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_deaths
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.
## 0 543 40699 63878 133227 158063
# calculate standard deviation
data.frame(skewness=skewness(original_data)) # calculate Cofficient of skewness
## skewness
## 1 0.3240957
data.frame(kurtosis=kurtosis(original_data)) # calculate Cofficient of kurtosis
## kurtosis
## 1 1.381315
data.frame(Standard.deviation =sd(original_data))
## Standard.deviation
## 1 63024.53
#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 1.693479 192.6369 84.80609 NaN Inf 0.2290658 0.05422684
# Print Model Parameters
model_bats
## BATS(1, {0,0}, 1, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Alpha: 0.5903846
## Beta: 0.1460504
## Damping Parameter: 1
##
## Seed States:
## [,1]
## [1,] -0.9843571
## [2,] -0.0233703
##
## Sigma: 192.6369
## AIC: 7069.399
#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] "0.016 % 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 157435 157458.6
## 2 2021-03-05 Friday 157548 157563.9
## 3 2021-03-06 Saturday 157656 157669.3
## 4 2021-03-07 Sunday 157756 157774.6
## 5 2021-03-08 Monday 157853 157879.9
## 6 2021-03-09 Tuesday 157930 157985.3
## 7 2021-03-10 Wednesday 158063 158090.6
## MAPE_bats_Model
## 1 0.015 %
## 2 0.01 %
## 3 0.008 %
## 4 0.012 %
## 5 0.017 %
## 6 0.035 %
## 7 0.017 %
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 158196.0
## 2 2021-03-12 Friday 158301.3
## 3 2021-03-13 Saturday 158406.6
## 4 2021-03-14 Sunday 158512.0
## 5 2021-03-15 Monday 158617.3
## 6 2021-03-16 Tuesday 158722.7
## 7 2021-03-17 Wednesday 158828.0
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 0.9986276 839.6221 28.97623 0.016 25.88978
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 23.58229 0.015 % 0.015 %
## 2 2021-03-05 Friday 15.92289 0.01 % 0.01 %
## 3 2021-03-06 Saturday 13.26348 0.008 % 0.008 %
## 4 2021-03-07 Sunday 18.60407 0.012 % 0.012 %
## 5 2021-03-08 Monday 26.94466 0.017 % 0.017 %
## 6 2021-03-09 Tuesday 55.28525 0.035 % 0.035 %
## 7 2021-03-10 Wednesday 27.62584 0.017 % 0.017 %
## TBATS Model
# Data Modeling
data_series<-ts(training_data)
model_TBATS<-forecast:::fitSpecificTBATS(data_series,use.box.cox=FALSE, use.beta=TRUE, seasonal.periods=c(6),use.damping=FALSE,k.vector=c(2))
accuracy(model_TBATS) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 1.67981 190.2337 89.75114 NaN Inf 0.2424226 0.06042829
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.5912045
## Beta: 0.1470497
## Damping Parameter: 1
## Gamma-1 Values: -0.002843247
## Gamma-2 Values: 0.004128876
##
## Seed States:
## [,1]
## [1,] 2.198960
## [2,] -1.346886
## [3,] -6.906433
## [4,] -12.970679
## [5,] -19.045215
## [6,] 7.142075
##
## Sigma: 190.2337
## AIC: 7070.703
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] "0.009 % 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 157435 157431.7
## 2 2021-03-05 Friday 157548 157557.2
## 3 2021-03-06 Saturday 157656 157651.8
## 4 2021-03-07 Sunday 157756 157757.0
## 5 2021-03-08 Monday 157853 157889.9
## 6 2021-03-09 Tuesday 157930 157970.9
## 7 2021-03-10 Wednesday 158063 158055.0
## MAPE_TBATS_Model
## 1 0.002 %
## 2 0.006 %
## 3 0.003 %
## 4 0.001 %
## 5 0.023 %
## 6 0.026 %
## 7 0.005 %
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 158180.4
## 2 2021-03-12 Friday 158275.0
## 3 2021-03-13 Saturday 158380.3
## 4 2021-03-14 Sunday 158513.2
## 5 2021-03-15 Monday 158594.1
## 6 2021-03-16 Tuesday 158678.2
## 7 2021-03-17 Wednesday 158803.7
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 0.9963939 458.8629 21.42109 0.009 10.33376
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 3.331479 0.002 % 0.002 %
## 2 2021-03-05 Friday 9.154587 0.006 % 0.006 %
## 3 2021-03-06 Saturday 4.240392 0.003 % 0.003 %
## 4 2021-03-07 Sunday 1.002494 0.001 % 0.001 %
## 5 2021-03-08 Monday 36.938047 0.023 % 0.023 %
## 6 2021-03-09 Tuesday 40.854240 0.026 % 0.026 %
## 7 2021-03-10 Wednesday 8.041190 0.005 % 0.005 %
## 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 -27.2825 200.4808 81.98246 -Inf Inf 0.221439 -0.1616733
# 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= 0.3777
##
## Smoothing parameters:
## alpha = 0.8642
## beta = 0.1275
##
## Initial states:
## l = -2.6471
## b = 2e-04
##
## sigma: 0.3753
##
## AIC AICc BIC
## 1750.255 1750.398 1770.527
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -27.2825 200.4808 81.98246 -Inf Inf 0.221439 -0.1616733
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 day by using holt Model for ==> Covid 19 deaths cases in india"
MAPE_Mean_All.Holt_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.Holt<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> Covid 19 deaths cases in india"
paste(MAPE_Mean_All.Holt,"%")
## [1] "0.008 % MAPE 7 day Covid 19 deaths cases in india %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> Covid 19 deaths cases in india"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2021-03-04 Thursday 157435 157450.7
## 2 2021-03-05 Friday 157548 157554.2
## 3 2021-03-06 Saturday 157656 157657.8
## 4 2021-03-07 Sunday 157756 157761.4
## 5 2021-03-08 Monday 157853 157865.1
## 6 2021-03-09 Tuesday 157930 157968.8
## 7 2021-03-10 Wednesday 158063 158072.5
## MAPE_holt_Model
## 1 0.01 %
## 2 0.004 %
## 3 0.001 %
## 4 0.003 %
## 5 0.008 %
## 6 0.025 %
## 7 0.006 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2021-03-11 Thursday 158176.3
## 2 2021-03-12 Friday 158280.1
## 3 2021-03-13 Saturday 158384.0
## 4 2021-03-14 Sunday 158487.9
## 5 2021-03-15 Monday 158591.9
## 6 2021-03-16 Tuesday 158695.9
## 7 2021-03-17 Wednesday 158799.9
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 0.9986231 293.701 17.13771 0.008 12.77392
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 15.667398 0.01 % 0.01 %
## 2 2021-03-05 Friday 6.203726 0.004 % 0.004 %
## 3 2021-03-06 Saturday 1.782413 0.001 % 0.001 %
## 4 2021-03-07 Sunday 5.403465 0.003 % 0.003 %
## 5 2021-03-08 Monday 12.066890 0.008 % 0.008 %
## 6 2021-03-09 Tuesday 38.772693 0.025 % 0.025 %
## 7 2021-03-10 Wednesday 9.520881 0.006 % 0.006 %
#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 = 6.9199, 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) = -2.6087, Truncation lag parameter = 5, p-value
## = 0.9511
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -3.1442, Lag order = 7, p-value = 0.09758
## 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 = 2.417, 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) = -130.11, 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 = -0.37585, Lag order = 7, p-value = 0.9873
## 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 = 0.057299, 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) = -569.12, 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 = -12.819, 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) : 6060.457
## ARIMA(0,2,1) : 5727.467
## ARIMA(0,2,2) : 5674.463
## ARIMA(0,2,3) : 5668.703
## ARIMA(0,2,4) : 5667.936
## ARIMA(0,2,5) : 5668.488
## ARIMA(1,2,0) : 5871.378
## ARIMA(1,2,1) : 5691.716
## ARIMA(1,2,2) : 5665.062
## ARIMA(1,2,3) : 5664.799
## ARIMA(1,2,4) : 5664.759
## ARIMA(2,2,0) : 5785.484
## ARIMA(2,2,1) : 5682.463
## ARIMA(2,2,2) : 5665.71
## ARIMA(2,2,3) : 5661.518
## ARIMA(3,2,0) : 5737.996
## ARIMA(3,2,1) : 5680.051
## ARIMA(3,2,2) : 5667.035
## ARIMA(4,2,0) : 5720.373
## ARIMA(4,2,1) : 5680.291
## ARIMA(5,2,0) : 5687.858
##
##
##
## Best model: ARIMA(2,2,3)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(2,2,3)
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## -0.5213 0.4419 -0.6850 -0.8120 0.6863
## s.e. 0.0995 0.0938 0.0778 0.0472 0.0577
##
## sigma^2 estimated as 36036: log likelihood=-2824.66
## AIC=5661.32 AICc=5661.52 BIC=5685.61
#Make changes in the source of auto arima to run the best model
arima.string <- function (object, padding = FALSE)
{
order <- object$arma[c(1, 6, 2, 3, 7, 4, 5)]
m <- order[7]
result <- paste("ARIMA(", order[1], ",", order[2], ",",
order[3], ")", sep = "")
if (m > 1 && sum(order[4:6]) > 0) {
result <- paste(result, "(", order[4], ",", order[5],
",", order[6], ")[", m, "]", sep = "")
}
if (padding && m > 1 && sum(order[4:6]) == 0) {
result <- paste(result, " ", sep = "")
if (m <= 9) {
result <- paste(result, " ", sep = "")
}
else if (m <= 99) {
result <- paste(result, " ", sep = "")
}
else {
result <- paste(result, " ", sep = "")
}
}
if (!is.null(object$xreg)) {
if (NCOL(object$xreg) == 1 && is.element("drift", names(object$coef))) {
result <- paste(result, "with drift ")
}
else {
result <- paste("Regression with", result, "errors")
}
}
else {
if (is.element("constant", names(object$coef)) || is.element("intercept",
names(object$coef))) {
result <- paste(result, "with non-zero mean")
}
else if (order[2] == 0 && order[5] == 0) {
result <- paste(result, "with zero mean ")
}
else {
result <- paste(result, " ")
}
}
if (!padding) {
result <- gsub("[ ]*$", "", result)
}
return(result)
}
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 2 2 3
strtoi(bestmodel[3])
## [1] 3
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="black", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## -0.5213 0.4419 -0.6850 -0.8120 0.6863
## s.e. 0.0995 0.0938 0.0778 0.0472 0.0577
##
## sigma^2 estimated as 35611: log likelihood = -2824.66, aic = 5661.32
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> Covid 19 deaths cases in india"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE
## Training set 1.467933 188.2662 82.17214 1.436279 1.969348 0.2219514
## ACF1
## Training set -0.005500256
x1_model1$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(2,2,3)
## Q* = 4.8113, df = 5, p-value = 0.4393
##
## 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 ==> 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 = 51.48, df = 20, p-value = 0.0001355
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 11034, 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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 day by using bats Model for ==> Covid 19 deaths cases in india"
MAPE_Mean_All.ARIMA_Model<-round(mean(MAPE_Per_Day),3)
MAPE_Mean_All.ARIMA<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> Covid 19 deaths cases in india"
paste(MAPE_Mean_All.ARIMA,"%")
## [1] "0.029 % MAPE 7 day Covid 19 deaths cases in india %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> Covid 19 deaths cases in india"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2021-03-04 Thursday 157435 157460.0
## 2 2021-03-05 Friday 157548 157574.8
## 3 2021-03-06 Saturday 157656 157683.7
## 4 2021-03-07 Sunday 157756 157796.1
## 5 2021-03-08 Monday 157853 157904.0
## 6 2021-03-09 Tuesday 157930 158015.8
## 7 2021-03-10 Wednesday 158063 158123.6
## MAPE_auto.arima_Model
## 1 0.016 %
## 2 0.017 %
## 3 0.018 %
## 4 0.025 %
## 5 0.032 %
## 6 0.054 %
## 7 0.038 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2021-03-11 Thursday 158235.1
## 2 2021-03-12 Friday 158343.0
## 3 2021-03-13 Saturday 158454.5
## 4 2021-03-14 Sunday 158562.4
## 5 2021-03-15 Monday 158673.8
## 6 2021-03-16 Tuesday 158781.8
## 7 2021-03-17 Wednesday 158893.1
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 0.9986241 2477.043 49.7699
## MAPE_Mean_All.ARIMA_Model MAD_auto.arima
## 1 0.029 45.27005
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 24.98493 0.016 %
## 2 2021-03-05 Friday 26.81935 0.017 %
## 3 2021-03-06 Saturday 27.70505 0.018 %
## 4 2021-03-07 Sunday 40.06750 0.025 %
## 5 2021-03-08 Monday 50.98852 0.032 %
## 6 2021-03-09 Tuesday 85.76149 0.054 %
## 7 2021-03-10 Wednesday 60.56351 0.038 %
## REOF_F_auto.arima
## 1 0.016 %
## 2 0.017 %
## 3 0.018 %
## 4 0.025 %
## 5 0.032 %
## 6 0.054 %
## 7 0.038 %
# 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] 0.008
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 | 0.016 | 0.009 | 0.008 | 0.029 | Holt 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