South ural state university, Chelyabinsk, Russian federation
# Imports
library(fpp2)
## Warning: package 'fpp2' was built under R version 4.0.3
## 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
## Warning: package 'ggplot2' was built under R version 4.0.3
## Warning: package 'forecast' was built under R version 4.0.3
##
library(forecast)
library(ggplot2)
library("readxl")
## Warning: package 'readxl' was built under R version 4.0.3
library(moments)
## Warning: package 'moments' was built under R version 4.0.3
library(forecast)
require(forecast)
require(tseries)
## Loading required package: tseries
## Warning: package 'tseries' was built under R version 4.0.3
require(markovchain)
## Loading required package: markovchain
## Warning: package 'markovchain' was built under R version 4.0.3
## 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
Full_original_data<-read_excel("F:/Phd/ALL Russia Analysis/SAARC milk production final.xlsx")
y_lab<- "SAARC milk production in Pakistan" # input name of data
Actual_date_interval <- c("1961/12/31","2018/12/31")
Forecast_date_interval <- c("2019/12/31","2025/12/31")
validation_data_days <-7
frequency<-"years"
# Data Preparation & calculate some of statistics measures
original_data<-Full_original_data$Pakistan
summary(original_data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4209000 5773750 10380500 12627086 19084250 28109000
sd(original_data) # calculate standard deviation
## [1] 7540331
skewness(original_data) # calculate Cofficient of skewness
## [1] 0.5334464
kurtosis(original_data) # calculate Cofficient of kurtosis
## [1] 1.880945
rows <- NROW(original_data)
training_data<-original_data[1:(rows-validation_data_days)]
testing_data<-original_data[(rows-validation_data_days+1):rows]
AD<-fulldate<-seq(as.Date(Actual_date_interval[1]),as.Date(Actual_date_interval[2]), frequency) #input range for actual date
FD<-seq(as.Date(Forecast_date_interval[1]),as.Date(Forecast_date_interval[2]), frequency) #input range forecasting date
N_forecasting_days<-nrow(data.frame(FD))
validation_dates<-tail(AD,validation_data_days)
validation_data_by_name<-weekdays(validation_dates)
forecasting_data_by_name<-weekdays(FD)
##bats model
# Data Modeling
data_series<-ts(training_data)
autoplot(data_series ,xlab=paste ("Time in ", frequency, sep=" "), ylab = y_lab, main=paste ("Actual Data :", y_lab, sep=" "))
model_bats<-bats(data_series)
accuracy(model_bats) # accuracy on training data
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 16437.32 166425 99196.88 0.2896213 1.073816 0.2616504 -0.03808877
# Print Model Parameters
model_bats
## BATS(0.544, {0,0}, 0.998, -)
##
## Call: bats(y = data_series)
##
## Parameters
## Lambda: 0.544361
## Alpha: 0.9867143
## Beta: 0.4119543
## Damping Parameter: 0.998458
##
## Seed States:
## [,1]
## [1,] 7707.8541597
## [2,] 0.0208483
## attr(,"lambda")
## [1] 0.5443614
##
## Sigma: 102.5477
## AIC: 1430.339
plot(model_bats,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4)
# Testing Data Evaluation
forecasting_bats <- predict(model_bats, h=N_forecasting_days+validation_data_days)
validation_forecast<-head(forecasting_bats$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 years by using bats Model for ==> SAARC milk production in Pakistan"
MAPE_Mean_All<-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 ==> SAARC milk production in Pakistan"
paste(MAPE_Mean_All,"%")
## [1] "0.751 % MAPE 7 years SAARC milk production in Pakistan %"
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 ==> SAARC milk production in Pakistan"
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 2012-12-31 понедельник 23652000 23604177
## 2 2013-12-31 вторник 24370000 24261379
## 3 2014-12-31 среда 25001000 24925762
## 4 2015-12-31 четверг 25744000 25597270
## 5 2016-12-31 суббота 26510000 26275848
## 6 2017-12-31 воскресенье 27298000 26961440
## 7 2018-12-31 понедельник 28109000 27653994
## MAPE_bats_Model
## 1 0.202 %
## 2 0.446 %
## 3 0.301 %
## 4 0.57 %
## 5 0.883 %
## 6 1.233 %
## 7 1.619 %
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 2019-12-31 вторник 28353455
## 2 2020-12-31 четверг 29059771
## 3 2021-12-31 пятница 29772889
## 4 2022-12-31 суббота 30492759
## 5 2023-12-31 воскресенье 31219327
## 6 2024-12-31 вторник 31952545
## 7 2025-12-31 среда 32692361
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="blue", 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
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,RMSE_bats,MAPE_Mean_All,MAD_bats) # analysis of Error by using Bats Model shows result of correlation ,MSE ,MPER
## correlation_bats RMSE_bats
## 1 0.9995564 243898.6
## MAPE_Mean_All MAD_bats
## 1 0.751 % MAPE 7 years SAARC milk production in Pakistan 200589.8
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 2012-12-31 понедельник 47822.94 0.202 % 0.203 %
## 2 2013-12-31 вторник 108620.65 0.446 % 0.448 %
## 3 2014-12-31 среда 75237.59 0.301 % 0.302 %
## 4 2015-12-31 четверг 146729.65 0.57 % 0.573 %
## 5 2016-12-31 суббота 234152.08 0.883 % 0.891 %
## 6 2017-12-31 воскресенье 336559.51 1.233 % 1.248 %
## 7 2018-12-31 понедельник 455005.94 1.619 % 1.645 %
## 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
## Training set 25338.39 179751.4 120493.9 0.2595034 1.455225 0.3178252
## ACF1
## Training set -0.01911074
# Print Model Parameters
model_TBATS
## TBATS(1, {0,0}, 1, {<6,2>})
##
## Call: NULL
##
## Parameters
## Alpha: 0.9868946
## Beta: 0.3584389
## Damping Parameter: 1
## Gamma-1 Values: -0.005289493
## Gamma-2 Values: 0.009289828
##
## Seed States:
## [,1]
## [1,] 4730320.9197
## [2,] 144576.0120
## [3,] 1161.5291
## [4,] -23156.1313
## [5,] 725.8252
## [6,] -25038.9612
##
## Sigma: 179751.4
## AIC: 1454.655
plot(model_TBATS,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", 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 years by using TBATS Model for ==> SAARC milk production in Pakistan"
MAPE_Mean_All<-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 ==> SAARC milk production in Pakistan"
paste(MAPE_Mean_All,"%")
## [1] "1.746 % MAPE 7 years SAARC milk production in Pakistan %"
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 ==> SAARC milk production in Pakistan"
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 2012-12-31 понедельник 23652000 23502822
## 2 2013-12-31 вторник 24370000 24121649
## 3 2014-12-31 среда 25001000 24779868
## 4 2015-12-31 четверг 25744000 25331920
## 5 2016-12-31 суббота 26510000 25948036
## 6 2017-12-31 воскресенье 27298000 26600471
## 7 2018-12-31 понедельник 28109000 27149451
## MAPE_TBATS_Model
## 1 0.631 %
## 2 1.019 %
## 3 0.884 %
## 4 1.601 %
## 5 2.12 %
## 6 2.555 %
## 7 3.414 %
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 2019-12-31 вторник 27768278
## 2 2020-12-31 четверг 28426497
## 3 2021-12-31 пятница 28978550
## 4 2022-12-31 суббота 29594665
## 5 2023-12-31 воскресенье 30247100
## 6 2024-12-31 вторник 30796080
## 7 2025-12-31 среда 31414907
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="blue", 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
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,RMSE_tbats,MAPE_Mean_All,MAD_tbats) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_tbats RMSE_tbats
## 1 0.9987025 537949.2
## MAPE_Mean_All MAD_tbats
## 1 1.746 % MAPE 7 years SAARC milk production in Pakistan 464254.6
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 2012-12-31 понедельник 149178.0 0.631 % 0.635 %
## 2 2013-12-31 вторник 248351.2 1.019 % 1.03 %
## 3 2014-12-31 среда 221131.7 0.884 % 0.892 %
## 4 2015-12-31 четверг 412079.5 1.601 % 1.627 %
## 5 2016-12-31 суббота 561964.3 2.12 % 2.166 %
## 6 2017-12-31 воскресенье 697528.8 2.555 % 2.622 %
## 7 2018-12-31 понедельник 959548.8 3.414 % 3.534 %
## 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
## Training set -15056.54 164178.6 79405.29 -0.06626589 0.6611748 0.2094463
## ACF1
## Training set -0.1201909
# 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= -0.249
##
## Smoothing parameters:
## alpha = 0.9986
## beta = 0.5667
##
## Initial states:
## l = 3.926
## b = 7e-04
##
## sigma: 2e-04
##
## AIC AICc BIC
## -651.6374 -650.3041 -641.9783
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -15056.54 164178.6 79405.29 -0.06626589 0.6611748 0.2094463
## ACF1
## Training set -0.1201909
# Testing Data Evaluation
forecasting_holt <- predict(model_holt, h=N_forecasting_days+validation_data_days,lambda = "auto")
validation_forecast<-head(forecasting_holt$mean,validation_data_days)
MAPE_Per_Day<-round( abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 years by using holt Model for ==> SAARC milk production in Pakistan"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_holt<-paste(round(MAPE_Per_Day,3),"%")
MAPE_holt_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in holt Model for ==> SAARC milk production in Pakistan"
paste(MAPE_Mean_All,"%")
## [1] "0.632 % MAPE 7 years SAARC milk production in Pakistan %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in holt Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in holt Model for ==> SAARC milk production in Pakistan"
data.frame(date_holt=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_holt=validation_forecast,MAPE_holt_Model)
## date_holt validation_data_by_name actual_data forecasting_holt
## 1 2012-12-31 понедельник 23652000 23654698
## 2 2013-12-31 вторник 24370000 24381244
## 3 2014-12-31 среда 25001000 25135875
## 4 2015-12-31 четверг 25744000 25919904
## 5 2016-12-31 суббота 26510000 26734715
## 6 2017-12-31 воскресенье 27298000 27581768
## 7 2018-12-31 понедельник 28109000 28462607
## MAPE_holt_Model
## 1 0.011 %
## 2 0.046 %
## 3 0.539 %
## 4 0.683 %
## 5 0.848 %
## 6 1.04 %
## 7 1.258 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_holt=tail(forecasting_holt$mean,N_forecasting_days))
## FD forecating_date forecasting_by_holt
## 1 2019-12-31 вторник 29378860
## 2 2020-12-31 четверг 30332248
## 3 2021-12-31 пятница 31324592
## 4 2022-12-31 суббота 32357815
## 5 2023-12-31 воскресенье 33433955
## 6 2024-12-31 вторник 34555167
## 7 2025-12-31 среда 35723735
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="blue", 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
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,RMSE_Holt,MAPE_Mean_All,MAD_Holt) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_Holt RMSE_Holt
## 1 0.9999184 208849.4
## MAPE_Mean_All MAD_Holt
## 1 0.632 % MAPE 7 years SAARC milk production in Pakistan 169544.4
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 2012-12-31 понедельник 2697.936 0.011 % 0.011 %
## 2 2013-12-31 вторник 11243.738 0.046 % 0.046 %
## 3 2014-12-31 среда 134875.030 0.539 % 0.537 %
## 4 2015-12-31 четверг 175903.989 0.683 % 0.679 %
## 5 2016-12-31 суббота 224714.844 0.848 % 0.841 %
## 6 2017-12-31 воскресенье 283768.436 1.04 % 1.029 %
## 7 2018-12-31 понедельник 353607.097 1.258 % 1.242 %
#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 ==> SAARC milk production in Pakistan"
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 = 1.3026, Truncation lag parameter = 3, p-value = 0.01
pp.test(data_series) # applay pp test
##
## Phillips-Perron Unit Root Test
##
## data: data_series
## Dickey-Fuller Z(alpha) = -1.4196, Truncation lag parameter = 3, p-value
## = 0.9786
## alternative hypothesis: stationary
adf.test(data_series) # applay adf test
##
## Augmented Dickey-Fuller Test
##
## data: data_series
## Dickey-Fuller = -1.9457, Lag order = 3, p-value = 0.5962
## 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="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main = "1nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub, cex.main,
## cex.lab, cex.sub, font.main, font.lab
##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 ==> SAARC milk production in Pakistan"
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 = 1.0309, Truncation lag parameter = 3, 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) = -28.598, Truncation lag parameter = 3, 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 = -1.9938, Lag order = 3, p-value = 0.5768
## 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="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab ,main = "2nd differenced series")
## Warning: Ignoring unknown parameters: col.main, col.lab, col.sub, cex.main,
## cex.lab, cex.sub, font.main, font.lab
##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 SAARC milk production in Pakistan"
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 = 0.059702, Truncation lag parameter = 3, 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) = -62.285, Truncation lag parameter = 3, 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 = -4.3805, Lag order = 3, 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) : 1328.649
## ARIMA(0,2,1) : 1316.333
## ARIMA(0,2,2) : 1318.577
## ARIMA(0,2,3) : 1320.952
## ARIMA(0,2,4) : 1323.391
## ARIMA(0,2,5) : 1325.159
## ARIMA(1,2,0) : 1319.856
## ARIMA(1,2,1) : 1318.576
## ARIMA(1,2,2) : Inf
## ARIMA(1,2,3) : Inf
## ARIMA(1,2,4) : Inf
## ARIMA(2,2,0) : 1319.76
## ARIMA(2,2,1) : 1320.951
## ARIMA(2,2,2) : Inf
## ARIMA(2,2,3) : Inf
## ARIMA(3,2,0) : 1321.209
## ARIMA(3,2,1) : 1323.417
## ARIMA(3,2,2) : Inf
## ARIMA(4,2,0) : 1323.637
## ARIMA(4,2,1) : 1326.021
## ARIMA(5,2,0) : 1325.644
##
##
##
## Best model: ARIMA(0,2,1)
model1 # show the result of autoarima
## Series: data_series
## ARIMA(0,2,1)
##
## Coefficients:
## ma1
## -0.5712
## s.e. 0.1130
##
## sigma^2 estimated as 2.524e+10: log likelihood=-656.04
## AIC=1316.07 AICc=1316.33 BIC=1319.86
#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("[ ]*$", "", result)
}
return(result)
}
source("stringthearima.R")
bestmodel <- arima.string(model1, padding = TRUE)
bestmodel <- substring(bestmodel,7,11)
bestmodel <- gsub(" ", "", bestmodel)
bestmodel <- gsub(")", "", bestmodel)
bestmodel <- strsplit(bestmodel, ",")[[1]]
bestmodel <- c(strtoi(bestmodel[1]),strtoi(bestmodel[2]),strtoi(bestmodel[3]))
bestmodel
## [1] 0 2 1
strtoi(bestmodel[3])
## [1] 1
#2. Using ACF and PACF Function
#par(mfrow=c(1,2)) # Code for making two plot in one graph
acf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab, main=paste("ACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot ACF "auto correlation function after taking second diffrences
pacf(diff2_x1,xlab = paste ("Time in ", frequency ,y_lab , sep=" "), col.main="black", col.lab="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab,main=paste("PACF-2nd differenced series ",y_lab, sep=" ",lag.max=20)) # plot PACF " Partial auto correlation function after taking second diffrences
library(forecast) # install library forecast
x1_model1= arima(data_series, order=c(bestmodel)) # Run Best model of auto arima for forecasting
x1_model1 # Show result of best model of auto arima
##
## Call:
## arima(x = data_series, order = c(bestmodel))
##
## Coefficients:
## ma1
## -0.5712
## s.e. 0.1130
##
## sigma^2 estimated as 2.472e+10: log likelihood = -656.04, aic = 1316.07
paste ("accuracy of autoarima Model For ==> ",y_lab, sep=" ")
## [1] "accuracy of autoarima Model For ==> SAARC milk production in Pakistan"
accuracy(x1_model1) # aacuracy of best model from auto arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 22995.25 154127 85842.84 0.2592826 0.72093 0.2264266 -0.0486627
x1_model1$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="blue", 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(0,2,1)
## Q* = 11.374, df = 9, p-value = 0.251
##
## Model df: 1. 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 ==> SAARC milk production in Pakistan"
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 = 9.0818, df = 20, p-value = 0.9819
library(tseries)
jarque.bera.test(x1_model1$residuals) # Do test jarque.bera.test
##
## Jarque Bera Test
##
## data: x1_model1$residuals
## X-squared = 242.57, 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='blue')
#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$mean,validation_data_days)
MAPE_Per_Day<-round(abs(((testing_data-validation_forecast)/testing_data)*100) ,3)
paste ("MAPE % For ",validation_data_days,frequency,"by using bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE % For 7 years by using bats Model for ==> SAARC milk production in Pakistan"
MAPE_Mean_All<-paste(round(mean(MAPE_Per_Day),3),"% MAPE ",validation_data_days,frequency,y_lab,sep=" ")
MAPE_auto_arima<-paste(round(MAPE_Per_Day,3),"%")
MAPE_auto.arima_Model<-paste(MAPE_Per_Day ,"%")
paste (" MAPE that's Error of Forecasting for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] " MAPE that's Error of Forecasting for 7 days in bats Model for ==> SAARC milk production in Pakistan"
paste(MAPE_Mean_All,"%")
## [1] "1.179 % MAPE 7 years SAARC milk production in Pakistan %"
paste ("MAPE that's Error of Forecasting day by day for ",validation_data_days," days in bats Model for ==> ",y_lab, sep=" ")
## [1] "MAPE that's Error of Forecasting day by day for 7 days in bats Model for ==> SAARC milk production in Pakistan"
data.frame(date_auto.arima=validation_dates,validation_data_by_name,actual_data=testing_data,forecasting_auto.arima=validation_forecast,MAPE_auto.arima_Model)
## date_auto.arima validation_data_by_name actual_data forecasting_auto.arima
## 1 2012-12-31 понедельник 23652000 23590412
## 2 2013-12-31 вторник 24370000 24225825
## 3 2014-12-31 среда 25001000 24861237
## 4 2015-12-31 четверг 25744000 25496650
## 5 2016-12-31 суббота 26510000 26132062
## 6 2017-12-31 воскресенье 27298000 26767474
## 7 2018-12-31 понедельник 28109000 27402887
## MAPE_auto.arima_Model
## 1 0.26 %
## 2 0.592 %
## 3 0.559 %
## 4 0.961 %
## 5 1.426 %
## 6 1.943 %
## 7 2.512 %
data.frame(FD,forecating_date=forecasting_data_by_name,forecasting_by_auto.arima=tail(forecasting_auto_arima$mean,N_forecasting_days))
## FD forecating_date forecasting_by_auto.arima
## 1 2019-12-31 вторник 28038299
## 2 2020-12-31 четверг 28673711
## 3 2021-12-31 пятница 29309124
## 4 2022-12-31 суббота 29944536
## 5 2023-12-31 воскресенье 30579949
## 6 2024-12-31 вторник 31215361
## 7 2025-12-31 среда 31850773
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="blue", col.sub="black", cex.main=1, cex.lab=1, cex.sub=1,font.main=4, font.lab=4, ylab=y_lab)
graph4
## 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
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,RMSE_auto.arima,MAPE_Mean_All,MAD_auto.arima) # analysis of Error by using Holt's linear model shows result of correlation ,MSE ,MPER
## correlation_auto.arima RMSE_auto.arima
## 1 0.9992705 383254.1
## MAPE_Mean_All MAD_auto.arima
## 1 1.179 % MAPE 7 years SAARC milk production in Pakistan 315350.5
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 2012-12-31 понедельник 61587.61 0.26 %
## 2 2013-12-31 вторник 144175.23 0.592 %
## 3 2014-12-31 среда 139762.84 0.559 %
## 4 2015-12-31 четверг 247350.45 0.961 %
## 5 2016-12-31 суббота 377938.06 1.426 %
## 6 2017-12-31 воскресенье 530525.68 1.943 %
## 7 2018-12-31 понедельник 706113.29 2.512 %
## REOF_F_auto.arima
## 1 0.261 %
## 2 0.595 %
## 3 0.562 %
## 4 0.97 %
## 5 1.446 %
## 6 1.982 %
## 7 2.577 %
# Choose Best model by least error
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using bats model and BATS Model, Holt's Linear Models , and autoarima for ==> SAARC milk production in Pakistan"
M1<-mean(REOF_A_bats)
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using TBATS Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using TBATS Model For ==> SAARC milk production in Pakistan"
M2<-mean(REOF_A_tbats1)
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using Holt's Linear << Exponential Smoothing >> For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using Holt's Linear << Exponential Smoothing >> For ==> SAARC milk production in Pakistan"
M3<-REOF_A_Holt11
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using auto arima Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using auto arima Model For ==> SAARC milk production in Pakistan"
M4<-mean(REOF_A_auto.arima)
paste("System Summarizes Error ==> ( MAPE ) of Forecasting by using autoarima Model For ==> ", y_lab , sep=" ")
## [1] "System Summarizes Error ==> ( MAPE ) of Forecasting by using autoarima Model For ==> SAARC milk production in Pakistan"
data.frame(validation_dates,forecating_date=forecasting_data_by_name,MAPE_bats_error=REOF_A_bats,MAPE_TBATS_error=REOF_A_tbats1,MAPE_Holt_error=REOF_A_Holt1,MAPE_autoarima_error = REOF_A_auto.arima)
## validation_dates forecating_date MAPE_bats_error MAPE_TBATS_error
## 1 2012-12-31 вторник 0.2021941 0.6307203
## 2 2013-12-31 четверг 0.4457146 1.0190857
## 3 2014-12-31 пятница 0.3009383 0.8844916
## 4 2015-12-31 суббота 0.5699567 1.6006818
## 5 2016-12-31 воскресенье 0.8832595 2.1198201
## 6 2017-12-31 вторник 1.2329090 2.5552376
## 7 2018-12-31 среда 1.6187198 3.4136712
## MAPE_Holt_error MAPE_autoarima_error
## 1 0.01140680 0.2603907
## 2 0.04613762 0.5916095
## 3 0.53947854 0.5590290
## 4 0.68328150 0.9608082
## 5 0.84766067 1.4256434
## 6 1.03952098 1.9434599
## 7 1.25798533 2.5120541
recommend_Model<-c(M1,M2,M3,M4)
best_recommended_model<-min(recommend_Model)
paste ("lodaing ..... ... . .Select Minimum MAPE from Models for select best Model ==> ", y_lab , sep=" ")
## [1] "lodaing ..... ... . .Select Minimum MAPE from Models for select best Model ==> SAARC milk production in Pakistan"
best_recommended_model
## [1] 0.6322102
paste ("Best Model For Forecasting ==> ",y_lab, sep=" ")
## [1] "Best Model For Forecasting ==> SAARC milk production in Pakistan"
if(best_recommended_model >= M1) {paste("System Recommend Bats Model That's better For forecasting==> ",y_lab, sep=" ")}
if(best_recommended_model >= M2) {paste("System Recommend That's better TBATS For forecasting ==> ",y_lab, sep=" ")}
if(best_recommended_model >= M3) {paste("System Recommend Holt's Linear Model < Exponential Smoothing Model > That's better For forecasting ==> ",y_lab, sep=" ")}
## [1] "System Recommend Holt's Linear Model < Exponential Smoothing Model > That's better For forecasting ==> SAARC milk production in Pakistan"
if(best_recommended_model >= M4) {paste("System Recommend auto arima Model That's better For forecasting ==> ",y_lab, sep=" ")}
message("System finished Forecasting by using autoarima and Holt's ,and TBATS Model ==>",y_lab, sep=" ")
## System finished Forecasting by using autoarima and Holt's ,and TBATS Model ==>SAARC milk production in Pakistan
message(" Thank you for using our System For Modelling ==> ",y_lab, sep=" ")
## Thank you for using our System For Modelling ==> SAARC milk production in Pakistan