# Retail Project

**Objective:** To forecast a real time series using ETS and ARIMA models.

**Data:** The data are monthly measures of retail trade volume in Australia, obtained from the ABS. Each student will be use a different time series, selected using their student ID number as follows. This is the same series that you used in Assignment 2.

```
library(fpp3)
<- function(student_id) {
get_my_data set.seed(student_id)
<- readr::read_rds("https://bit.ly/monashretaildata")
all_data while(TRUE) {
<- filter(all_data, `Series ID` == sample(`Series ID`, 1))
retail if(!any(is.na(fill_gaps(retail)$Turnover))) return(retail)
}
}# Replace the argument with your student ID
<- get_my_data(12345678) retail
```

**Assignment value:** This assignment is worth 20% of the overall unit assessment.

**Report:**

You should produce forecasts of the series using ETS and ARIMA models. Write a report in Rmarkdown or Quarto format of your analysis explaining carefully what you have done and why you have done it. Your report should include the following elements.

- A discussion of the statistical features of the original data, including the effect of COVID-19 on your series. [4 marks]
- Explanation of transformations and differencing used. You should use a unit-root test as part of the discussion. [5 marks]
- A description of the methodology used to create a short-list of appropriate ARIMA models and ETS models. Include discussion of AIC values as well as results from applying the models to a test-set consisting of the last 24 months of the data provided. [6 marks]
- Choose one ARIMA model and one ETS model based on this analysis and show parameter estimates, residual diagnostics, forecasts and prediction intervals for both models. Diagnostic checking for both models should include ACF graphs and the Ljung-Box test. [8 marks]
- Comparison of the results from each of your preferred models. Which method do you think gives the better forecasts? Explain with reference to the test-set. [2 marks]
- Apply your two chosen models to the full data set, re-estimating the parameters but not changing the model structure. Produce out-of-sample point forecasts and 80% prediction intervals for each model for two years past the end of the data provided. [4 marks]
- Obtain up-to-date data from the ABS website (Table 11). You may need to use the previous release of data, rather than the latest release. Compare your forecasts with the actual numbers. How well did you do? [5 marks]
- A discussion of benefits and limitations of the models for your data. [3 marks]
- Graphs should be properly labelled, including appropriate units of measurement. [3 marks]

**Notes**

- Your submission must include the Rmarkdown or Quarto file (.Rmd or .qmd), and should run without error.
- There will be a 5 marks penalty if file does not run without error.
- When using the updated ABS data set, do not edit the downloaded file in any way.
- There is no need to provide the updated ABS data with your submission.

**Due: 24 May 2024**

**Submit**