Time Series S05
Group 3
6/23/2020
Import the necessary libraries
library(fpp2)## Warning: package 'fpp2' was built under R version 3.6.3## Loading required package: ggplot2## Loading required package: forecast## Warning: package 'forecast' was built under R version 3.6.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Loading required package: fma## Warning: package 'fma' was built under R version 3.6.3## Loading required package: expsmooth## Warning: package 'expsmooth' was built under R version 3.6.3library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(imputeTS)## Warning: package 'imputeTS' was built under R version 3.6.3Load the dataset
data_project <- readxl::read_excel("Data Set for Class.xls")
head(data_project)## # A tibble: 6 x 7
## SeriesInd group Var01 Var02 Var03 Var05 Var07
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 40669 S03 30.6 123432400 30.3 30.5 30.6
## 2 40669 S02 10.3 60855800 10.0 10.2 10.3
## 3 40669 S01 26.6 10369300 25.9 26.2 26.0
## 4 40669 S06 27.5 39335700 26.8 27.0 27.3
## 5 40669 S05 69.3 27809100 68.2 68.7 69.2
## 6 40669 S04 17.2 16587400 16.9 16.9 17.1Subset the dataset
S05 <- subset(data_project, group == 'S05', select = c(SeriesInd, Var02, Var03))
summary(S05)## SeriesInd Var02 Var03
## Min. :40669 Min. : 4156600 Min. : 55.94
## 1st Qu.:41304 1st Qu.: 11201200 1st Qu.: 77.21
## Median :41946 Median : 14578800 Median : 84.87
## Mean :41945 Mean : 16791350 Mean : 82.97
## 3rd Qu.:42586 3rd Qu.: 20021200 3rd Qu.: 89.74
## Max. :43221 Max. :118023500 Max. :103.95
## NA's :141 NA's :145Get the subsets Var02 and Var03
var02 <- S05 %>% filter(SeriesInd <= 43021) %>% select(Var02)var03 <- S05 %>% filter(SeriesInd <= 43021) %>% select(Var03)Explore the subsets Var02
summary(var02)## Var02
## Min. : 4156600
## 1st Qu.: 11201200
## Median : 14578800
## Mean : 16791350
## 3rd Qu.: 20021200
## Max. :118023500
## NA's :1Var02 has 1 missing value
Explore the subsets Var03
summary(var03)## Var03
## Min. : 55.94
## 1st Qu.: 77.21
## Median : 84.87
## Mean : 82.97
## 3rd Qu.: 89.74
## Max. :103.95
## NA's :5Var03 has 5 missing values Median and mean are in the same order. #### converse Var02 and Var03 to time series
var02 <- ts(var02)
str(var02)## Time-Series [1:1622, 1] from 1 to 1622: 27809100 30174700 35044700 27192100 24891800 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "Var02"var03 <- ts(var03)
str(var03)## Time-Series [1:1622, 1] from 1 to 1622: 68.2 68.8 69.3 69.4 69.2 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "Var03"Imputing missing values
var02 <- na_interpolation(var02)
summary(var02)## Var02
## Min. : 4156600
## 1st Qu.: 11206550
## Median : 14575700
## Mean : 16788872
## 3rd Qu.: 20014325
## Max. :118023500var03 <- na_interpolation(var03)
summary(var03)## Var03
## Min. : 55.94
## 1st Qu.: 77.25
## Median : 84.88
## Mean : 82.97
## 3rd Qu.: 89.71
## Max. :103.95Visualization
autoplot(var02) + ggtitle("Time Series S05-Var02")
Trend non seasonal time series
autoplot(var03) + ggtitle("Time Series S05-Var03")
Trend non seasonal time serie. It can also be cyclic time series
The distribution of data
par(mfrow= c(1,2))
hist(var02)
boxplot(var02)
Va02 is right skewed. It need to be centralised.
par(mfrow= c(1,2))
hist(var03)
boxplot(var03)
Var03 is nearly normal distributed and has outliers at the left.
ACF of Var02 difference
autoplot(diff(var02))
ggAcf(diff(var02))
There is one order correlation
ACF of Var03 difference
autoplot(diff(var03))
ggAcf(diff(var03))
The ACF shows one order correlation
Subset the train set
train.var02 <- window(var02, end = as.integer(length(var02)*0.8))train.var03 <- window(var03, end = as.integer(length(var03)*0.8))Look for lambda transformation
lambda2 <- BoxCox.lambda(var02)lambda3 <- BoxCox.lambda(var03)Apply the models to the train sets
forecast horizon here the length of test set
h <- length(var02)- as.integer(length(var03)*0.8)Get the arima model for Var02
farima.var02 <- train.var02 %>% auto.arima(lambda = lambda2, stepwise = FALSE) %>% forecast(h = h)Get the arima model for Var03
farima.var03 <- train.var03 %>% auto.arima(lambda = lambda2, stepwise = FALSE) %>% forecast(h = h)ETS model
Get the ets model for Var02
fets.var02 <- train.var02 %>% ets(lambda = lambda2) %>% forecast(h = h)Get the arima ets for Var03
fets.var03 <- train.var03 %>% ets(lambda = lambda2) %>% forecast(h = h)Naive model for Var02
naive.var02 <- naive(train.var02, h=h)Naive model for Var03
naive.var03 <- naive(train.var03, h=h)Accuracy compare to the naive model
RMSE accuracy of Var02 arima model
accuracy(farima.var02, var02)["Test set", "RMSE"]## [1] 5213174RMSE accuracy of Var02 ets model
accuracy(fets.var02, var02)["Test set", "RMSE"]## [1] 5383844RMSE accuracy of Var02 naive model
accuracy(naive.var02, var02)["Test set", "RMSE"]## [1] 5289689Comparing the RMSEs, the arima model for Var02 is the best.
RMSE accuracy for Var03 arima model
accuracy(farima.var03, var03)["Test set", "RMSE"]## [1] 8.585339RMSE accuracy of Var03 ets model
accuracy(fets.var03, var03)["Test set", "RMSE"]## [1] 8.564458RMSE accuracy for Var03 naive model
accuracy(naive.var03, var03)["Test set", "RMSE"]## [1] 8.564479comparing with the RMSE, the naive method for Var03 is better than the arima of the same data. ETS model is the best
Ljung-Box test of the naive residuals
Box.test(residuals(naive.var03))##
## Box-Pierce test
##
## data: residuals(naive.var03)
## X-squared = 13.752, df = 1, p-value = 0.0002086Forecast the time series
farima.var02 <- var02 %>% auto.arima(lambda = lambda2, stepwise = FALSE) %>% forecast(h = 140)fets.var03 <- var03 %>% ets(lambda = lambda2) %>% forecast(h = 140)Var02 forecast
autoplot(farima.var02)
##### Var03 forecast
autoplot(fets.var03)
Check the residuals if the model is valid
Var02 residuals
checkresiduals(farima.var02)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,2)
## Q* = 8.5874, df = 7, p-value = 0.2836
##
## Model df: 3. Total lags used: 10with p-value greater than 0.05, there is convaincing evidence that residuals for Var02 are white noise. On ACF, the residuals are uncorrelated. The histogram shows that the residuals are normal distributed.
Var03 residuals
checkresiduals(fets.var03)
##
## Ljung-Box test
##
## data: Residuals from ETS(A,N,N)
## Q* = 31.226, df = 8, p-value = 0.0001281
##
## Model df: 2. Total lags used: 10with p-value greater than 0.05, there is convaincing evidence that residuals for Var03 are white noise. On ACF, the residuals are uncorrelated. The histogram shows that the residuals are normal distributed.