## Description

*The Analysis is on US Retail Sales: Food Services and Drinking Places: NAICS 722 Millions of dollars:*

*NSA *

*NSA url link: http://www.economagic.com/em-cgi/data.exe/cenret/nrt722nsa.*

*Sample period is from January 2007 to September 2018 and consists of one-hundred and forty-one observations.*

*General description:*

The intention of this project report is to allow students to apply the time-series forecasting techniques they learnt in Module 3 and Module 4 to forecast the next 12 months of the retail sales data they selected. Conduct __at least__ the following suggested analysis in Minitab, copy and paste the relevant printouts and graphs in a Word document, and provide descriptions and comments. This Report 2 must be double-space typed and presented in a professional manner. Other than the correctness of the analysis, presentation and organization of the report also counts.

*Format of the Project Report 2: *

(1) Your name and e-mail address.

(2) Give a title for your report, and write an introduction / purpose of the study.

(3) Data source and description

Give a general description of the retail sales data you selected.

In your description, you need to include the definition of the data and data source (URL link), for

example: US Retail Sales: Home Furnishings Stores: NAICS 4422: Millions of dollars: NSA

URL link: http://www.economagic.com/em-cgi/data.exe/cenret/n...

Also, mention the sample period: e.g., from 2007 January to 2018 ?month

Total number of observations is ______. (You should have more than 100 observations).

Any other details/descriptions you would like to add.

(4) Statistical Analysis

Input the sales data into the Minitab. Perform the following analysis, copy and paste the relevant computer printouts and graphs to the report, and be sure to provide comments and descriptions.

The main objective is to forecast the sales data for the next 12 months, using the time-series forecasting techniques we learnt in Module 3 and Module 4, namely, Naïve method, Moving average method, and the 3 exponential smoothing methods. Which method gives the best forecasts? Specifically, try each of these methods, and compare based on the accuracy measures, and select a better method.

*Note:* selection is generally based on the accuracy measures MAD, MSD, and MAPE that are provided in Minitab. A better (or more accurate) method gives smaller values in these measures. In case these measures are not consistent, we adopt the convention that selection is based on MSD (or called MSE). That is, select the method that gives a smaller MSD (or MSE). For interpretation, take the square root of MSD (or MSE) and get the RMSE, which is somewhat like the standard deviation of the forecast errors.

(a) For __moving average, __try MA of order 1 to 12, MA(1) to MA(12), to forecast the next 12 months.

Note that MA(1) is the same as Naïve method. Select the best MA order based on the accuracy measure MSD. Summarize the results in a table.

Comment and discuss the accuracy measures, and the forecasts made (including the Prediction Interval).

(b) Use __simple smoothing__ method to forecast the next 12 months.

Use Minitab to pick the best smoothing constant α for your sales data. In case your Minitab version does not have the option to pick the best α, find a better one using trial-and-error, i.e., try α from 0.1, 0.2, …, 0.9 and fine tune. Summarize the results in a table.

Comment and discuss the accuracy measures, and the forecasts made (including the Prediction Interval).

(c) Use __Holt’s double smoothing__ method to forecast the next 12 months.

Use Minitab to pick the best smoothing constants α and γ for your sales data. In case your Minitab version does not have the option to pick the best smoothing constants, find a better one using trial-and-error. For instance, try a small, median, and large value of α (say 0.2, 0.5, 0.8) and similarly for γ , and then fine tune. Summarize the results in a table.

Comment and discuss the accuracy measures, and the forecasts made (including the Prediction Interval).

(d) Use __Winters’ triple smoothing__ method to forecast the next 12 months.

Minitab does not automatically pick the best smoothing constants α, γ and δ, we can find a better one using trial-and-error. For instance, try a small, median, and large value of α (say 0.2, 0.5, 0.8), and similarly for γ and δ, and fine tune. Summarize the results in a table.

Also, plot the Level, Trend, and Seasonal components from the Winters’ method, comment and discuss the behaviors of these components. For example, was the time trend increased steadily, or is there some periods that grew faster/slower. For the level, it is generally increasing if the data has an upward trend. Based on the seasonal indices, you can say something about which are the best and worst seasons, and does it make sense for this type of sales? etc

(You can ignore the first 12 months or so due to the effect of starting values).

(e) Another approach: Forecast based on individual month

The idea is if we want to forecast January, use only past January observations. Similarly for Feb, March, …, December.

Construct a series that consist of only that month *i* (*i* = 1, 2, …, 12), and use an appropriate method (in the example, Holt’s double smoothing method seems to be appropriate) to forecast the next month.

To create the month *i* series, use

*Data > unstack column *

*And follow instructions to unstack “Sales” by “month”. *

Then __for each monthly series__, forecast 1 step ahead. (For example, using the Holt’s double smoothing method with the best smoothing constants chosen by Minitab. In case your Minitab version does not have the option to pick the best smoothing constants, find a better one using trial-and-error. For instance, try a small, median, and large value of α and similarly for γ. For simplicity, you can use the same smoothing constants for all months.)

For each month’s results, comment and discuss the accuracy measures, and the forecast made (including the Prediction Interval).

Finally, compare these forecasts and accuracy measures (say MSD) with the forecasts and accuracy measures made by the best method you selected above (in the example, it is the Winters’ triple smoothing method). Comments and discuss. In general, there is no definite answer as to which set of forecasts is better, but we can compare their MSD’s and see which approach generally gives smaller MSD.

(5) Summary and Conclusion

Write a summary and conclusion based on the analysis that you have done. This part should be non-technically written so that a non-technical supervisor should be able to read and understand.

Note:

Every sales data is unique, e.g., electronic stores sales probably behaves differently from say furniture stores sales. The structure/analysis I provided above serves just as a guideline or framework for the report, you may want to expand on that and add anything you think is interesting. So unlike a test that we just answer the questions, try to elaborate more. In other words, besides just answer the basic statistical questions raised, feel free to add discussions / questions / insights/ further analysis / graphs etc into the report to better forecast the particular sales data you are studying.

__Report 2 submission guidelines:__

- Save your Minitab analysis in a Minitab project file:

- In
*File*, choose “*Save Project As*”, and save the analysis you have done in a Minitab project file. Name your Minitab project file beginning with your name, and a key word of your sales data. e.g., RongZheng_HomeSales.MPJ (Minitab project file has the extension *.MPJ)

- Project Report 2 follows similar naming convention. e.g., RongZheng_HomeSales_Report2.docx

- Submit both the Project Report 2 and the Minitab project file in Western Online:

- Go to WesterOnline, in “Assessment”, choose “Assignment”, choose “Project Report 2”, and follow instruction to submit your report.
- It is important to submit these
__two__documents, the report 2 will receive a score of 0 without the Minitab project file.

__This Report 2 must be double-space typed and presented in a professional manner. Other than the correctness of the analysis, presentation/organization/style of the report also counts. This Project Report 2 counts 10% towards the final grade; and 1% will be assigned to the presentation/organization/style of the report. There is penalty for late submission.__