Right on Target for Time Series Forecasting

 

 

Christopher W. Craighead

Auburn University

Department of Management

Lowder Building, Suite 401

Auburn University, AL 36849

Phone: 334-844-6461

FAX: 334-844-5159

Email: craigcw@auburn.edu

 

 

MOTIVATION

Forecasting is an important topic that is taught in various arenas such as logistics (Closs, Melnyk, Stank & Swink 2000), operations management (Closs, Melnyk, Stank & Swink 2000), accounting (Walker & Ainsworth 2001), economics (Miller 2000), and supply chain management (Johnson & Pyke 2000).  However, teaching the forecasting techniques is often a difficult task.  Students’ understanding of the covered quantitative material is often limited to “plug and chug” and therefore the knowledge of the underlying concepts is limited (Nilson 1998), which provides the motivation for this in-class exercise.  Specifically, the exercise is designed to illustrate the concepts related to time series forecasting with the intent of enabling a “mental connection” to the tools.

CLASSROOM TECHNIQUES

To prepare for the activity, the instructor should purchase an inexpensive dartboard (likely under $10) with light, plastic-tipped darts.  The instructor should introduce forecasting and may discuss the importance of forecasting, the scope of forecasts, the types of decisions that are influenced by forecasts and the types of forecasting techniques.  However, it is important that the instructor not cover the concepts that are introduced with the exercise—see Table 1 for a summary of the concepts.

(Insert Table 1 about here)

Basics of the Technique

­Explaining the motivation and introducing the in-class exercise—The instructor should explain to students that much of the difficulty with understanding time series forecasting stems from the lack of a “picture” in mind that illustrates the concepts.  A solid grasp of the concepts of time series forecasting will likely improve their ability to perform the mechanics of the tool, evaluate the results, and improve the forecasting tool.  The instructor should then explain that in order to help the students grasp the concepts and give them a picture in their mind, “we are going to throw darts.” 

Getting started—After obtaining a volunteer, the instructor should explain that the bullseye (i.e., the center circle) represents the demand and that the dart represents a forecast of the demand.  The instructor should hold (as far away from their body as possible) the dartboard on the chalk/white board at the front of the room and then have the student (positioned 8-10 feet away) throw a few darts (3-4 should be sufficient).  The likely result is he/she will not hit the bullseye each time (if at all).  At this point, the instructor should pause and briefly discuss the first lesson of the exercise:  When attempting to forecast demand (illustrated by throwing the dart at the bullseye), there is a good chance that the forecast (the dart) will not hit the demand point (bullseye).

Changing Distance—The next step is to have the student move extremely close (approximately 18 inches) from the dartboard.  Once the instructor tells the student to try again, the student will likely place all of the darts in the bullseye without throwing them.  The instructor should then have the student move far away (16-20 feet) from the dartboard and have him/her throw a set of darts in a normal fashion with the dart and throwing arm in front of their body (to minimize velocity!).  The likely result is that the student will not even hit the dartboard.  At this point, the instructor should pause and briefly discuss another lesson:  The distance of the student from the dartboard may be thought of as the distance of the demand point in the future and therefore, as the demand point’s distance in the future is increased, both the chance of missing it and the magnitude of the miss will increase.

Time Series Embellishments of the Technique

Moving the Target (Random Movement)—The instructor should have the student return to their original position (8-10 feet) and instruct him/her to throw another set of darts.  Each time the student throws the dart, the instructor should immediately move (while the dart is in flight) the target either up or down slightly.  The movement should not be in a pattern (e.g., up, down, up) and should only be a few inches at a time.  At this point, the instructor should pause and briefly discuss another lesson:  When forecasting demand, you are indeed trying to hit a moving target.  There are several components of a time series.  The slight movements of the dartboard may represent the random component.

Moving the Target (Trend Movement)—When the student throws a dart, the instructor should immediately move (while the dart is in flight) the target up (approximately 18 inches) at an angle as shown in Figure 1.  The likely result will be the dart will hit the wall where the dartboard was in its original position.  When the student throws another dart, the dartboard should once again be moved up at an angle as shown in Figure 1.  The result of the throw will likely be the same.  The instructor should repeat this at least one more time.  At this point, the instructor should pause and briefly discuss another lesson:  As a reminder, there are several components of a time series.  The consistent (relatively speaking) movement of the demand (bullseye) either up or down represents the trend component. 

(insert Figure 1 about here)

At some point during this portion of the exercise, the student may recognize the pattern and throw the dart where he/she thinks the instructor will move the dartboard.  If this occurs, the next lesson is made apparent!  Whether the student adapts his/her throw or not, the instructor should recap the trend movement.  This may be accomplished by moving the dartboard in the same manner as he/she did during the “live” exercise and mark an “X” on the board to illustrate each position.  The trend will be made clear on the board as the series of Xs will show the upward movement.  The instructor should follow the Xs on the board and show how the throw should be adjusted to target the next X along the trend path.  The instructor should then pause and briefly discuss another lesson:  In time series forecasting, the forecaster should look for patterns in the demand movement.  If a pattern is recognized, the forecaster should adjust the next forecast to target where the demand point will be, not where it is currently.

Moving the Target (Seasonal Movement)—When the student throws a dart, the instructor should immediately move the target up at an angle as shown in Figure 2.  The process should be repeated at least three more times, following the pattern shown in Figure 2.  The student may or may not recognize the pattern.  The instructor should recap the movement of the dartboard (as before) indicating each position with an “X” on the board.  At this point, the instructor should pause and briefly discuss another lesson:  This “up and down” pattern may represent the seasonal component of a time series. The instructor may want to discuss a product with a clear seasonal influence to clarify this concept.  Also, the instructor should reemphasize the lesson that once the pattern is recognized, the forecast (dart) should be adjusted accordingly—the instructor may show this relative to the Xs on the board.

(Insert Figure 2 about here)

“Keeping Score”

After dismissing the volunteer, the instructor should point out the need to “keep score.”  The instructor should place 4 darts on the dartboard at various distances from the bullseye with two of the darts positioned above the bullseye and two below it.  The instructor should relate MAD to the dartboard and the 4 darts by indicating that “MAD may be thought of as an average distance of the darts to the bullseye.”  The instructor should then move all of the darts below the bullseye.  The instructor should ask the class what the forecaster should do if he/she had “missed” the demand points as shown on the dartboard.  The class will likely respond that the “dart should be thrown higher.”  The instructor should confirm the accuracy of their assessment and then introduce Bias as a measure of whether the forecasting method was, on average, missing below or above the demand point and therefore may indicate how the forecasting method could be “tweaked” to more accurately target the demand point.     

STUDENT REACTIONS

During the entire exercise, the class appeared to be engaged in the activity—the students would often cheer (e.g., when the volunteer would hit the target) and laugh (e.g., when the volunteer would miss due to the instructor moving the dartboard).  During several class periods following the exercise, the students were taught the mechanics of and concepts related to exponential smoothing.  Overall, the darts exercise appeared to by an effective reference point during the lectures and discussion.           

A brief questionnaire was completed by the class after the final exponential smoothing lecture.  The results (n=54) were positive as 94% of the students either agreed or strongly agreed that the method was effective in helping them learn and 100% agreed or strongly agreed that the method was an interesting approach to introduce the concepts.  In addition, the comments from the survey were extremely positive.  Selected comments include, “It was perfect for keeping me interested and making me think,” “Very effective and creative way of teaching!” and “Entertaining visual aid for learning.”

It should be noted that the responses are based on perceptions and therefore should be followed with more formal assessments of the exercise.  This follow-up may take on many forms.  For example, students may be split into groups where one is exposed to the exercise and one is not.  An assessment tool (e.g., quiz) could be administered to both and then results could be compared.

DISCUSSION

Overall, the darts exercise appears to be an effective and novel method for introducing the concepts of time series forecasting.  The students’ response to the method was overwhelmingly positive and the instructor found it useful as a reference point during the classes that followed.  One may make the observation that the exercise captures too much precious class time, yet it is estimated that with refinement, the amount of time could be reduced to 8-9 minutes (the first time took 11 minutes).  This would appear to be a small “cost” when the potential benefits are considered.  Based on the students’ responses, the technique appears to provide an attentive audience and an effective mechanism for student learning of the time series concepts.  By illustrating the concepts, the technique allows students with a visual learning style (Fleming & Mills 1992) to take advantage of the class time.  Further, since the students are writing (notes), listening (to the lecture), and seeing (the darts exercise), they are involved in a multiple-sense presentation that offers a better learning approach for all students no matter their primary learning style (Nilson 1998).   

 

REFERENCES

Closs, D.J., Melnyk, S.A., Stank, T.P. & Swink, M., (2000), “An Integrated Curriculum for Teaching Supply Chain Management at Michigan State University,” POM Series in Technology and Operations Management, vol. 2, pp.43-56.

 

Fleming, N.D. & Mills, C., (1992), “Not Another Inventory, Rather a Catalyst for Reflection,” To Improve the Academy, vol. 11, pp. 137-155.

 

Johnson, M. E. & Pyke, D.F., (2000), “A Framework for Teaching Supply Chain Management,” Production and Operations Management, vol. 9, no. 1, pp. 2-18.

 

Miller, J.R., (2000), “Economics in the Integrated Business Curriculum,” Journal of Education for Business, Nov/Dec, pp.113-118.

 

Nilson, L.B., (1998), Teaching at its Best: A Research-Based Resource for College Instructors, Anklin Publishing Company, Bolton, MA

 

Walker, K.B. & Ainsworth, P.L., (2001), “Developing a Process Approach in the Business Core Curriculum,” Issues in Accounting Education, vol. 16, no. 1, pp. 41-66.

 

FIGURES AND TABLE

 

Table 1: Overview of Darts Exercise

Technique	Distance	Dartboard Movement	Concepts/Lessons Learned
Basic	8-10 feet	None	Basic logic of forecasting
Changing Distance	2 feet then 16-20 feet	None	The effects of forecasting horizon
Random Movement	8-10 feet	Slight distance (1-2 inches) in a random fashion	Components of Time Series: Random
Trend Movement	8-10 feet	Substantial distance (18 inches) in a pattern as shown in Figure 1.	Components of Time Series: Trend
Seasonal Movement	8-10 feet	Substantial distance (18 inches) in a pattern as shown in Figure 2.	Components of Time Series: Seasonality
Keeping Score	NA*	NA*	Forecast Accuracy: MAD and Bias

*NA=Not applicable (darts are placed on dartboard by the instructor)

 

 

 

 

 

 

 

 

Figure 1: Movement to Illustrate Trend Component

 

 

 

 

 

 

 

 

 

 

Figure 2: Movement to Illustrate Seasonal Component