Jawaharlal Nehru Krishi Vishwavidyalaya, India
#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
##Global vriable##
Full_original_data <- read_excel("F:/Phd/Covid 19 in SAARC/Covid 19 in SAARC.xlsx", sheet = "india") # path of your data ( time series data)
original_data<-Full_original_data$Cumulative_cases
y_lab <- "Covid 19 deaths cases in india" # input name of data
Actual_date_interval <- c("2020/03/01","2021/03/10")
Forecast_date_interval <- c("2021/03/11","2021/03/17")
validation_data_days <-7
frequency<-"day"
country.name <- "india"
# Data Preparation & calculate some of statistics measures
summary(original_data) # Summary your time series
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 17265 1964536 4197111 9095806 11262707
# calculate standard deviation
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.4240798
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 1.438539
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 4425430
#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
##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 training 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 228.2447 13180.27 6055.134 NaN Inf 0.2310183 0.07705743
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.4266192
## Beta: 0.1583616
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -25.093285
## [2,] 2.274036
##
## Sigma: 13180.27
## AIC: 10669.67
#ploting BATS Model
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 day by using bats Model for ==> Covid 19 deaths cases in india"
MAPE_Mean_All.bats_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.bats<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_bats<-paste(round(MAPE_Per_Day,3),"%")
MAPE_bats_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Covid 19 deaths cases in india"
paste(MAPE_Mean_All.bats,"%")
## [1] "0.067 % MAPE 7 day Covid 19 deaths cases in india %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Covid 19 deaths cases in india"
data.frame(date_bats=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_bats=validation_forecast,MAPE_bats_Model)
## date_bats validation_data_by_name actual_data forecasting_bats
## 1 2021-03-04 Thursday 11156923 11156331
## 2 2021-03-05 Friday 11173761 11171731
## 3 2021-03-06 Saturday 11192088 11187131
## 4 2021-03-07 Sunday 11210799 11202531
## 5 2021-03-08 Monday 11229398 11217932
## 6 2021-03-09 Tuesday 11244786 11233332
## 7 2021-03-10 Wednesday 11262707 11248732
## MAPE_bats_Model
## 1 0.005 %
## 2 0.018 %
## 3 0.044 %
## 4 0.074 %
## 5 0.102 %
## 6 0.102 %
## 7 0.124 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_bats=tail(forecasting_bats$mean,N_forecasting_days))
## FD forecating_date forecasting_by_bats
## 1 2021-03-11 Thursday 11264132
## 2 2021-03-12 Friday 11279532
## 3 2021-03-13 Saturday 11294932
## 4 2021-03-14 Sunday 11310332
## 5 2021-03-15 Monday 11325733
## 6 2021-03-16 Tuesday 11341133
## 7 2021-03-17 Wednesday 11356533
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph1
## Error of forecasting
Error_bats<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_bats<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_bats<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_bats<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_bats<-sqrt(sum((Error_bats^2))/validation_data_days) # Root mean square forecast error
MSE_bats<-(sum((Error_bats^2))/validation_data_days) # Root mean square forecast error
MAD_bats<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_bats<-c(Error_bats)
REOF_Abats<-c(paste(round(REOF_A_bats,3),"%"))
REOF_Fbats<-c(paste(round(REOF_F_bats,3),"%"))
data.frame(correlation_bats,MSE_bats,RMSE_bats,MAPE_Mean_All.bats_Model,MAD_bats) # analysis of Error by using Bats Model shows result of correlation ,MSE ,MPER
## correlation_bats MSE_bats RMSE_bats MAPE_Mean_All.bats_Model MAD_bats
## 1 0.9997318 79339385 8907.266 0.067 7534.549
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_bats,REOF_Abats,REOF_Fbats) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_bats REOF_Abats REOF_Fbats
## 1 2021-03-04 Thursday 591.9493 0.005 % 0.005 %
## 2 2021-03-05 Friday 2029.8159 0.018 % 0.018 %
## 3 2021-03-06 Saturday 4956.6825 0.044 % 0.044 %
## 4 2021-03-07 Sunday 8267.5492 0.074 % 0.074 %
## 5 2021-03-08 Monday 11466.4158 0.102 % 0.102 %
## 6 2021-03-09 Tuesday 11454.2824 0.102 % 0.102 %
## 7 2021-03-10 Wednesday 13975.1491 0.124 % 0.124 %
## 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 227.5411 12983.43 6475.681 NaN Inf 0.2470632 0.07428195
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.4319085
## Beta: 0.1605974
## Damping Parameter: 1
## Gamma-1 Values: -0.003149591
## Gamma-2 Values: 0.005012398
##
## Seed States:
## [,1]
## [1,] 117.57024
## [2,] -72.81235
## [3,] -1163.38465
## [4,] -396.77379
## [5,] -728.23597
## [6,] 353.48945
##
## Sigma: 12983.43
## AIC: 10668.85
plot(model_TBATS,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
# Testing Data Evaluation
forecasting_tbats <- predict(model_TBATS, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_tbats$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 day by using TBATS Model for ==> Covid 19 deaths cases in india"
MAPE_Mean_All.TBATS_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.TBATS<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_TBATS<-paste(round(MAPE_Per_Day,3),"%")
MAPE_TBATS_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in TBATS Model for ==> Covid 19 deaths cases in india"
paste(MAPE_Mean_All.TBATS,"%")
## [1] "0.068 % MAPE 7 day Covid 19 deaths cases in india %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in TBATS Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in TBATS Model for ==> Covid 19 deaths cases in india"
data.frame(date_TBATS=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_TBATS=validation_forecast,MAPE_TBATS_Model)
## date_TBATS validation_data_by_name actual_data forecasting_TBATS
## 1 2021-03-04 Thursday 11156923 11153751
## 2 2021-03-05 Friday 11173761 11171724
## 3 2021-03-06 Saturday 11192088 11188389
## 4 2021-03-07 Sunday 11210799 11204370
## 5 2021-03-08 Monday 11229398 11219511
## 6 2021-03-09 Tuesday 11244786 11232040
## 7 2021-03-10 Wednesday 11262707 11246716
## MAPE_TBATS_Model
## 1 0.028 %
## 2 0.018 %
## 3 0.033 %
## 4 0.057 %
## 5 0.088 %
## 6 0.113 %
## 7 0.142 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_TBATS=tail(forecasting_tbats$mean,N_forecasting_days))
## FD forecating_date forecasting_by_TBATS
## 1 2021-03-11 Thursday 11264690
## 2 2021-03-12 Friday 11281355
## 3 2021-03-13 Saturday 11297336
## 4 2021-03-14 Sunday 11312477
## 5 2021-03-15 Monday 11325006
## 6 2021-03-16 Tuesday 11339682
## 7 2021-03-17 Wednesday 11357656
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph2
## Error of forecasting TBATS Model
Error_tbats<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_tbats1<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_tbats<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_tbats<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_tbats<-sqrt(sum((Error_tbats^2))/validation_data_days) # Root mean square forecast error
MSE_tbats<-(sum((Error_tbats^2))/validation_data_days) # Root mean square forecast error
MAD_tbats<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_tbats<-c(Error_tbats)
REOF_A_tbats<-c(paste(round(REOF_A_tbats1,3),"%"))
REOF_F_tbats<-c(paste(round(REOF_F_tbats,3),"%"))
data.frame(correlation_tbats,MSE_tbats,RMSE_tbats,MAPE_Mean_All.TBATS_Model,MAD_tbats) # analysis of Error by using TBATS model shows result of correlation ,MSE ,MPER
## correlation_tbats MSE_tbats RMSE_tbats MAPE_Mean_All.TBATS_Model MAD_tbats
## 1 0.9989753 83590656 9142.793 0.068 7708.645
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_tbats,REOF_A_tbats,REOF_F_tbats) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_tbats REOF_A_tbats REOF_F_tbats
## 1 2021-03-04 Thursday 3172.368 0.028 % 0.028 %
## 2 2021-03-05 Friday 2036.990 0.018 % 0.018 %
## 3 2021-03-06 Saturday 3698.565 0.033 % 0.033 %
## 4 2021-03-07 Sunday 6429.207 0.057 % 0.057 %
## 5 2021-03-08 Monday 9886.975 0.088 % 0.088 %
## 6 2021-03-09 Tuesday 12745.822 0.113 % 0.113 %
## 7 2021-03-10 Wednesday 15990.591 0.142 % 0.142 %
## 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 -1784.803 14083.39 5355.172 NaN Inf 0.204313 -0.2062556
# 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= 0.2949
##
## Smoothing parameters:
## alpha = 0.7943
## beta = 0.1578
##
## Initial states:
## l = -3.3946
## b = 0.0031
##
## sigma: 0.4689
##
## AIC AICc BIC
## 1939.861 1940.004 1960.133
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -1784.803 14083.39 5355.172 NaN Inf 0.204313 -0.2062556
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 day by using holt Model for ==> Covid 19 deaths cases in india"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> Covid 19 deaths cases in india"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.1 % MAPE 7 day Covid 19 deaths cases in india %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> Covid 19 deaths cases in india"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2021-03-04 Thursday 11156923 11154378
## 2 2021-03-05 Friday 11173761 11169170
## 3 2021-03-06 Saturday 11192088 11183976
## 4 2021-03-07 Sunday 11210799 11198796
## 5 2021-03-08 Monday 11229398 11213629
## 6 2021-03-09 Tuesday 11244786 11228477
## 7 2021-03-10 Wednesday 11262707 11243338
## MAPE_holt_Model
## 1 0.023 %
## 2 0.041 %
## 3 0.072 %
## 4 0.107 %
## 5 0.14 %
## 6 0.145 %
## 7 0.172 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2021-03-11 Thursday 11258213
## 2 2021-03-12 Friday 11273102
## 3 2021-03-13 Saturday 11288005
## 4 2021-03-14 Sunday 11302922
## 5 2021-03-15 Monday 11317852
## 6 2021-03-16 Tuesday 11332797
## 7 2021-03-17 Wednesday 11347756
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph3
## Error of forecasting by using Holt's linear model
Error_Holt<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_Holt1<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_Holt<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_Holt<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_Holt<-sqrt(sum((Error_Holt^2))/validation_data_days) # Root mean square forecast error
MSE_Holt<-(sum((Error_Holt^2))/validation_data_days) # Root mean square forecast error
MAD_Holt<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_Holt<-c(Error_Holt)
REOF_A_Holt<-c(paste(round(REOF_A_Holt1,3),"%"))
REOF_F_Holt<-c(paste(round(REOF_F_Holt,3),"%"))
REOF_A_Holt11<-mean(abs(((testing_data-validation_forecast)/testing_data)*100))
data.frame(correlation_Holt,MSE_Holt,RMSE_Holt,MAPE_Mean_All.Holt_Model,MAD_Holt) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_Holt MSE_Holt RMSE_Holt MAPE_Mean_All.Holt_Model MAD_Holt
## 1 0.9997226 161034066 12689.92 0.1 11242.58
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_Holt,REOF_A_Holt,REOF_F_Holt) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_Holt REOF_A_Holt REOF_F_Holt
## 1 2021-03-04 Thursday 2544.963 0.023 % 0.023 %
## 2 2021-03-05 Friday 4590.892 0.041 % 0.041 %
## 3 2021-03-06 Saturday 8111.996 0.072 % 0.073 %
## 4 2021-03-07 Sunday 12003.266 0.107 % 0.107 %
## 5 2021-03-08 Monday 15768.695 0.14 % 0.141 %
## 6 2021-03-09 Tuesday 16309.276 0.145 % 0.145 %
## 7 2021-03-10 Wednesday 19369.001 0.172 % 0.172 %
#Auto arima model
##################
require(tseries) # need to install tseries tj test Stationarity in time series
paste ("tests For Check Stationarity in series ==> ",y_lab, sep=" ")
## [1] "tests For Check Stationarity in series ==> Covid 19 deaths cases in india"
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 = 6.7529, Truncation lag parameter = 5, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -2.3528, Truncation lag parameter = 5, p-value
## = 0.9585
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
## Warning in adf.test(data_series): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -4.1766, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
ndiffs(data_series) # Doing first diffrencing on data
## [1] 2
#Taking the first difference
diff1_x1<-diff(data_series)
autoplot(diff1_x1, xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", ylab=y_lab,main = "1nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub
##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 ==> Covid 19 deaths cases in india"
kpss.test(diff1_x1) # applay kpss test after taking first differences
## Warning in kpss.test(diff1_x1): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: diff1_x1
## KPSS Level = 2.6829, 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) = -133.46, Truncation lag parameter = 5, p-value
## = 0.01
## alternative hypothesis: stationary
adf.test(diff1_x1) # applay adf test after taking first differences
## Warning in adf.test(diff1_x1): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: diff1_x1
## Dickey-Fuller = -0.28007, Lag order = 7, p-value = 0.99
## alternative hypothesis: stationary
#Taking the second difference
diff2_x1=diff(diff1_x1)
autoplot(diff2_x1, xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", ylab=y_lab ,main = "2nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub
##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 Covid 19 deaths cases in india"
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 = 0.052879, 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) = -574.57, 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 = -11.767, 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) : 9706.402
## ARIMA(0,2,1) : 9358.667
## ARIMA(0,2,2) : 9258.286
## ARIMA(0,2,3) : 9253.054
## ARIMA(0,2,4) : 9254.79
## ARIMA(0,2,5) : 9254.382
## ARIMA(1,2,0) : 9505.114
## ARIMA(1,2,1) : 9303.774
## ARIMA(1,2,2) : 9252.218
## ARIMA(1,2,3) : 9243.619
## ARIMA(1,2,4) : Inf
## ARIMA(2,2,0) : 9388.879
## ARIMA(2,2,1) : 9279.157
## ARIMA(2,2,2) : 9252.361
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 9332.426
## ARIMA(3,2,1) : 9274.907
## ARIMA(3,2,2) : 9248.451
## ARIMA(4,2,0) : 9312.259
## ARIMA(4,2,1) : 9273.657
## ARIMA(5,2,0) : 9271.711
##
##
##
## Best model: ARIMA(1,2,3)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(1,2,3)
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.9522 -2.3512 1.8461 -0.4792
## s.e. 0.0299 0.0595 0.1103 0.0562
##
## sigma^2 estimated as 168336440: log likelihood=-4616.74
## AIC=9243.48 AICc=9243.62 BIC=9263.72
#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("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 1 2 3
strtoi(bestmodel[3])
## [1] 3
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.9522 -2.3512 1.8461 -0.4792
## s.e. 0.0299 0.0595 0.1103 0.0562
##
## sigma^2 estimated as 166748360: log likelihood = -4616.74, aic = 9243.48
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Covid 19 deaths cases in india"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 143.8378 12882.76 5688.494 1.372526 2.51792 0.2170301 0.0245581
x1_model1$x # show result of best model from auto arima
## NULL
checkresiduals(x1_model1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab) # checkresiduals from best model from using auto arima
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,2,3)
## Q* = 10.222, df = 6, p-value = 0.1156
##
## Model df: 4. Total lags used: 10
paste("Box-Ljung test , Ljung-Box test For Modelling for ==> ",y_lab, sep=" ")
## [1] "Box-Ljung test , Ljung-Box test For Modelling for ==> Covid 19 deaths cases in india"
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 = 231.2, df = 20, p-value < 2.2e-16
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 6859.6, df = 2, p-value < 2.2e-16
#Actual Vs Fitted
plot(data_series, col='red',lwd=2, main="Actual vs Fitted Plot", xlab='Time in (days)', ylab=y_lab) # plot actual and Fitted model
lines(fitted(x1_model1), col='black')
#Test data
x1_test <- ts(testing_data, start =(rows-validation_data_days+1) ) # make testing data in time series and start from rows-6
forecasting_auto_arima <- forecast(x1_model1, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_auto_arima$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 day by using bats Model for ==> Covid 19 deaths cases in india"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Covid 19 deaths cases in india"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.029 % MAPE 7 day Covid 19 deaths cases in india %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Covid 19 deaths cases in india"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2021-03-04 Thursday 11156923 11156991
## 2 2021-03-05 Friday 11173761 11173302
## 3 2021-03-06 Saturday 11192088 11189798
## 4 2021-03-07 Sunday 11210799 11206472
## 5 2021-03-08 Monday 11229398 11223314
## 6 2021-03-09 Tuesday 11244786 11240316
## 7 2021-03-10 Wednesday 11262707 11257472
## MAPE_auto.arima_Model
## 1 0.001 %
## 2 0.004 %
## 3 0.02 %
## 4 0.039 %
## 5 0.054 %
## 6 0.04 %
## 7 0.046 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2021-03-11 Thursday 11274772
## 2 2021-03-12 Friday 11292212
## 3 2021-03-13 Saturday 11309783
## 4 2021-03-14 Sunday 11327480
## 5 2021-03-15 Monday 11345296
## 6 2021-03-16 Tuesday 11363226
## 7 2021-03-17 Wednesday 11381265
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=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph4
MAPE_Mean_All.ARIMA
## [1] "0.029 % MAPE 7 day Covid 19 deaths cases in india"
## Error of forecasting
Error_auto.arima<-abs(testing_data-validation_forecast) # Absolute error of forecast (AEOF)
REOF_A_auto.arima<-abs(((testing_data-validation_forecast)/testing_data)*100) #Relative error of forecast (divided by actual)(REOF_A)
REOF_F_auto.arima<-abs(((testing_data-validation_forecast)/validation_forecast)*100) #Relative error of forecast (divided by forecast)(REOF_F)
correlation_auto.arima<-cor(testing_data,validation_forecast, method = c("pearson")) # correlation coefficient between predicted and actual values
RMSE_auto.arima<-sqrt(sum((Error_auto.arima^2))/validation_data_days) # Root mean square forecast error
MSE_auto.arima<-(sum((Error_auto.arima^2))/validation_data_days) # Root mean square forecast error
MAD_auto.arima<-abs((sum(testing_data-validation_forecast))/validation_data_days) # average forecast accuracy
AEOF_auto.arima<-c(Error_auto.arima)
REOF_auto.arima1<-c(paste(round(REOF_A_auto.arima,3),"%"))
REOF_auto.arima2<-c(paste(round(REOF_F_auto.arima,3),"%"))
data.frame(correlation_auto.arima,MSE_auto.arima,RMSE_auto.arima,MAPE_Mean_All.ARIMA_Model,MAD_auto.arima) # analysis of Error by using Auto ARIMAA model shows result of correlation ,MSE ,MPER
## correlation_auto.arima MSE_auto.arima RMSE_auto.arima
## 1 0.9995999 15511472 3938.461
## MAPE_Mean_All.ARIMA_Model MAD_auto.arima
## 1 0.029 3256.607
data.frame(validation_dates,Validation_day_name=validation_data_by_name,AEOF_auto.arima,REOF_A_auto.arima=REOF_auto.arima1,REOF_F_auto.arima=REOF_auto.arima2) # Analysis of error shows result AEOF,REOF_A,REOF_F
## validation_dates Validation_day_name AEOF_auto.arima REOF_A_auto.arima
## 1 2021-03-04 Thursday 68.21188 0.001 %
## 2 2021-03-05 Friday 459.09742 0.004 %
## 3 2021-03-06 Saturday 2289.54999 0.02 %
## 4 2021-03-07 Sunday 4327.03163 0.039 %
## 5 2021-03-08 Monday 6084.00333 0.054 %
## 6 2021-03-09 Tuesday 4469.52156 0.04 %
## 7 2021-03-10 Wednesday 5235.25761 0.046 %
## REOF_F_auto.arima
## 1 0.001 %
## 2 0.004 %
## 3 0.02 %
## 4 0.039 %
## 5 0.054 %
## 6 0.04 %
## 7 0.047 %
# Table for MAPE For counry
best_recommended_model <- min(MAPE_Mean_All.bats_Model,MAPE_Mean_All.TBATS_Model,MAPE_Mean_All.Holt_Model,MAPE_Mean_All.ARIMA_Model)
paste("System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Choose Least Error ==> ( MAPE %) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> Covid 19 deaths cases in india"
best_recommended_model
## [1] 0.029
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")}
result<-c(x1,x2,x3,x4)
table.error<-data.frame(country.name,BATS.Model=MAPE_Mean_All.bats_Model,TBATS.Model=MAPE_Mean_All.TBATS_Model,Holt.Model=MAPE_Mean_All.Holt_Model,ARIMA.Model=MAPE_Mean_All.ARIMA_Model,Best.Model=result)
library(ascii)
print(ascii(table(table.error)), type = "rest")
##
## +---+--------------+------------+-------------+------------+-------------+-------------+------+
## | | country.name | BATS.Model | TBATS.Model | Holt.Model | ARIMA.Model | Best.Model | Freq |
## +===+==============+============+=============+============+=============+=============+======+
## | 1 | india | 0.067 | 0.068 | 0.1 | 0.029 | ARIMA Model | 1.00 |
## +---+--------------+------------+-------------+------------+-------------+-------------+------+
message("System finished Forecasting by using autoarima and Holt's ,TBATS, and SIR Model ==>",y_lab, sep=" ")
## System finished Forecasting by using autoarima and Holt's ,TBATS, and SIR Model ==>Covid 19 deaths cases in india
message(" Thank you for using our System For Modelling ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling ==> Covid 19 deaths cases in india