Australian Bureau of Statistics (ABS) provides retail data for different groups and different states as well as the aggregate numbers. Table 11 " Retail Turnover, State by Industry Subgroup, Original" contains the data you can use in this part. You can select the state and the group you wish to analyse or you can use the aggregated data. The file contains monthly retail turnover data from April, 1982 to June, 2011. You are hired as a forecasting consultant to analyse the retail data as there is a concern that Australia retail sector is getting softer.

You, as an econometrics expert, need to analyse, generate and assess forecasts for monthly sales retail turnover for the rest of 2011.

After consulting with your peers, you decide to consider three models/methods for application to this dataset to generate forecasts.

Models/Methods:

A Naïve

B Decomposition

C A model of your choice.

(i) Perform an exploratory analysis on the entire dataset and discuss the important aspects of the data. Show all RELEVANT output (e.g. graphs, tables).

(ii) Choose a suitable decomposition model for model B while clearly motivating your choice using your answer in part (i) and any other relevant information i.e. choose between a multiplicative OR an additive model.

(iii) Choose a suitable model C while again clearly motivating your choice^*.

* Bonus marks are available for more complicated or formal models that are well chosen based on (i), if parts (iv)-(xiii) are done well, to acknowledge the extra work required for such models. However, simple models are still acceptable with full marks still possible for parts (iv)-(xiii) in that case.   

You have to use at least 6 years as the in-sample period, and your hold-out sample for forecasting should have at least 12 points.

(iv) Clearly present and discuss the trend-cycle, seasonal and error components in the in-sample data, as assessed by model B. Contrast these components between the models B and C if appropriate.

(v)  Choose a model form for the trend component (one for Model B and also for model C, but only if appropriate) and clearly and properly justify your choice.

(vi)  Discuss and compare how well, or otherwise, the models A, B (including trend as in (v)) and C fit the data in the in-sample period. Use statistical tests if appropriate.

(vii)  Forecast the hold-out year, of monthly turnover data using Models A-C, using only the chosen in-sample period. Provide a table of these forecasts as well as a graph, together with the actual turnover for the last 12 months.

(viii) Assess the accuracy of each model and compare the models for forecast performance in the appropriate ways. Identify the best forecasting model and why you chose it as best.

(ix) Provide 95% interval forecasts for sales in the last 12 month for each model. Clearly present the method you used to obtain such interval estimates. As much as you can, discuss, interpret and compare these intervals. Are they accurate? Is one model better than the others here?

(x) Choose a forecast model from A-C, motivating your choice. Then, update it with the latest available data, and then generate both point and 95% interval forecasts for the rest of 2011. Present these in an appropriate manner. Further, discuss how accurate you think these 2011 forecasts might turn out to be, with justification.

(xi) Prepare an executive summary^** outlining and summarising your analysis, providing your forecasts in a form suitable for the evening news. Use layman's terms, since the majority of the viewers did not take the advanced forecasting course and do not understand statistical notation.