1. 1 Population Forecasting Time Series Forecasting Techniques Wayne Foss, MBA, MAI Wayne Foss Appraisals, Inc. Email: wfoss@fossconsult.com

2. 2 Extrapolation Techniques n Real Estate Analysts - faced with a difficult task n long-term projections for small areas such as »Counties »Cities and/or »Neighborhoods n Reliable short-term projections for small areas n Reliable long-term projections for regions countries n Forecasting task complicated by: n Reliable, Timely and Consistent information

3. 3 Sources of Forecasts n Public and Private Sector Forecasts n Public: California Department of Finance n Private: CACI n Forecasts may be based on large quantities of current and historical data

4. 4 Projections are Important n Comprehensive plans for the future n Community General Plans for »Residential Land Uses »Commercial Land Uses »Related Land Uses n Transportation Systems n Sewage Systems n Schools

5. 5 Definitions n Estimate: n “is an indirect measure of a present or past condition that can be directly measured.” n Projection (or Prediction): n “are calculations of future conditions that would exist as a result of adopting a set of underlying assumptions.” n Forecast: n “is a judgmental statement of what the analyst believes to be the most likely future.”

6. 6 Projections vs. Forecasts n The distinction between projections and forecasts are important because: n Analysts often use projections when they should be using forecasts. n Projections are mislabeled as forecasts n Analysts prepare projections that they know will be accepted as forecasts without evaluating the assumptions implicit in their analytic results.

7. 7 Procedure n Using Aggregate data from the past to project the future. n Data Aggregated in two ways: »total populations or employment without identifying the subcomponents of local populations or the economy n I.e.: age or occupational makeup »deals only with aggregate trends from the past without attempting to account for the underlying demographic and economic processes that caused the trends. n Less appealing than the cohort-component techniques or economic analysis techniques that consider the underlying components of change.

8. 8 Why Use Aggregate Data? n Easier to obtain and analyze n Conserves time and costs n Disaggregated population or employment data often is unavailable for small areas

9. 9 Extrapolation: A Two Stage Process n Curve Fitting - n Analyzes past data to identify overall trends of growth or decline n Curve Extrapolation - n Extends the identified trend to project the future

10. 10 Assumptions and Conventions n Graphic conventions Assume: n Independent variable:x axis n Dependent variable:y axis n This suggests that population change (y axis) is dependent on (caused by) the passage of time! n Is this true or false?

11. 11 Assumptions and Conventions n Population change reflects the change in aggregate of three factors: n births n deaths n migration n These factors are time related and are caused by other time related factors: n health levels n economic conditions n Time is a proxy that reflects the net effect of a large number of unmeasured events.

12. 12 Caveats n The extrapolation technique should never be used to blindly assume that past trends of growth or decline will continue into the future. n Past trends observed, not because they will always continue, but because they generally provide the best available information about the future. n Must carefully analyze: n Determine whether past trends can be expected to continue, or n If continuation seems unlikely, alternatives must be considered

13. 13 Alternative Extrapolation Curves n Linear n Geometric n Parabolic n Modified Exponential n Gompertz n Logistic

14. 14 Linear Curve n Formula:Yc = a + bx n a = constant or intercept n b = slope n Substituting values of x yields Yc n Conventions of the formula: n curve increases without limit if the b value > 0 n curve is flat if the b value = 0 n curve decreases without limit if the b value < 0

15. 15 Linear Curve

16. 16 Geometric Curve n Formula:Yc = ab x n a = constant (intercept) n b = 1 plus growth rate (slope) n Difference between linear and geometric curves: n Linear:constant incremental growth n Geometric:constant growth rate n Conventions of the formula: n if b value > 1 curve increases without limit n b value = 1, then the curve is equal to a n if b value < 1 curve approaches 0 as x increases

17. 17 Geometric Curve

18. 18 Parabolic Curve n Formula:Yc = a + bx + cx 2 n a = constant (intercept) n b = equal to the slope n c = when positive: curve is concave upward when = 0, curve is linear when = 0, curve is linear when negative, curve is concave downward when negative, curve is concave downward growth increments increase or decrease as the x variable increases growth increments increase or decrease as the x variable increases n Caution should be exercised when using for long range projections. n Assumes growth or decline has no limits

19. 19 Parabolic Curve

20. 20 Modified Exponential Curve n Formula:Yc = c + ab x n c = Upper limit n b = ratio of successive growth n a = constant n This curve recognizes that growth will approach a limit n Most municipal areas have defined areas »i.e.: boundaries of cities or counties

21. 21 Modified Exponential Curve

22. 22 Gompertz Curve n Formula:Log Yc = log c + log a(b x ) n c = Upper limit n b = ratio of successive growth n a = constant n Very similar to the Modified Exponential Curve n Curve describes: n initially quite slow growth n increases for a period, then n growth tapers off n very similar to neighborhood and/or city growth patterns over the long term

23. 23 Gompertz Curve

24. 24 Logistic Curve n Formula: Yc = 1 / Yc -1 where Yc -1 = c + ab X n c = Upper limit n b = ratio of successive growth n a = constant n Identical to the Modified Exponential and Gompertz curves, except: n observed values of the modified exponential curve and the logarithms of observed values of the Gompertz curve are replaced by the reciprocals of the observed values. n Result: the ratio of successive growth increments of the reciprocals of the Yc values are equal to a constant n Appeal: Same as the Gompertz Curve

25. 25 Logistic Curve

26. 26 Selecting Appropriate Extrapolation Projections n First: Plot the Data n What does the trend look like? n Does it take the shape of any of the six curves n Curve Assumptions n Linear: if growth increments - or the first differences for the observation data are approximately equal - n Geometric: growth increments are equal to a constant

27. 27 Selecting Appropriate Extrapolation Projections, con’t n Curve Assumptions n Parabolic: Characterized by constant 2nd differences (differences between the first difference and the dependent variable) if the 2nd differences are approximately equal n Modified Exponential: characterized by first differences that decline or increase by a constant percentage; ratios of successive first differences are approximately equal

28. 28 Selecting Appropriate Extrapolation Projections, con’t n Curve Assumptions n Gompertz: Characterized by first differences in the logarithms of the dependent variable that decline by a constant percentage n Logistic: characterized by first differences in the reciprocals of the observation value that decline by a constant percentage n Observation data rarely correspond to any assumption underlying the extrapolation curves

29. 29 Selecting Appropriate Extrapolation Projections, con’t n Test Results using measures of dispersion n CRV (Coefficient of relative variation) n ME (Mean Error) n MAPE (Mean Absolute Percentage Error) n In General: Curve with the lowest CRV,ME and MAPE should be considered the best fit for the observation data n Judgement is required n Select the Curve that produces results consistent with the most likely future

30. 30 Selecting Appropriate Extrapolation Projections, con’t

31. 31 Housing Unit Method n Formulas: n 1) HH g = ((BP*N)-D+HU a )*OCC n 2) POP g = HH g * PHH n 3) POP f = POP c + POP g »Where: HH g Growth In Number of Households –BPAverage Number of Bldg. Permits issued per year since most recent census –NForecast period in Years –HU a No. of Housing Units in Annexed Area –OCCOccupancy Rate –POP g Population Growth –PHHPersons per Household –POP c Population at last census –POP f Population Forecast

32. 32 Housing Unit Method Example n Forecast Growth in Number of Housing Units n 1) HH g = ((BP*N)-D+HU a )*OCC »HH g = ((193*5)-0+0)*95.1% »HH g = 918 n Forecast Growth in Population n 2) POP g = HH g * PHH »POP g = 918 * 2.74 »POP g = 2,515 n Forecast Total Population n 3) POP f = POP c + POP g »POP f = 126,003 + 2,515 »POP f = 128,518

33. 33 So That’s Population Forecasting Wayne Foss, MBA, MAI, Fullerton, CA USA Email: waynefoss@usa.net