1.
Your aim in the first part of the assignment is to build an ARIMA model and use this to forecast. Recall the first step in ARIMA modelling is to stabilize the variance of your data. If you decided that your data required a transformation in the previous assignments you will be required to use the same transformation for what follows (unless you have a reason to change your mind).
Visually inspect your data and decide what differencing is required to achieve stationarity. Plot the data at every step and comment on each plot justifying your actions. (No more than 50 words per plot).
2.
Plot the ACF and PACF of the stationary data. Reading from these choose an appropriate ARIMA model. Make sure you justify your choice. (No more than 70 words in total – do not revise the theory – describe what you see on your plots and decide what ARIMA orders may be appropriate. Also note that it is highly likely that the ACF and PACF plots will be very messy. Do the best you can.)
3.
Check the whiteness of the residuals from the fitted ARIMA model. Based on these evaluate and if necessary review the ARIMA model specified in Q2. (No more than 50 words).
4.
Consider three (up to five if you think you need them) alternative ARIMA models based on your choice in Q2 and Q3. Use information criteria to choose the best model you have considered so far. (Very briefly justify each choice with no more than 1 or 2 lines each).
5.
Use auto.arima to choose a model. How does this compare with your chosen model from Q4? Perform residual diagnostics analysis for this model. (No more than 50 words).
6.
Use again auto.arima but this time set stepwise=FALSE and approximation=FALSE. What are you going here? Is the model chosen this time different to Q5? If yes perform residual diagnostics analysis for this model. (No more than 50 words).
7.
If needed use an appropriate test set to choose the ARIMA model you want to use for forecasting. Which model have you selected and why? (No more than 50 words).
8.
Generate and plot forecasts and forecast intervals from the chosen model for the period 2017-2018. Comment on these. (No more than 50 words
9.
You have now considered several modelling frameworks and built several models for your data set. In this part of the assignment you will evaluate these and choose one to generate forecasts for the next 24 months of your data.
RetailDataIndividualFull.xlsx includes data for the period 2017-2018. Plot your series and now include the last two years’ worth of observations.
(Please see requirement in Question 13 (point 2) on how to read in your data).
10.
On the same graph, plot the point forecasts you have generated for the 2017-2018 period from alternative methods/models you have studied throughout the semester. These should include forecasts generated from:
• a benchmark from assignment 2;
• an ets model from assignment 3;
• an ARIMA model from assignment 4.
Visually inspect the forecasts and comment on any anomalies you may observe. (No more than 50 words. Think about complete presentation and optimum visualisation here).
11.
Summarise the accuracy of the competing forecasts in an appropriate table by calculating the RMSE, MAPE and MASE over the period 2017-2018 and choose the best model/method from this evaluation. Comment on how different these measures are between the competing models. (No more than 50 words for the comments).
12.
Use the top model, generate and plot forecasts and 80% forecast intervals for your series for the period 2019-2020. Briefly comment on these. (No more than 50 words).