Using Time Series Modeling to Forecast Enrollments

1. Using Time Series Modeling to Forecast Enrollments Robert J. Marsh, Ph.D. Associate Dean of Research and Assessment North Central Michigan College MI/AIR, November 8, 2013

2. Why forecast enrollment? • Declining enrollment since 2010 • Declining property tax base • Declining state appropriation • Uncertain budgeting process due to lack of data • ACCURATE FORECASTS ARE MORE IMPORTANT THAN EVER

3. Previous forecasts • Intuitive, sense of potential population • Trends in HS graduations • Conversations with HS counselors • Conversations with workforce organizations and advisory boards • Assume flat enrollment for budget; be pleased with an increase • Assume a 2-3% year-over-year increase • Held steady for many years • Extrapolate from recent terms’ trend • Monitor statewide trends among CCs • No data-informed methodology

4. An enrollment forecast model • Possible factors • Area population • Tuition • Area unemployment • High school graduate census • Past enrollments • Competition, especially online • Tuition differential, four-year vs. community college • Attitude towards education in general • Community colleges in particular

5. Regression approach • Identify factors (xi), find coefficients (bi) • Identifying relevant or interesting (or pertinent) factors • Enrollments can be more dependent on past enrollments than outside factors

6. Area population • Sometimes highly correlated, but not always. Pop change ~ 2% CH change ~ 26%

7. Time series forecasting • Relies on past demand to forecast future • Stores only one past period’s demand (originally necessary) • Typically forecasts one period ahead

8. Time series forecasting • Simple: forecast = immediate past period • Moving average: average of n past periods

9. Exponential Smoothing • Originated in the production/operations management field, 50+ years ago (management science) • Primary formula where a is the “smoothing coefficient” • Relies on the past period’s actual (At-1) and forecast (Ft-1) values. • An a close to 1.0 results in a very reactive model, one more responsive to very recent actual data. • All that needed to be stored were the immediate past actual and forecast values. (Holt, 1957)

10. Exponential Smoothing • Each period’s forecast builds on all past periods, although only immediate past period’s needs to be stored

11. “Exponential” Smoothing • Reliance on progressively older data drops off exponentially

12. Exponential Smoothing with trend • Trends within our actual enrollment patterns. • Add a trend component where b is the “trend factor” (Holt & Winters, 1960; Hopp& Spearman, 2011)

13. Seasonality • Enrollment is seasonal, with fall typically being higher than winter • Add a seasonality factor by superimposing a sinusoidal function • Exclude summers (much lower) Fall Winter

14. Seasonality • Sine function is periodic over 2p, every two periods (every fall) the forecast tends to be higher. (Middleton, 2010)

15. Methodology • Obtained 30 years of enrollment data (credit hours) • 60 periods (no summers) • Built model in Excel® 2011 • Used Solver®to “optimize” the model • Minimized sum of squared differences (the objective function, Z) by varying a, b, H, nand f

16. Excel®-spreadsheet Parameters

17. Excel®-Solver® Z a, b, H, n, f a b f

18. Results • Initially used actual data through Winter 2011-12 to forecast Fall 2012-13 • Discovered strong “starting point dependency” within the non-linear model in Solver • Not optimal; best described as heuristic Results through Winter 2011-12, showing “best”: MAPE = 3.3%. Using model would have produced a 1.7% error for W12 *

19. Results • Used “best” from W12 to forecast Fall 2012 • F12 forecast = 21,980 • F12 actual = 21,878 • Difference = 0.5% • Model MAPE = 3.3% • Incorporated actual F12 data into model to forecast Winter 2013 *

20. Results • Used “best” from F12 to forecast Winter 2013 • W13 forecast = 19,783 • W13 actual = 21,081 • Difference = – 6.2% • Model MAPE = 3.4% • Resulted in an under-forecast • Assumes past practices continue • More focused recruitment effort made

21. Model fit

22. Discussion • Model is not optimal • Non linear objective function; heuristic methodology • Does not include any outside variables (as written) • Solver® is blunt instrument • Can be built on simple software platform • Good visualization with graphs • Relies on known data • Very quick to update and do what-if analysis • Pretty accurate

23. I’m happy to share Bob Marsh North Central Michigan College 231.439.6353 rmarsh@ncmich.edu

24. Discussion ?