564137.61 | 0.87 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 20 | 2021-04-13 | Tuesday | 2599850.00 | 2587140.23 | 0.489 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 21 | 2021-04-14 | Wednesday | 2621116.00 | 2610203.82 | 0.416 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 22 | 2021-04-15 | Thursday | 2642242.00 | 2633419.02 | 0.334 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 23 | 2021-04-16 | Friday | 2660088.00 | 2656801.75 | 0.124 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 24 | 2021-04-17 | Saturday | 2675874.00 | 2680362.84 | 0.168 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 25 | 2021-04-18 | Sunday | 2688025.00 | 2703695.42 | 0.583 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 26 | 2021-04-19 | Monday | 2695327.00 | 2726698.04 | 1.164 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 27 | 2021-04-20 | Tuesday | 2704571.00 | 2749761.63 | 1.671 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 28 | 2021-04-21 | Wednesday | 2718493.00 | 2772976.83 | 2.004 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 29 | 2021-04-22 | Thursday | 2731256.00 | 2796359.56 | 2.384 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 30 | 2021-04-23 | Friday | 2742122.00 | 2819920.65 | 2.837 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 31 | 2021-04-24 | Saturday | 2751632.00 | 2843253.23 | 3.33 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 32 | 2021-04-25 | Sunday | 2758856.00 | 2866255.85 | 3.893 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 33 | 2021-04-26 | Monday | 2762323.00 | 2889319.44 | 4.597 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 34 | 2021-04-27 | Tuesday | 2768034.00 | 2912534.64 | 5.22 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 35 | 2021-04-28 | Wednesday | 2776927.00 | 2935917.37 | 5.725 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 36 | 2021-04-29 | Thursday | 2785353.00 | 2959478.46 | 6.251 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 37 | 2021-04-30 | Friday | 2792142.00 | 2982811.04 | 6.829 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 38 | 2021-05-01 | Saturday | 2798617.00 | 3005813.66 | 7.404 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 39 | 2021-05-02 | Sunday | 2803233.00 | 3028877.25 | 8.049 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 40 | 2021-05-03 | Monday | 2805756.00 | 3052092.45 | 8.78 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 41 | 2021-05-04 | Tuesday | 2808052.00 | 3075475.18 | 9.523 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 42 | 2021-05-05 | Wednesday | 2811951.00 | 3099036.27 | 10.209 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 43 | 2021-05-06 | Thursday | 2818378.00 | 3122368.85 | 10.786 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 44 | 2021-05-07 | Friday | 2824425.00 | 3145371.47 | 11.363 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
## | 45 | 2021-05-08 | Saturday | 2829196.00 | 3168435.06 | 11.991 % |
## +----+------------+-------------------------+-------------+-------------------+------------------+
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 | 2021-05-09 | Sunday | 3191650.26 | 3168320.97 | 3155971.19 | 3214979.54 | 3227329.32 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3215032.99 | 3191480.55 | 3179012.64 | 3238585.43 | 3251053.34 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3238594.08 | 3214822.29 | 3202238.26 | 3262365.87 | 3274949.89 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3261926.66 | 3237940.04 | 3225242.30 | 3285913.28 | 3298611.02 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3284929.28 | 3260731.81 | 3247922.45 | 3309126.75 | 3321936.11 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3307992.87 | 3283586.93 | 3270667.20 | 3332398.81 | 3345318.53 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3331208.06 | 3306595.42 | 3293566.27 | 3355820.71 | 3368849.86 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3354590.80 | 3329773.83 | 3316636.51 | 3379407.77 | 3392545.08 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3378151.89 | 3353133.85 | 3339890.10 | 3403169.93 | 3416413.68 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3401484.47 | 3376269.32 | 3362921.22 | 3426699.62 | 3440047.72 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3424487.09 | 3399078.29 | 3385627.68 | 3449895.89 | 3463346.49 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3447550.68 | 3421950.22 | 3408398.15 | 3473151.14 | 3486703.20 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3470765.87 | 3444975.18 | 3431322.41 | 3496556.57 | 3510209.34 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3494148.61 | 3468169.69 | 3454417.28 | 3520127.53 | 3533879.94 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3517709.70 | 3491545.40 | 3477694.86 | 3543874.00 | 3557724.54 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3541042.28 | 3514696.12 | 3500749.30 | 3567388.44 | 3581335.25 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3564044.90 | 3537519.94 | 3523478.48 | 3590569.85 | 3604611.32 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3587108.49 | 3560406.43 | 3546271.21 | 3613810.55 | 3627945.76 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3610323.68 | 3583445.69 | 3569217.33 | 3637201.68 | 3651430.03 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 3633706.42 | 3606654.21 | 3592333.63 | 3660758.63 | 3675079.20 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 3657267.51 | 3630043.61 | 3615632.15 | 3684491.40 | 3698902.87 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 3680600.09 | 3653207.67 | 3638706.99 | 3707992.51 | 3722493.18 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
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 -79.51092 2684.228 1305.333 NaN Inf 0.2745257 0.2493017
# 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= 0.2875
##
## Smoothing parameters:
## alpha = 0.8678
## beta = 0.3122
##
## Initial states:
## l = -3.4791
## b = -3e-04
##
## sigma: 0.259
##
## AIC AICc BIC
## 1526.135 1526.271 1546.648
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -79.51092 2684.228 1305.333 NaN Inf 0.2745257 0.2493017
# 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 45 days by using holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
paste(MAPE_Mean_All.Holt,"%")
## [1] "5.188 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Poland %"
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 45 days in holt Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-03-25 | Thursday | 2154821.00 | 2142345.99 | 0.579 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 2 | 2021-03-26 | Friday | 2189966.00 | 2165581.53 | 1.113 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 2221725.00 | 2188996.07 | 1.473 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 2250991.00 | 2212590.43 | 1.706 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 5 | 2021-03-29 | Monday | 2267964.00 | 2236365.41 | 1.393 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 2288826.00 | 2260321.86 | 1.245 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 2321717.00 | 2284460.58 | 1.605 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 2356970.00 | 2308782.41 | 2.044 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 9 | 2021-04-02 | Friday | 2387511.00 | 2333288.17 | 2.271 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 2415584.00 | 2357978.69 | 2.385 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 2438542.00 | 2382854.79 | 2.284 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 12 | 2021-04-05 | Monday | 2448463.00 | 2407917.31 | 1.656 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 2456709.00 | 2433167.07 | 0.958 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 2471617.00 | 2458604.92 | 0.526 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 2499507.00 | 2484231.67 | 0.611 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 16 | 2021-04-09 | Friday | 2528006.00 | 2510048.17 | 0.71 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 2552898.00 | 2536055.25 | 0.66 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 2574631.00 | 2562253.75 | 0.481 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 19 | 2021-04-12 | Monday | 2586647.00 | 2588644.50 | 0.077 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 2599850.00 | 2615228.35 | 0.592 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 2621116.00 | 2642006.13 | 0.797 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 2642242.00 | 2668978.69 | 1.012 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 23 | 2021-04-16 | Friday | 2660088.00 | 2696146.87 | 1.356 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 2675874.00 | 2723511.51 | 1.78 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 2688025.00 | 2751073.45 | 2.346 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 26 | 2021-04-19 | Monday | 2695327.00 | 2778833.55 | 3.098 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 2704571.00 | 2806792.65 | 3.78 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 2718493.00 | 2834951.60 | 4.284 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 2731256.00 | 2863311.25 | 4.835 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 30 | 2021-04-23 | Friday | 2742122.00 | 2891872.45 | 5.461 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 2751632.00 | 2920636.04 | 6.142 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 2758856.00 | 2949602.90 | 6.914 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 33 | 2021-04-26 | Monday | 2762323.00 | 2978773.86 | 7.836 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 2768034.00 | 3008149.78 | 8.675 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 2776927.00 | 3037731.52 | 9.392 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 2785353.00 | 3067519.95 | 10.13 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 37 | 2021-04-30 | Friday | 2792142.00 | 3097515.90 | 10.937 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 2798617.00 | 3127720.26 | 11.759 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 2803233.00 | 3158133.87 | 12.66 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 40 | 2021-05-03 | Monday | 2805756.00 | 3188757.61 | 13.651 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 2808052.00 | 3219592.33 | 14.656 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 2811951.00 | 3250638.89 | 15.601 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 2818378.00 | 3281898.17 | 16.446 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 44 | 2021-05-07 | Friday | 2824425.00 | 3313371.03 | 17.311 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 2829196.00 | 3345058.34 | 18.234 % |
## +----+------------+-------------------------+-------------+------------------+-----------------+
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 | 2021-05-09 | Sunday | 3376960.97 | 2559598.14 | 2189540.95 | 4365099.68 | 4964004.79 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3409079.79 | 2562813.69 | 2181504.83 | 4437691.65 | 5063364.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3441415.66 | 2565796.56 | 2173169.68 | 4511491.76 | 5164725.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3473969.47 | 2568548.51 | 2164541.28 | 4586514.90 | 5268119.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3506742.09 | 2571071.31 | 2155625.36 | 4662776.10 | 5373577.21 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3539734.38 | 2573366.68 | 2146427.62 | 4740290.58 | 5481131.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3572947.23 | 2575436.35 | 2136953.72 | 4819073.77 | 5590814.45 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3606381.52 | 2577282.04 | 2127209.29 | 4899141.25 | 5702658.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3640038.11 | 2578905.45 | 2117199.93 | 4980508.79 | 5816697.05 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3673917.90 | 2580308.27 | 2106931.19 | 5063192.35 | 5932963.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3708021.76 | 2581492.18 | 2096408.62 | 5147208.06 | 6051492.32 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3742350.58 | 2582458.86 | 2085637.72 | 5232572.22 | 6172317.67 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3776905.23 | 2583209.98 | 2074623.97 | 5319301.34 | 6295474.64 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3811686.60 | 2583747.19 | 2063372.81 | 5407412.07 | 6420998.63 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3846695.57 | 2584072.17 | 2051889.67 | 5496921.25 | 6548925.48 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3881933.03 | 2584186.55 | 2040179.94 | 5587845.93 | 6679291.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3917399.88 | 2584092.00 | 2028249.00 | 5680203.28 | 6812133.44 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3953096.98 | 2583790.16 | 2016102.19 | 5774010.70 | 6947488.49 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3989025.25 | 2583282.67 | 2003744.82 | 5869285.74 | 7085394.31 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4025185.56 | 2582571.19 | 1991182.19 | 5966046.14 | 7225889.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4061578.80 | 2581657.34 | 1978419.57 | 6064309.80 | 7369011.11 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4098205.88 | 2580542.77 | 1965462.20 | 6164094.83 | 7514799.68 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
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
##################
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Forecasting cumulative Covid 19 Infection cases in Poland"
kpss.test(data_series) # applay kpss test
## Warning in kpss.test(data_series): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: data_series
## KPSS Level = 5.83, 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) = 0.92708, 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 = -0.99858, Lag order = 7, p-value = 0.9386
## 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 ==> Forecasting cumulative Covid 19 Infection cases in Poland"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 4.0027, Truncation lag parameter = 5, p-value = 0.01
pp.test(diff1_x1) # applay pp test after taking first differences
## Warning in pp.test(diff1_x1): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: diff1_x1
## Dickey-Fuller Z(alpha) = -34.672, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.64341, Lag order = 7, p-value = 0.9752
## 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 Forecasting cumulative Covid 19 Infection cases in Poland"
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 = 0.18627, 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) = -453.07, 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 = -7.5056, 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) : 8360.113
## ARIMA(0,2,1) : 8256.93
## ARIMA(0,2,2) : 8250.052
## ARIMA(0,2,3) : 8252.034
## ARIMA(0,2,4) : 8217.45
## ARIMA(0,2,5) : 8205.835
## ARIMA(1,2,0) : 8310.175
## ARIMA(1,2,1) : 8251.025
## ARIMA(1,2,2) : 8252.072
## ARIMA(1,2,3) : 8253.792
## ARIMA(1,2,4) : 8204.097
## ARIMA(2,2,0) : 8291.035
## ARIMA(2,2,1) : 8250.601
## ARIMA(2,2,2) : 8191.93
## ARIMA(2,2,3) : 8238.013
## ARIMA(3,2,0) : 8275.246
## ARIMA(3,2,1) : 8244.853
## ARIMA(3,2,2) : 8174.075
## ARIMA(4,2,0) : 8261.746
## ARIMA(4,2,1) : 8236.541
## ARIMA(5,2,0) : 8222.867
##
##
##
## Best model: ARIMA(3,2,2)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(3,2,2)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.8821 -0.3805 -0.2771 -1.5385 0.8529
## s.e. 0.0593 0.0619 0.0519 0.0380 0.0425
##
## sigma^2 estimated as 5442695: log likelihood=-4080.94
## AIC=8173.88 AICc=8174.08 BIC=8198.47
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 3 2 2
strtoi(bestmodel[3])
## [1] 2
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" ") , ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in", frequency ,y_lab , sep=" "), ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.8821 -0.3805 -0.2771 -1.5385 0.8529
## s.e. 0.0593 0.0619 0.0519 0.0380 0.0425
##
## sigma^2 estimated as 5381541: log likelihood = -4080.94, aic = 8173.88
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Forecasting cumulative Covid 19 Infection cases in Poland"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 137.0867 2314.619 995.0878 1.015724 1.551364 0.2092777 -0.02536305
x1_model1$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(3,2,2)
## Q* = 45.626, df = 5, p-value = 1.082e-08
##
## 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 ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 = 148.75, 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 = 10828, 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 45 days by using bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "4.194 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Poland %"
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 45 days in bats Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-03-25 | Thursday | 2154821.00 | 2150015.70 | 0.223 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 2 | 2021-03-26 | Friday | 2189966.00 | 2178809.33 | 0.509 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 3 | 2021-03-27 | Saturday | 2221725.00 | 2203775.10 | 0.808 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 4 | 2021-03-28 | Sunday | 2250991.00 | 2225977.72 | 1.111 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 5 | 2021-03-29 | Monday | 2267964.00 | 2247352.23 | 0.909 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 6 | 2021-03-30 | Tuesday | 2288826.00 | 2270108.35 | 0.818 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 7 | 2021-03-31 | Wednesday | 2321717.00 | 2295163.95 | 1.144 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 8 | 2021-04-01 | Thursday | 2356970.00 | 2321951.68 | 1.486 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 9 | 2021-04-02 | Friday | 2387511.00 | 2349009.51 | 1.613 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 10 | 2021-04-03 | Saturday | 2415584.00 | 2375009.31 | 1.68 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 11 | 2021-04-04 | Sunday | 2438542.00 | 2399493.10 | 1.601 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 12 | 2021-04-05 | Monday | 2448463.00 | 2422967.35 | 1.041 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 13 | 2021-04-06 | Tuesday | 2456709.00 | 2446421.12 | 0.419 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 14 | 2021-04-07 | Wednesday | 2471617.00 | 2470661.04 | 0.039 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 15 | 2021-04-08 | Thursday | 2499507.00 | 2495881.97 | 0.145 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 16 | 2021-04-09 | Friday | 2528006.00 | 2521674.77 | 0.25 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 17 | 2021-04-10 | Saturday | 2552898.00 | 2547380.91 | 0.216 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 18 | 2021-04-11 | Sunday | 2574631.00 | 2572521.16 | 0.082 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 19 | 2021-04-12 | Monday | 2586647.00 | 2597036.75 | 0.402 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 20 | 2021-04-13 | Tuesday | 2599850.00 | 2621240.67 | 0.823 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 21 | 2021-04-14 | Wednesday | 2621116.00 | 2645564.16 | 0.933 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 22 | 2021-04-15 | Thursday | 2642242.00 | 2670284.81 | 1.061 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 23 | 2021-04-16 | Friday | 2660088.00 | 2695396.65 | 1.327 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 24 | 2021-04-17 | Saturday | 2675874.00 | 2720669.32 | 1.674 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 25 | 2021-04-18 | Sunday | 2688025.00 | 2745824.94 | 2.15 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 26 | 2021-04-19 | Monday | 2695327.00 | 2770707.73 | 2.797 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 27 | 2021-04-20 | Tuesday | 2704571.00 | 2795349.81 | 3.356 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 28 | 2021-04-21 | Wednesday | 2718493.00 | 2819915.83 | 3.731 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 29 | 2021-04-22 | Thursday | 2731256.00 | 2844581.93 | 4.149 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 30 | 2021-04-23 | Friday | 2742122.00 | 2869431.97 | 4.643 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 31 | 2021-04-24 | Saturday | 2751632.00 | 2894427.24 | 5.189 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 32 | 2021-04-25 | Sunday | 2758856.00 | 2919452.91 | 5.821 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 33 | 2021-04-26 | Monday | 2762323.00 | 2944399.16 | 6.591 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 34 | 2021-04-27 | Tuesday | 2768034.00 | 2969223.54 | 7.268 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 35 | 2021-04-28 | Wednesday | 2776927.00 | 2993962.22 | 7.816 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 36 | 2021-04-29 | Thursday | 2785353.00 | 3018693.68 | 8.377 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 37 | 2021-04-30 | Friday | 2792142.00 | 3043485.16 | 9.002 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 38 | 2021-05-01 | Saturday | 2798617.00 | 3068356.06 | 9.638 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 39 | 2021-05-02 | Sunday | 2803233.00 | 3093276.19 | 10.347 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 40 | 2021-05-03 | Monday | 2805756.00 | 3118192.90 | 11.136 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 41 | 2021-05-04 | Tuesday | 2808052.00 | 3143065.85 | 11.93 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 42 | 2021-05-05 | Wednesday | 2811951.00 | 3167887.85 | 12.658 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 43 | 2021-05-06 | Thursday | 2818378.00 | 3192682.51 | 13.281 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 44 | 2021-05-07 | Friday | 2824425.00 | 3217484.57 | 13.916 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
## | 45 | 2021-05-08 | Saturday | 2829196.00 | 3242317.68 | 14.602 % |
## +----+-----------------+-------------------------+-------------+------------------------+-----------------------+
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 | 2021-05-09 | Sunday | 3267182.94 | 3043769.10 | 2925500.96 | 3490596.77 | 3608864.91 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3292062.68 | 3061461.74 | 2939388.98 | 3522663.62 | 3644736.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3316934.37 | 3079070.59 | 2953153.10 | 3554798.16 | 3680715.64 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3341784.54 | 3096584.13 | 2966782.88 | 3586984.95 | 3716786.21 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3366614.77 | 3114005.14 | 2980281.68 | 3619224.40 | 3752947.86 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3391437.84 | 3131346.70 | 2993662.76 | 3651528.98 | 3789212.92 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3416268.14 | 3148623.04 | 3006940.29 | 3683913.23 | 3825595.98 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3441113.06 | 3165841.58 | 3020121.66 | 3716384.54 | 3862104.46 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3465970.12 | 3183000.30 | 3033205.12 | 3748939.95 | 3898735.12 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3490830.32 | 3200091.18 | 3046183.18 | 3781569.46 | 3935477.46 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3515684.62 | 3217106.38 | 3059048.60 | 3814262.85 | 3972320.63 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3540529.15 | 3234043.04 | 3071799.09 | 3847015.25 | 4009259.20 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3565366.44 | 3250904.35 | 3084438.18 | 3879828.52 | 4046294.70 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3590202.70 | 3267696.87 | 3096972.60 | 3912708.53 | 4083432.80 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3615043.51 | 3284426.39 | 3109408.26 | 3945660.63 | 4120678.76 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3639890.73 | 3301095.11 | 3121747.55 | 3978686.35 | 4158033.92 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3664742.16 | 3317701.37 | 3133989.07 | 4011782.96 | 4195495.25 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3689593.61 | 3334241.67 | 3146129.72 | 4044945.54 | 4233057.49 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3714441.69 | 3350713.38 | 3158167.24 | 4078170.00 | 4270716.13 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 3739285.63 | 3367116.34 | 3170101.82 | 4111454.91 | 4308469.43 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 3764127.19 | 3383452.80 | 3181935.95 | 4144801.58 | 4346318.43 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 3788969.16 | 3399725.90 | 3193672.97 | 4178212.42 | 4384265.36 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
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] "4.194 % MAPE 45 days Forecasting cumulative Covid 19 Infection cases in Poland"
## Ensembling (Average)
weight.model<-0.90# optimization 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_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)
y1<-if(re_bestmodel >= MAPE_Mean_All.bats_Model) {re_BATS*weight.model
} else {
(re_BATS*(1-weight.model))/4
}
y2<-if(re_bestmodel >= MAPE_Mean_All.TBATS_Model) {re_TBATS*weight.model
} else {
(re_TBATS*(1-weight.model))/4
}
y3<-if(re_bestmodel >= MAPE_Mean_All.Holt_Model) {re_holt*weight.model
} else {
(re_holt*(1-weight.model))/4
}
y4<-if(re_bestmodel >= MAPE_Mean_All.ARIMA_Model) {re_autoarima*weight.model
} else {
(re_autoarima*(1-weight.model))/4
}
y5<-if(re_bestmodel >= MAPE_Mean_All_NNAR) {re_NNAR*weight.model
} else {
(re_NNAR*(1-weight.model))/4
}
Ensembling.Average<-(y1+y2+y3+y4+y5)
# Testing Data Evaluation
validation_forecast<-head(Ensembling.Average,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 Ensembling (Average) for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 45 days by using Ensembling (Average) for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 45 days in Ensembling Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
paste(MAPE_Mean_EnsemblingAverage,"%")
## [1] "2.305 %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in Ensembling Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 45 days in Ensembling Model for ==> Forecasting cumulative Covid 19 Infection cases in Poland"
print(ascii(data.frame(date_Ensembling=validation_dates,validation_data_by_name,actual_data=testing_data,Ensembling=validation_forecast,MAPE_Ensembling)), type = "rest")
##
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | | date_Ensembling | validation_data_by_name | actual_data | Ensembling | MAPE_Ensembling |
## +====+=================+=========================+=============+============+=================+
## | 1 | 2021-03-25 | Thursday | 2154821.00 | 2146478.75 | 0.387 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 2 | 2021-03-26 | Friday | 2189966.00 | 2172756.23 | 0.786 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 3 | 2021-03-27 | Saturday | 2221725.00 | 2199369.31 | 1.006 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 4 | 2021-03-28 | Sunday | 2250991.00 | 2226223.29 | 1.1 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 5 | 2021-03-29 | Monday | 2267964.00 | 2253221.72 | 0.65 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 6 | 2021-03-30 | Tuesday | 2288826.00 | 2280255.50 | 0.374 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 7 | 2021-03-31 | Wednesday | 2321717.00 | 2307157.25 | 0.627 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 8 | 2021-04-01 | Thursday | 2356970.00 | 2333720.15 | 0.986 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 9 | 2021-04-02 | Friday | 2387511.00 | 2359724.29 | 1.164 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 10 | 2021-04-03 | Saturday | 2415584.00 | 2384950.49 | 1.268 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 11 | 2021-04-04 | Sunday | 2438542.00 | 2409212.51 | 1.203 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 12 | 2021-04-05 | Monday | 2448463.00 | 2432368.72 | 0.657 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 13 | 2021-04-06 | Tuesday | 2456709.00 | 2454306.11 | 0.098 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 14 | 2021-04-07 | Wednesday | 2471617.00 | 2474946.23 | 0.135 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 15 | 2021-04-08 | Thursday | 2499507.00 | 2494241.31 | 0.211 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 16 | 2021-04-09 | Friday | 2528006.00 | 2512154.60 | 0.627 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 17 | 2021-04-10 | Saturday | 2552898.00 | 2528672.81 | 0.949 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 18 | 2021-04-11 | Sunday | 2574631.00 | 2543814.84 | 1.197 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 19 | 2021-04-12 | Monday | 2586647.00 | 2557622.71 | 1.122 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 20 | 2021-04-13 | Tuesday | 2599850.00 | 2570173.20 | 1.141 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 21 | 2021-04-14 | Wednesday | 2621116.00 | 2581570.93 | 1.509 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 22 | 2021-04-15 | Thursday | 2642242.00 | 2591916.88 | 1.905 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 23 | 2021-04-16 | Friday | 2660088.00 | 2601306.54 | 2.21 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 24 | 2021-04-17 | Saturday | 2675874.00 | 2609829.68 | 2.468 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 25 | 2021-04-18 | Sunday | 2688025.00 | 2617561.78 | 2.621 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 26 | 2021-04-19 | Monday | 2695327.00 | 2624584.37 | 2.625 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 27 | 2021-04-20 | Tuesday | 2704571.00 | 2630990.14 | 2.721 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 28 | 2021-04-21 | Wednesday | 2718493.00 | 2636860.90 | 3.003 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 29 | 2021-04-22 | Thursday | 2731256.00 | 2642269.95 | 3.258 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 30 | 2021-04-23 | Friday | 2742122.00 | 2647281.18 | 3.459 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 31 | 2021-04-24 | Saturday | 2751632.00 | 2651938.24 | 3.623 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 32 | 2021-04-25 | Sunday | 2758856.00 | 2656284.19 | 3.718 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 33 | 2021-04-26 | Monday | 2762323.00 | 2660368.63 | 3.691 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 34 | 2021-04-27 | Tuesday | 2768034.00 | 2664229.97 | 3.75 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 35 | 2021-04-28 | Wednesday | 2776927.00 | 2667901.91 | 3.926 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 36 | 2021-04-29 | Thursday | 2785353.00 | 2671414.78 | 4.091 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 37 | 2021-04-30 | Friday | 2792142.00 | 2674784.36 | 4.203 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 38 | 2021-05-01 | Saturday | 2798617.00 | 2678029.55 | 4.309 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 39 | 2021-05-02 | Sunday | 2803233.00 | 2681177.37 | 4.354 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 40 | 2021-05-03 | Monday | 2805756.00 | 2684244.23 | 4.331 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 41 | 2021-05-04 | Tuesday | 2808052.00 | 2687242.79 | 4.302 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 42 | 2021-05-05 | Wednesday | 2811951.00 | 2690184.47 | 4.33 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 43 | 2021-05-06 | Thursday | 2818378.00 | 2693069.41 | 4.446 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 44 | 2021-05-07 | Friday | 2824425.00 | 2695904.23 | 4.55 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
## | 45 | 2021-05-08 | Saturday | 2829196.00 | 2698706.37 | 4.612 % |
## +----+-----------------+-------------------------+-------------+------------+-----------------+
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_Ensembling=tail(Ensembling.Average,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+---------------------------+
## | | FD | forecating_date | forecasting_by_Ensembling |
## +====+============+=================+===========================+
## | 1 | 2021-05-09 | Sunday | 2701484.16 |
## +----+------------+-----------------+---------------------------+
## | 2 | 2021-05-10 | Monday | 2704242.71 |
## +----+------------+-----------------+---------------------------+
## | 3 | 2021-05-11 | Tuesday | 2706986.12 |
## +----+------------+-----------------+---------------------------+
## | 4 | 2021-05-12 | Wednesday | 2709707.62 |
## +----+------------+-----------------+---------------------------+
## | 5 | 2021-05-13 | Thursday | 2712407.90 |
## +----+------------+-----------------+---------------------------+
## | 6 | 2021-05-14 | Friday | 2715099.76 |
## +----+------------+-----------------+---------------------------+
## | 7 | 2021-05-15 | Saturday | 2717788.14 |
## +----+------------+-----------------+---------------------------+
## | 8 | 2021-05-16 | Sunday | 2720475.60 |
## +----+------------+-----------------+---------------------------+
## | 9 | 2021-05-17 | Monday | 2723164.02 |
## +----+------------+-----------------+---------------------------+
## | 10 | 2021-05-18 | Tuesday | 2725844.44 |
## +----+------------+-----------------+---------------------------+
## | 11 | 2021-05-19 | Wednesday | 2728515.30 |
## +----+------------+-----------------+---------------------------+
## | 12 | 2021-05-20 | Thursday | 2731187.33 |
## +----+------------+-----------------+---------------------------+
## | 13 | 2021-05-21 | Friday | 2733863.74 |
## +----+------------+-----------------+---------------------------+
## | 14 | 2021-05-22 | Saturday | 2736545.84 |
## +----+------------+-----------------+---------------------------+
## | 15 | 2021-05-23 | Sunday | 2739234.68 |
## +----+------------+-----------------+---------------------------+
## | 16 | 2021-05-24 | Monday | 2741920.70 |
## +----+------------+-----------------+---------------------------+
## | 17 | 2021-05-25 | Tuesday | 2744601.77 |
## +----+------------+-----------------+---------------------------+
## | 18 | 2021-05-26 | Wednesday | 2747287.96 |
## +----+------------+-----------------+---------------------------+
## | 19 | 2021-05-27 | Thursday | 2749981.81 |
## +----+------------+-----------------+---------------------------+
## | 20 | 2021-05-28 | Friday | 2752683.99 |
## +----+------------+-----------------+---------------------------+
## | 21 | 2021-05-29 | Saturday | 2755395.07 |
## +----+------------+-----------------+---------------------------+
## | 22 | 2021-05-30 | Sunday | 2758105.17 |
## +----+------------+-----------------+---------------------------+
graph5<-autoplot(Ensembling.Average,xlab = paste ("Time in", frequency ,y_lab,"by using Ensembling models" , sep=" "), ylab=y_lab)
graph5
# 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_EnsemblingAverage)
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 ==> Forecasting cumulative Covid 19 Infection cases in Poland"
best_recommended_model
## [1] 2.305
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_EnsemblingAverage) {paste("Ensembling")}
panderOptions('table.split.table', Inf)
paste("Forecasting by using BATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using BATS Model ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-05-09 | Sunday | 3196247.36 | 2977845.19 | 2862230.06 | 2977845.19 | 2862230.06 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3219596.97 | 2994446.75 | 2875259.42 | 2994446.75 | 2875259.42 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3242946.59 | 3010980.28 | 2888184.74 | 3010980.28 | 2888184.74 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3266296.20 | 3027446.46 | 2901007.04 | 3027446.46 | 2901007.04 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3289645.82 | 3043845.92 | 2913727.32 | 3043845.92 | 2913727.32 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3312995.43 | 3060179.31 | 2926346.54 | 3060179.31 | 2926346.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3336345.05 | 3076447.24 | 2938865.65 | 3076447.24 | 2938865.65 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3359694.66 | 3092650.31 | 2951285.57 | 3092650.31 | 2951285.57 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3383044.28 | 3108789.10 | 2963607.18 | 3108789.10 | 2963607.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3406393.89 | 3124864.17 | 2975831.34 | 3124864.17 | 2975831.34 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3429743.51 | 3140876.09 | 2987958.91 | 3140876.09 | 2987958.91 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3453093.12 | 3156825.38 | 2999990.71 | 3156825.38 | 2999990.71 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3476442.74 | 3172712.57 | 3011927.54 | 3172712.57 | 3011927.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3499792.35 | 3188538.18 | 3023770.18 | 3188538.18 | 3023770.18 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3523141.97 | 3204302.70 | 3035519.39 | 3204302.70 | 3035519.39 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3546491.58 | 3220006.62 | 3047175.92 | 3220006.62 | 3047175.92 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3569841.20 | 3235650.42 | 3058740.51 | 3235650.42 | 3058740.51 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3593190.81 | 3251234.56 | 3070213.85 | 3251234.56 | 3070213.85 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3616540.42 | 3266759.49 | 3081596.65 | 3266759.49 | 3081596.65 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 3639890.04 | 3282225.66 | 3092889.58 | 3282225.66 | 3092889.58 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 3663239.65 | 3297633.51 | 3104093.30 | 3297633.51 | 3104093.30 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 3686589.27 | 3312983.45 | 3115208.48 | 3312983.45 | 3115208.48 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using TBATS Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using TBATS Model ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-05-09 | Sunday | 3191650.26 | 3168320.97 | 3155971.19 | 3214979.54 | 3227329.32 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3215032.99 | 3191480.55 | 3179012.64 | 3238585.43 | 3251053.34 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3238594.08 | 3214822.29 | 3202238.26 | 3262365.87 | 3274949.89 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3261926.66 | 3237940.04 | 3225242.30 | 3285913.28 | 3298611.02 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3284929.28 | 3260731.81 | 3247922.45 | 3309126.75 | 3321936.11 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3307992.87 | 3283586.93 | 3270667.20 | 3332398.81 | 3345318.53 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3331208.06 | 3306595.42 | 3293566.27 | 3355820.71 | 3368849.86 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3354590.80 | 3329773.83 | 3316636.51 | 3379407.77 | 3392545.08 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3378151.89 | 3353133.85 | 3339890.10 | 3403169.93 | 3416413.68 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3401484.47 | 3376269.32 | 3362921.22 | 3426699.62 | 3440047.72 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3424487.09 | 3399078.29 | 3385627.68 | 3449895.89 | 3463346.49 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3447550.68 | 3421950.22 | 3408398.15 | 3473151.14 | 3486703.20 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3470765.87 | 3444975.18 | 3431322.41 | 3496556.57 | 3510209.34 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3494148.61 | 3468169.69 | 3454417.28 | 3520127.53 | 3533879.94 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3517709.70 | 3491545.40 | 3477694.86 | 3543874.00 | 3557724.54 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3541042.28 | 3514696.12 | 3500749.30 | 3567388.44 | 3581335.25 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3564044.90 | 3537519.94 | 3523478.48 | 3590569.85 | 3604611.32 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3587108.49 | 3560406.43 | 3546271.21 | 3613810.55 | 3627945.76 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3610323.68 | 3583445.69 | 3569217.33 | 3637201.68 | 3651430.03 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 3633706.42 | 3606654.21 | 3592333.63 | 3660758.63 | 3675079.20 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 3657267.51 | 3630043.61 | 3615632.15 | 3684491.40 | 3698902.87 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 3680600.09 | 3653207.67 | 3638706.99 | 3707992.51 | 3722493.18 |
## +----+------------+-----------------+----------------------+------------+------------+------------+------------+
paste("Forecasting by using Holt's Linear Trend Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Holt's Linear Trend Model ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-05-09 | Sunday | 3376960.97 | 2559598.14 | 2189540.95 | 4365099.68 | 4964004.79 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3409079.79 | 2562813.69 | 2181504.83 | 4437691.65 | 5063364.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3441415.66 | 2565796.56 | 2173169.68 | 4511491.76 | 5164725.08 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3473969.47 | 2568548.51 | 2164541.28 | 4586514.90 | 5268119.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3506742.09 | 2571071.31 | 2155625.36 | 4662776.10 | 5373577.21 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3539734.38 | 2573366.68 | 2146427.62 | 4740290.58 | 5481131.59 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3572947.23 | 2575436.35 | 2136953.72 | 4819073.77 | 5590814.45 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3606381.52 | 2577282.04 | 2127209.29 | 4899141.25 | 5702658.54 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3640038.11 | 2578905.45 | 2117199.93 | 4980508.79 | 5816697.05 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3673917.90 | 2580308.27 | 2106931.19 | 5063192.35 | 5932963.62 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3708021.76 | 2581492.18 | 2096408.62 | 5147208.06 | 6051492.32 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3742350.58 | 2582458.86 | 2085637.72 | 5232572.22 | 6172317.67 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3776905.23 | 2583209.98 | 2074623.97 | 5319301.34 | 6295474.64 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3811686.60 | 2583747.19 | 2063372.81 | 5407412.07 | 6420998.63 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3846695.57 | 2584072.17 | 2051889.67 | 5496921.25 | 6548925.48 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3881933.03 | 2584186.55 | 2040179.94 | 5587845.93 | 6679291.50 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3917399.88 | 2584092.00 | 2028249.00 | 5680203.28 | 6812133.44 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3953096.98 | 2583790.16 | 2016102.19 | 5774010.70 | 6947488.49 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3989025.25 | 2583282.67 | 2003744.82 | 5869285.74 | 7085394.31 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 4025185.56 | 2582571.19 | 1991182.19 | 5966046.14 | 7225889.00 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 4061578.80 | 2581657.34 | 1978419.57 | 6064309.80 | 7369011.11 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 4098205.88 | 2580542.77 | 1965462.20 | 6164094.83 | 7514799.68 |
## +----+------------+-----------------+---------------------+------------+------------+------------+------------+
paste("Forecasting by using ARIMA Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using ARIMA Model ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-05-09 | Sunday | 3267182.94 | 3043769.10 | 2925500.96 | 3490596.77 | 3608864.91 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 2 | 2021-05-10 | Monday | 3292062.68 | 3061461.74 | 2939388.98 | 3522663.62 | 3644736.38 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 3 | 2021-05-11 | Tuesday | 3316934.37 | 3079070.59 | 2953153.10 | 3554798.16 | 3680715.64 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 4 | 2021-05-12 | Wednesday | 3341784.54 | 3096584.13 | 2966782.88 | 3586984.95 | 3716786.21 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 5 | 2021-05-13 | Thursday | 3366614.77 | 3114005.14 | 2980281.68 | 3619224.40 | 3752947.86 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 6 | 2021-05-14 | Friday | 3391437.84 | 3131346.70 | 2993662.76 | 3651528.98 | 3789212.92 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 7 | 2021-05-15 | Saturday | 3416268.14 | 3148623.04 | 3006940.29 | 3683913.23 | 3825595.98 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 8 | 2021-05-16 | Sunday | 3441113.06 | 3165841.58 | 3020121.66 | 3716384.54 | 3862104.46 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 9 | 2021-05-17 | Monday | 3465970.12 | 3183000.30 | 3033205.12 | 3748939.95 | 3898735.12 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 10 | 2021-05-18 | Tuesday | 3490830.32 | 3200091.18 | 3046183.18 | 3781569.46 | 3935477.46 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 11 | 2021-05-19 | Wednesday | 3515684.62 | 3217106.38 | 3059048.60 | 3814262.85 | 3972320.63 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 12 | 2021-05-20 | Thursday | 3540529.15 | 3234043.04 | 3071799.09 | 3847015.25 | 4009259.20 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 13 | 2021-05-21 | Friday | 3565366.44 | 3250904.35 | 3084438.18 | 3879828.52 | 4046294.70 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 14 | 2021-05-22 | Saturday | 3590202.70 | 3267696.87 | 3096972.60 | 3912708.53 | 4083432.80 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 15 | 2021-05-23 | Sunday | 3615043.51 | 3284426.39 | 3109408.26 | 3945660.63 | 4120678.76 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 16 | 2021-05-24 | Monday | 3639890.73 | 3301095.11 | 3121747.55 | 3978686.35 | 4158033.92 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 17 | 2021-05-25 | Tuesday | 3664742.16 | 3317701.37 | 3133989.07 | 4011782.96 | 4195495.25 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 18 | 2021-05-26 | Wednesday | 3689593.61 | 3334241.67 | 3146129.72 | 4044945.54 | 4233057.49 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 19 | 2021-05-27 | Thursday | 3714441.69 | 3350713.38 | 3158167.24 | 4078170.00 | 4270716.13 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 20 | 2021-05-28 | Friday | 3739285.63 | 3367116.34 | 3170101.82 | 4111454.91 | 4308469.43 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 21 | 2021-05-29 | Saturday | 3764127.19 | 3383452.80 | 3181935.95 | 4144801.58 | 4346318.43 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
## | 22 | 2021-05-30 | Sunday | 3788969.16 | 3399725.90 | 3193672.97 | 4178212.42 | 4384265.36 |
## +----+------------+-----------------+---------------------------+------------+------------+------------+------------+
paste("Forecasting by using NNAR Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using NNAR Model ==> Forecasting cumulative Covid 19 Infection cases in Poland"
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 | 2021-05-09 | Sunday | 2639647.91 |
## +----+------------+-----------------+---------------------+
## | 2 | 2021-05-10 | Monday | 2639831.56 |
## +----+------------+-----------------+---------------------+
## | 3 | 2021-05-11 | Tuesday | 2639987.61 |
## +----+------------+-----------------+---------------------+
## | 4 | 2021-05-12 | Wednesday | 2640120.22 |
## +----+------------+-----------------+---------------------+
## | 5 | 2021-05-13 | Thursday | 2640232.89 |
## +----+------------+-----------------+---------------------+
## | 6 | 2021-05-14 | Friday | 2640328.61 |
## +----+------------+-----------------+---------------------+
## | 7 | 2021-05-15 | Saturday | 2640409.92 |
## +----+------------+-----------------+---------------------+
## | 8 | 2021-05-16 | Sunday | 2640479.00 |
## +----+------------+-----------------+---------------------+
## | 9 | 2021-05-17 | Monday | 2640537.68 |
## +----+------------+-----------------+---------------------+
## | 10 | 2021-05-18 | Tuesday | 2640587.53 |
## +----+------------+-----------------+---------------------+
## | 11 | 2021-05-19 | Wednesday | 2640629.86 |
## +----+------------+-----------------+---------------------+
## | 12 | 2021-05-20 | Thursday | 2640665.83 |
## +----+------------+-----------------+---------------------+
## | 13 | 2021-05-21 | Friday | 2640696.37 |
## +----+------------+-----------------+---------------------+
## | 14 | 2021-05-22 | Saturday | 2640722.32 |
## +----+------------+-----------------+---------------------+
## | 15 | 2021-05-23 | Sunday | 2640744.35 |
## +----+------------+-----------------+---------------------+
## | 16 | 2021-05-24 | Monday | 2640763.06 |
## +----+------------+-----------------+---------------------+
## | 17 | 2021-05-25 | Tuesday | 2640778.96 |
## +----+------------+-----------------+---------------------+
## | 18 | 2021-05-26 | Wednesday | 2640792.46 |
## +----+------------+-----------------+---------------------+
## | 19 | 2021-05-27 | Thursday | 2640803.92 |
## +----+------------+-----------------+---------------------+
## | 20 | 2021-05-28 | Friday | 2640813.66 |
## +----+------------+-----------------+---------------------+
## | 21 | 2021-05-29 | Saturday | 2640821.93 |
## +----+------------+-----------------+---------------------+
## | 22 | 2021-05-30 | Sunday | 2640828.96 |
## +----+------------+-----------------+---------------------+
paste("Forecasting by using Ensembling Model ==> ", y_lab , sep=" ")
## [1] "Forecasting by using Ensembling Model ==> Forecasting cumulative Covid 19 Infection cases in Poland"
print(ascii(data.frame(FD,forecating_date=forecasting_data_by_name,forecasting.Ensembling=tail(Ensembling.Average,N_forecasting_days))), type = "rest")
##
## +----+------------+-----------------+------------------------+
## | | FD | forecating_date | forecasting.Ensembling |
## +====+============+=================+========================+
## | 1 | 2021-05-09 | Sunday | 2701484.16 |
## +----+------------+-----------------+------------------------+
## | 2 | 2021-05-10 | Monday | 2704242.71 |
## +----+------------+-----------------+------------------------+
## | 3 | 2021-05-11 | Tuesday | 2706986.12 |
## +----+------------+-----------------+------------------------+
## | 4 | 2021-05-12 | Wednesday | 2709707.62 |
## +----+------------+-----------------+------------------------+
## | 5 | 2021-05-13 | Thursday | 2712407.90 |
## +----+------------+-----------------+------------------------+
## | 6 | 2021-05-14 | Friday | 2715099.76 |
## +----+------------+-----------------+------------------------+
## | 7 | 2021-05-15 | Saturday | 2717788.14 |
## +----+------------+-----------------+------------------------+
## | 8 | 2021-05-16 | Sunday | 2720475.60 |
## +----+------------+-----------------+------------------------+
## | 9 | 2021-05-17 | Monday | 2723164.02 |
## +----+------------+-----------------+------------------------+
## | 10 | 2021-05-18 | Tuesday | 2725844.44 |
## +----+------------+-----------------+------------------------+
## | 11 | 2021-05-19 | Wednesday | 2728515.30 |
## +----+------------+-----------------+------------------------+
## | 12 | 2021-05-20 | Thursday | 2731187.33 |
## +----+------------+-----------------+------------------------+
## | 13 | 2021-05-21 | Friday | 2733863.74 |
## +----+------------+-----------------+------------------------+
## | 14 | 2021-05-22 | Saturday | 2736545.84 |
## +----+------------+-----------------+------------------------+
## | 15 | 2021-05-23 | Sunday | 2739234.68 |
## +----+------------+-----------------+------------------------+
## | 16 | 2021-05-24 | Monday | 2741920.70 |
## +----+------------+-----------------+------------------------+
## | 17 | 2021-05-25 | Tuesday | 2744601.77 |
## +----+------------+-----------------+------------------------+
## | 18 | 2021-05-26 | Wednesday | 2747287.96 |
## +----+------------+-----------------+------------------------+
## | 19 | 2021-05-27 | Thursday | 2749981.81 |
## +----+------------+-----------------+------------------------+
## | 20 | 2021-05-28 | Friday | 2752683.99 |
## +----+------------+-----------------+------------------------+
## | 21 | 2021-05-29 | Saturday | 2755395.07 |
## +----+------------+-----------------+------------------------+
## | 22 | 2021-05-30 | Sunday | 2758105.17 |
## +----+------------+-----------------+------------------------+
result<-c(x1,x2,x3,x4,x5,x6)
table.error<-data.frame(country.name,NNAR.model=MAPE_Mean_All_NNAR, BATS.Model=MAPE_Mean_All.bats_Model,TBATS.Model=MAPE_Mean_All.TBATS_Model,Holt.Model=MAPE_Mean_All.Holt_Model,ARIMA.Model=MAPE_Mean_All.ARIMA_Model,Ensemblingt=MAPE_Mean_EnsemblingAverage,Best.Model=result)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------------+------+
## | | country.name | NNAR.model | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Ensemblingt | Best.Model | Freq |
## +===+==============+============+============+=============+============+=============+=============+============+======+
## | 1 | Poland | 2.897 | 3.462 | 3.43 | 5.188 | 4.194 | 2.305 | Ensembling | 1.00 |
## +---+--------------+------------+------------+-------------+------------+-------------+-------------+------------+------+
MAPE.Value<-c(MAPE_Mean_All_NNAR,MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model,MAPE_Mean_EnsemblingAverage)
Model<-c("NNAR.model","BATS.Model","TBATS.Model","Holt.Model","ARIMA.Model","Ensembling.weight")
channel_data<-data.frame(Model,MAPE.Value)
# Normally, the entire expression below would be assigned to an object, but we're
# going bare bones here.
ggplot(channel_data, aes(x = Model, y = MAPE.Value)) +
geom_bar(stat = "identity") +
geom_text(aes(label = MAPE.Value)) + # x AND y INHERITED. WE JUST NEED TO SPECIFY "label"
coord_flip() +
scale_y_continuous(expand = c(0, 0))
message("System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and Ensembling Model ==>",y_lab, sep=" ")
## System finished Modelling and Forecasting by using BATS, TBATS, Holt's Linear Trend,ARIMA Model, and Ensembling Model ==>Forecasting cumulative Covid 19 Infection cases in Poland
message(" Thank you for using our System For Modelling and Forecasting ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling and Forecasting ==> Forecasting cumulative Covid 19 Infection cases in Poland