OM 252, Winter 2025

HW 3

Assigned: Jan 23, 2025, 9 AM

Due: Jan 29, 2025, 11:59 PM

Instructions: Each assignment will include a PDF file (like this one) with the assignment questions and an Excel file with an Answers sheet and any data or models we provide. You must download both the PDF and Excel files. You must enter your answers in the Answers sheet of the same Excel file you downloaded, then save and upload the Excel file. You must upload the same Excel file you downloaded. Further instructions are provided in the Online Assignment Tools Guide (see Assignments on Canvas).

Put your answers in the appropriate cells (salmon-colored cells) in the Answers sheet. Use paste special … values for all numerical answers. The other cells in the Answers sheet are locked, which means you won’t be able to enter values into those cells. Do not change the format of cells in the Answers sheet. Save your file with the appropriate name and in the proper format (“HW#_ID.xlsx”).

Marking will be based on the answers in the Answers worksheet of the file you upload. We will only look at the rest of the file if there is an appeal (and even then, the answers in the Answers sheet take precedence.) If you wish to appeal a mark, the uploaded file must include your supporting work for each question. It is a good idea to make one worksheet for each question.

Total points: 35, of which 2 points are for following the submission instructions provided above.

Forecasting Number of Building Permits Issued in Edmonton

In this assignment, we use a different data set related to the number of building permits issued by the City of Edmonton. Our interest is in forecasting the number of permits issued in the future. The “Data” sheet shows the total number of permits issued for every month from January 2015 to December 2024.

You will use this data for all of your work on this assignment. Here is a plot of the monthly data:

Let us begin by plotting the data.

From Figure 1, We observe an annual seasonal pattern in the data. The number of permits issued is substantially higher between April and November. Between December and March, the number of permits issued dropped significantly. This suggests that a forecasting method incorporating seasonality should perform better than methods ignoring seasonality. First, we will compare the SES, DES, and TES  methods in terms of one-month-ahead forecasts and then forecasts for two years into the future using the holdout strategy.

Part 1: One-day-ahead forecasts

1.    (3 pts.) Using the data provided in the “Data” sheet, calculate the average number of permits issued each month from 2015 to 2024.

In this part, we will perform. a within-sample comparison of SES, DES, and TES based on how these methods perform. at one-month-ahead forecasting for January 2016 to December 2022. We leave out January 2015 to December 2015 for the initialization of TES. We leave out January 2023 to December  2024 for an out-of-sample comparison of the methods; see Part 2 of the assignment.

Note that when you are using SES and DES you can start forecasting earlier than January 2016, but in order to have a fair comparison between the three methods, we calculate the RMSE only for January 2016 to December 2022. We also calculate the RMSE for January 2021 to December 2022 as it gives us a more recent, and a more relevant, performance measure.

2.    (1 pt. feasibility, 3 pts. consistency, 1 pt. optimality) Use the SES method to calculate the one- month-ahead forecasts for January 2016 to December 2022. Use solver to find the value of LS that minimizes the RMSE for January 2016 to December 2022. Keep LS in the range 0.05 to 0.95. Report the following:

•    LS

•    RMSE for January 2016 to December 2022

•    Forecasts for January 2021 to December 2022

•    RMSE for January 2021 to December 2022

3.    (1 pt. feasibility, 3 pts. consistency, 1 pt. optimality) Use the DES method to calculate the one-month-ahead forecasts for January 2016 to December 2022. Use solver to find the values of LS and TS that minimize the RMSE for January 2016 to December 2022. Keep LS and TS in the range 0.05 to 0.95. Report the following:

•    LS, TS

•    RMSE for January 2016 to December 2022

•    Forecasts for January 2021 to December 2022

•    RMSE for January 2021 to December 2022

4.    (1 pt. feasibility, 3 pts. consistency, 1 pt. optimality) Use the TES method to calculate the one-month-ahead forecasts for January 2016 to December 2022. Use solver to find the values of LS, TS, and SS that minimize the RMSE for January 2016 to December 2012. Keep LS, TS, and SS in   the range 0.05 to 0.95. Report the following:

•    LS, TS, SS

•    RMSE for January 2016 to December 2022

•    Forecasts for January 2021 to December 2022

•    RMSE for January 2021 to December 2022

Part 2: Holdout analysis with multiple-days-ahead forecasts

In this part, treat January 2016 to December 2022 as the training data and January 2023 to December 2024 as the holdout data.

5.    (5 pts.) Use the SES method to compute forecasts for January 2023 to December 2024. Use the value of LS that you found in Question 2. Report the following:

•    Forecasts for January 2023 to December 2024, calculated assuming that the learning phase ends at the end of December 2022

•    The RMSE for January 2023 to December 2024

6.    (5 pts.) Use the DES method to compute forecasts for January 2023 to December 2024. Use the values of LS and TS that you found in Question 3. Report the following:

•    Forecasts for January 2023 to December 2024, calculated assuming that the learning phase ends at the end of December 2022

•    The RMSE for January 2023 to December 2024

7.     (5 pts.) Use the TES method to compute forecasts for January 2023 to December 2024. Use the LS, TS, and SS values found in Question 4. Report the following:

•    Forecasts for January 2023 to December 2024, calculated assuming that the learning phase ends at the end of December 2022

•    The RMSE for January 2023 to December 2024

8.     (For practice and will not be marked) Based on the analysis you have done, which method do you recommend?