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Population Forecasting Time Series Forecasting Techniques Wayne Foss, DBA, MAI, CRE, FRICS Foss Consulting Population Forecasting Time Series Forecasting Techniques Wayne Foss, DBA, MAI, CRE, FRICS Foss Consulting Group Email: wfoss@fossconsult. com 1

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Extrapolation Techniques n Real Estate Analysts - faced with a difficult task n long-term 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 Reliable short-term projections for small areas n Reliable long-term projections for regions countries n n Forecasting task complicated by: n Reliable, Timely and Consistent information 4

Sources of Forecasts n Public and Private Sector Forecasts Public: California Department of Finance Sources of Forecasts n Public and Private Sector Forecasts Public: California Department of Finance n Private: ERSI n n Forecasts may be based on large quantities of current and historical data 5

Projections are Important n Comprehensive plans for the future n Community General Plans for Projections are Important n Comprehensive plans for the future n Community General Plans for » Residential Land Uses » Commercial Land Uses » Related Land Uses n n n Transportation Systems Sewage Systems Schools 6

Definitions n Estimate: n n Projection (or Prediction): n n “is an indirect measure Definitions n Estimate: n n Projection (or Prediction): n n “is an indirect measure of a present or past condition that can be directly measured. ” “are calculations of future conditions that would exist as a result of adopting a set of underlying assumptions. ” Forecast: n “is a judgmental statement of what the analyst believes to be the most likely future. ” 7

Projections vs. Forecasts n The distinction between projections and forecasts are important because: Analysts Projections vs. Forecasts n The distinction between projections and forecasts are important because: 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. n 8

Procedure n Using Aggregate data from the past to project the future. n Data 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. 9

Why Use Aggregate Data? n Easier to obtain and analyze n Conserves time and 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 10

Extrapolation: A Two Stage Process n Curve Fitting n n Analyzes past data to Extrapolation: A Two Stage Process n Curve Fitting n n Analyzes past data to identify overall trends of growth or decline Curve Extrapolation n Extends the identified trend to project the future 11

Assumptions and Conventions n Graphic conventions Assume: Independent variable: n Dependent variable: n x Assumptions and Conventions n Graphic conventions Assume: Independent variable: n Dependent variable: n x axis 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? 12

Assumptions and Conventions n Population change reflects the change in aggregate of three factors: Assumptions and Conventions n Population change reflects the change in aggregate of three factors: births n deaths n migration n n These factors are time related however they are caused by other time related factors: health levels n economic conditions n n Time is a proxy that reflects the net effect of a 13 large number of unmeasured events.

Caveats n The extrapolation technique should never be used to blindly assume that past 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 n Past trends observed, not because they will always continue, but because they generally provide the best available information about the future. Must carefully analyze: Determine whether past trends can be expected to continue, or n If continuation seems unlikely, alternatives must be 14 considered n

Alternative Extrapolation Curves Linear n Geometric n Parabolic n Modified Exponential n Gompertz n Alternative Extrapolation Curves Linear n Geometric n Parabolic n Modified Exponential n Gompertz n Logistic n 15

Linear Curve n Formula: Yc = a + bx a = constant or intercept Linear Curve n Formula: Yc = a + bx 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 n 16

Linear Curve 17 Linear Curve 17

Geometric Curve n Formula: n n n a = constant (intercept) b = 1 Geometric Curve n Formula: n n n a = constant (intercept) b = 1 plus growth rate (slope) Difference between linear and geometric curves: n n n Yc = abx Linear: Geometric: constant incremental growth constant growth rate Conventions of the formula: n n n if b value > 1 curve increases without limit b value = 1, then the curve is equal to a if b value < 1 curve approaches 0 as x increases 18

Geometric Curve 19 Geometric Curve 19

Parabolic Curve n Formula: n n n Yc = a + bx + cx Parabolic Curve n Formula: n n n Yc = a + bx + cx 2 a = constant (intercept) b = equal to the slope c = when positive: curve is concave upward when = 0, curve is linear when negative, curve is concave downward growth increments increase or decrease as the x variable increases Caution should be exercised when using for long range projections. n Assumes growth or decline has no limits 20 n

Parabolic Curve 21 Parabolic Curve 21

Modified Exponential Curve n Formula: n n Yc = c + abx c = Modified Exponential Curve n Formula: n n Yc = c + abx c = Upper limit b = ratio of successive growth a = constant This curve recognizes that growth will approach a limit n Most municipal areas have defined areas » i. e. : boundaries of cities or counties 22

Modified Exponential Curve 23 Modified Exponential Curve 23

Gompertz Curve n Formula: n n n c = Upper limit b = ratio Gompertz Curve n Formula: n n n c = Upper limit b = ratio of successive growth a = constant Very similar to the Modified Exponential Curve describes: n n Log Yc = log c + log a(bx) initially quite slow growth increases for a period, then growth tapers off very similar to neighborhood and/or city growth patterns over the long term 24

Gompertz Curve 25 Gompertz Curve 25

Logistic Curve n Formula: Yc = 1 / Yc-1 where Yc-1 = c + Logistic Curve n Formula: Yc = 1 / Yc-1 where Yc-1 = c + ab. X n n Identical to the Modified Exponential and Gompertz curves, except: n n n c = Upper limit b = ratio of successive growth a = constant 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. Result: the ratio of successive growth increments of the reciprocals of the Yc values are equal to a constant Appeal: Same as the Gompertz Curve 26

Logistic Curve 27 Logistic Curve 27

Selecting Appropriate Extrapolation Projections n First: Plot the Data What does the trend look Selecting Appropriate Extrapolation Projections n First: Plot the Data What does the trend look like? n Does it take the shape of any of the six curves n n Curve Assumptions Linear: if growth increments - or the first differences for the observation data are approximately equal n Geometric: growth increments are equal to a constant n 28

Selecting Appropriate Extrapolation Projections, con’t n Curve Assumptions Parabolic: Characterized by constant 2 nd Selecting Appropriate Extrapolation Projections, con’t n Curve Assumptions Parabolic: Characterized by constant 2 nd differences (differences between the first difference and the dependent variable) if the 2 nd 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 n 29

Selecting Appropriate Extrapolation Projections, con’t n Curve Assumptions Gompertz: Characterized by first differences in Selecting Appropriate Extrapolation Projections, con’t n Curve Assumptions 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 n Observation data rarely correspond to any assumption underlying the extrapolation curves 30

Selecting Appropriate Extrapolation Projections, con’t n Test Results using measures of dispersion CRV (Coefficient Selecting Appropriate Extrapolation Projections, con’t n Test Results using measures of dispersion 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 31 n

Selecting Appropriate Extrapolation Projections, con’t 32 Selecting Appropriate Extrapolation Projections, con’t 32

Selecting Appropriate Extrapolation Projections, con’t 33 Selecting Appropriate Extrapolation Projections, con’t 33

Housing Unit Method n Formulas: 1) n 2) n 3) n HHg = ((BP*N)-D+HUa)*OCC Housing Unit Method n Formulas: 1) n 2) n 3) n HHg = ((BP*N)-D+HUa)*OCC POPg = HHg * PHH POPf = POPc + POPg » Where: HHg – – – – – Growth In Number of Households BP Average Number of Bldg. Permits issued per year since most recent census N Forecast period in Years D Demolitions (number) HUa No. of Housing Units in Annexed Area OCC Occupancy Rate POPg Population Growth PHH Persons per Household 34 POPc Population at last census POPf Population Forecast

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Housing Unit Method Example n Forecast Growth in Number of Housing Units n n Housing Unit Method Example n Forecast Growth in Number of Housing Units n n HHg = ((BP*N)-D+HUa)*OCC » HHg = ((193*5)-0+0)*95. 1% » HHg = 918 Forecast Growth in Population n n 1) 2) POPg = HHg * PHH » POPg = 918 * 2. 74 » POPg = 2, 515 Forecast Total Population n 3) POPf = POPc + POPg » POPf = 126, 003 + 2, 515 » POPf = 128, 518 36

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So That’s Population Forecasting Wayne Foss, DBA, MAI, CRE, FRICS, Fullerton, CA USA Email: So That’s Population Forecasting Wayne Foss, DBA, MAI, CRE, FRICS, Fullerton, CA USA Email: waynefoss@usa. net 38