Loading Library

load("workspace.RData")

## Registered S3 methods overwritten by 'ggplot2':
##   method         from 
##   [.quosures     rlang
##   c.quosures     rlang
##   print.quosures rlang

## Registered S3 method overwritten by 'xts':
##   method     from
##   as.zoo.xts zoo

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## Registered S3 methods overwritten by 'forecast':
##   method             from    
##   fitted.fracdiff    fracdiff
##   residuals.fracdiff fracdiff

library(fpp2)

## Warning: package 'fpp2' was built under R version 3.6.1

## Loading required package: ggplot2

## Loading required package: forecast

## Warning: package 'forecast' was built under R version 3.6.1

## Loading required package: fma

## Warning: package 'fma' was built under R version 3.6.1

## Loading required package: expsmooth

## Warning: package 'expsmooth' was built under R version 3.6.1

Converting into time series

df <- read.csv("Breakfast.csv",header=TRUE)
cbf.ts <- ts(df[,"Continental.B.F"],frequency=7)
str(cbf.ts)

##  Time-Series [1:115] from 1 to 17.3: 25 25 25 35 41 30 40 40 40 40 ...

Visualizing

autoplot(cbf.ts)+
ggtitle("Number of People Ordering Continental BF") +
xlab("Week") +
ylab("Number of People")

Calculating the ACF and PCF

acf(cbf.ts)

pacf(cbf.ts)

it seems to be an MA process of the order 1.

The following Models are tried:

1. ETS: This is a generalised model for Exponential Smoothing
2. ARIMA:
3. STL:STL is a versatile and robust method for decomposing time series. STL is an acronym for “Seasonal and Trend decomposition using Loess”, while Loess is a method for estimating nonlinear relationships.
4. NNAR:Neural Network Autoregression
5. TBATS:a combination of Fourier terms with an exponential smoothing state space model and a Box-Cox transformation.
6. Combination: is the average of all models

train <- window(cbf.ts, end=c(12,5))
h <- length(cbf.ts) - length(train)
ETS <- forecast(ets(train), h=h)
ARIMA <- forecast(auto.arima(train, lambda=0, biasadj=TRUE),
h=h)
STL <- stlf(train, lambda=0, h=h, biasadj=TRUE)
NNAR <- forecast(nnetar(train), h=h)
TBATS <- forecast(tbats(train, biasadj=TRUE), h=h)
Combination <- (ETS[["mean"]] + ARIMA[["mean"]] +
STL[["mean"]] + NNAR[["mean"]] + TBATS[["mean"]])/5
autoplot(cbf.ts) +
autolayer(ETS, series="ETS", PI=FALSE) +
autolayer(ARIMA, series="ARIMA", PI=FALSE) +
autolayer(STL, series="STL", PI=FALSE) +
autolayer(NNAR, series="NNAR", PI=FALSE) +
autolayer(TBATS, series="TBATS", PI=FALSE) +
autolayer(Combination, series="Combination") +
xlab("week") + ylab("Number of People Ordering Continental Breakfast") +
ggtitle("Number of People Ordering Continental Breakfast")

c(ETS = accuracy(ETS, cbf.ts)["Test set","MAPE"],
ARIMA = accuracy(ARIMA, cbf.ts)["Test set","MAPE"],
`STL-ETS` = accuracy(STL, cbf.ts)["Test set","MAPE"],
NNAR = accuracy(NNAR, cbf.ts)["Test set","MAPE"],
TBATS = accuracy(TBATS, cbf.ts)["Test set","MAPE"],
Combination =
accuracy(Combination, cbf.ts)["Test set","MAPE"])

##         ETS       ARIMA     STL-ETS        NNAR       TBATS Combination 
##   10.853219    9.739436   12.364599   10.220758   12.131538   10.714648

As can be seen ARIMA works the best with MAPE of 9.73%

Checking of demand for stationarity.

library(urca)

## Warning: package 'urca' was built under R version 3.6.1

Lets Apply the KPSS root test to see if the differencing is required

cbf.ts %>%  ur.kpss() %>% summary()

## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 4 lags. 
## 
## Value of test-statistic is: 0.1962 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739

So the value of test statistics is 0.192 which is less than the critical values, so differencing is not required and series is stationary.

save.image("workspace.Rdata")