1. Business and Economic Forecasting Chapter 5
Business and Economic Forecasting is a critical managerial activity which comes in two forms:
Quantitative Forecasting % Gives the precise amount
or percentage
Qualitative Forecasting
Gives the expected direction
Up, down, or about the same
2008 Thomson * South-Western 1

2. Managerial Challenge Excess Fiber Optic Capacity
High-speed data installation grew exponentially
But adoption follows a typical S-curve pattern, similar to the adoption rate of TV
Access grew too fast, leading to excess capacity around the time of the tech bubble in 2001
The challenge is to predict demand properly
100%
Color TVs
Internet
Access

3. The Significance of Forecasting
Both public and private enterprises operate under conditions of uncertainty.
Management wishes to limit this uncertainty by predicting changes in cost, price, sales, and interest rates.
Accurate forecasting can help develop strategies to promote profitable trends and to avoid unprofitable ones.
A forecast is a prediction concerning the future. Good forecasting will reduce, but not eliminate, the uncertainty that all managers feel. 2

4. Hierarchy of Forecasts
The selection of forecasting techniques depends in part on the level of economic aggregation involved.
The hierarchy of forecasting is:
National Economy (GDP, interest rates, inflation, etc.)
sectors of the economy (durable goods)
industry forecasts (all automobile manufacturers)
firm forecasts (Ford Motor Company)
Product forecasts (The Ford Focus) 3

5. Forecasting Criteria
The choice of a particular forecasting method depends on several criteria:
costs of the forecasting method compared with its gains
complexity of the relationships among variables
time period involved
lead time between receiving information and the decision to be made
accuracy needed in forecast 4

6. Accuracy of Forecasting
The accuracy of a forecasting model is measured by how close the actual variable, Y, ends up to the forecasting variable, Y.
Forecast error is the difference. (Y - Y)
Models differ in accuracy, which is often based on the square root of the average squared forecast error over a series of N forecasts and actual figures
Called a root mean square error, RMSE.
RMSE = {  (Y - Y)2 / N } ^ ^ ^ 5

7. Quantitative Forecasting
Deterministic Time Series
Looks For Patterns
Ordered by Time
No Underlying Structure
Econometric Models
Explains relationships
Supply & Demand
Regression Models
Like technical
security analysis
Like fundamental
security analysis 20

8. Time Series Examine Patterns in the Past
Dependent Variable X X X
Forecasted Amounts
TIME To
The data may offer secular trends, cyclical variations, seasonal
variations, and random fluctuations. 21

9. Time Series Examine Patterns in the Past
Dependent Variable
Secular Trend X X X
Forecasted Amounts
TIME To
The data may offer secular trends, cyclical variations, seasonal
variations, and random fluctuations. 21

10. Time Series Examine Patterns in the Past
Dependent Variable
Secular Trend
Cyclical Variation X X X
Forecasted Amounts
TIME To
The data may offer secular trends, cyclical variations, seasonal
variations, and random fluctuations. 21

11. Elementary Time Series Models for Economic Forecasting
NO Trend
Naive Forecast
Yt+1 = Yt
Method best when there is no trend, only random error
Graphs of sales over time with and without trends
When trending down, the Naïve predicts too high     ^  
time
Trend     
time 23

12. 2. Naïve forecast with adjustments for secular trends^
Yt+1 = Yt + (Yt - Yt-1 )
This equation begins with last period’s forecast, Yt.
Plus an ‘adjustment’ for the change in the amount between periods Yt and Yt-1.
When the forecast is trending up, this adjustment works better than the pure naïve forecast method #1.

13. 3. Linear Trend & 4. Constant rate of growth
Linear Trend Growth Uses a Semi-log Regression
Used when trend has a constant AMOUNT of change
Yt = a + b•T, where
Yt are the actual observations and
T is a numerical time variable
Used when trend is a constant PERCENTAGE rate
Log Yt = a + b•T,
where b is the continuously compounded growth rate 26

14. More on Constant Rate of Growth Model a proof^
Suppose: Yt = Y0( 1 + G) t where g is the annual growth rate
Take the natural log of both sides:
Ln Yt = Ln Y0 + t • Ln (1 + G)
but Ln ( 1 + G )  g, the equivalent continuously compounded growth rate
SO: Ln Yt = Ln Y0 + t • g
Ln Yt = a + b • t
where b is the growth rate ^ 27

15. Numerical Examples: 6 observations
MTB > Print c1-c3.
Sales Time Ln-sales
Using this sales
data, estimate
sales in period 7
using a linear and
a semi-log
functional
form 28

16. The linear regression equation is Sales = 85.0 + 12.7 Time
Predictor Coef Stdev t-ratio p
Constant
Time
s = R-sq = 99.0% R-sq(adj) = 98.8%
The semi-log regression equation is
Ln-sales = Time
Predictor Coef Stdev t-ratio p
Constant
Time
s = R-sq = 99.9% R-sq(adj) = 99.9% 29

17. Forecasted Sales @ Time = 7
Linear Model
Sales = Time
Sales = ( 7)
Sales = 173.9
Semi-Log Model
Ln-sales = Time
Ln-sales = ( 7 )
Ln-sales =
To anti-log:
e = 179.0
linear   30

18. Sales Time Ln-sales
semi-log
linear
Semi-log is
exponential 7
Which prediction
do you prefer? 31

19. 5. Declining Rate of Growth Trend
A number of marketing penetration models use a slight modification of the constant rate of growth model
In this form, the inverse of time is used
Ln Yt = b1 – b2 ( 1/t )
This form is good for patterns like the one to the right
It grows, but at continuously a declining rate Y
time

20. 6. Seasonal Adjustments: The Ratio to Trend Method
Take ratios of the actual to the forecasted values for past years.
Find the average ratio. This is the seasonal adjustment
Adjust by this percentage by multiply your forecast by the seasonal adjustment
If average ratio is 1.02, adjust forecast upward 2%
12 quarters of data            
I II III IV I II III IV I II III IV
Quarters designated with roman numerals. 32

21. 7. Seasonal Adjustments: Dummy Variables
Let D = 1, if 4th quarter and 0 otherwise
Run a new regression:
Yt = a + b•T + c•D
the “c” coefficient gives the amount of the adjustment for the fourth quarter. It is an Intercept Shifter.
With 4 quarters, there can be as many as three dummy variables; with 12 months, there can be as many as 11 dummy variables
EXAMPLE: Sales = •T + 18•D
12 Observations from the first quarter of 2005 to 2007-IV.
Forecast all of 2008.
Sales(2008-I) = 430; Sales(2008-II) = 440; Sales(2008-III) = 450; Sales(2008-IV) = 478 33

22. Soothing Techniques 8. Moving Averages
A smoothing forecast method for data that jumps around
Best when there is no trend
3-Period Moving Ave is:
Yt+1 = [Yt + Yt-1 + Yt-2]/3
For more periods, add them up and take the average
Dependent Variable * * *
Forecast
Line is
Smoother * *
TIME 24

23. Smoothing Techniques 9. First-Order Exponential Smoothing
A hybrid of the Naive and Moving Average methods
Yt+1 = w•Yt +(1-w)Yt
A weighted average of past actual and past forecast, with a weight of w
Each forecast is a function of all past observations
Can show that forecast is based on geometrically declining weights.
Yt+1 = w .•Yt +(1-w)•w•Yt-1 +
(1-w)2•w•Yt-1 + …
Find lowest RMSE to pick the best w. ^ ^ ^ ^ 25

24. First-Order Exponential Smoothing Example for w = .50
Actual Sales Forecast
initial seed required
(100) + .5(100) = 100
115
130 ? 1 2 3 4 5

25. First-Order Exponential Smoothing Example for w = .50
Actual Sales Forecast
initial seed required
(100) + .5(100) = 100
(120) + .5(100) = 110
130 ? 1 2 3 4 5

26. First-Order Exponential Smoothing Example for w = .50
Actual Sales Forecast
initial seed required
(100) + .5(100) = 100
(120) + .5(100) = 110
(115) + .5(110) =
? .5(130) + .5(112.50) = 1 2 3 4 5
MSE = {( )2 + ( )2 + ( )2}/3 =
RMSE =  = 15.61
Period 5
Forecast

27. Qualitative Forecasting 10. Barometric Techniques
Direction of sales can be indicated by other variables.
PEAK
Motor Control Sales
peak
Index of Capital Goods
TIME
4 Months
Example: Index of Capital Goods is a “leading indicator”
There are also lagging indicators and coincident indicators 15

28. Time given in months from change
LEADING INDICATORS*
M2 money supply (-14.4)
S&P 500 stock prices (-11.1)
Building permits (-15.4)
Initial unemployment claims (-12.9)
Contracts and orders for plant and equipment (-7.3)
COINCIDENT INDICATORS
Nonagricultural payrolls (+.8)
Index of industrial production (-1.1)
Personal income less transfer payment (-.4)
LAGGING INDICATORS
Prime rate (+17.9)
Change in labor cost per unit of output (+6.4)
*Survey of Current Business, 1995
See pages in the textbook 16

29. Handling Multiple Indicators
Diffusion Index: Suppose 11 forecasters predict stock prices in 6 months, up or down. If 4 predict down and seven predict up, the Diffusion Index is 7/11, or 63.3%.
above 50% is a positive diffusion index
Composite Index: One indicator rises 4% and another rises 6%. Therefore, the Composite Index is a 5% increase.
used for quantitative forecasting 18

30. Qualitative Forecasting 11. Surveys and Opinion Polling Techniques
Common Survey Problems
New Products have no
historical data -- Surveys
can assess interest in new
ideas.
Sample bias--
telephone, magazine
Biased questions--
advocacy surveys
Ambiguous questions
Respondents may lie on questionnaires
Survey Research Center
of U. of Mich. does repeat
surveys of households on
Big Ticket items (Autos) 14

31. Qualitative Forecasting 12. Expert Opinion
The average forecast from several experts is a Consensus Forecast.
Mean
Median
Mode
Truncated Mean
Proportion positive or negative 11

32. Conference Board – macroeconomic predictions
EXAMPLES:
IBES, First Call, and Zacks Investment -- earnings forecasts of stock analysts of companies
Conference Board – macroeconomic predictions
Livingston Surveys--macroeconomic forecasts of economists
Individual economists tend to be less accurate over time than the ‘consensus forecast’. 12

33. Qd = a + b•P + c•I + d•Ps + e•Pc
13. Econometric Models
Specify the variables in the model
Estimate the parameters
single equation or perhaps several stage methods
Qd = a + b•P + c•I + d•Ps + e•Pc
But forecasts require estimates for future prices, future income, etc.
Often combine econometric models with time series estimates of the independent variable.
Garbage in Garbage out 35

34. example Qd = 400 - .5•P + 2•Y + .2•Ps
anticipate pricing the good at P = $20
Income (Y) is growing over time, the estimate is: Ln Yt = •T, and next period is T = 17.
Y = e2.910 =
The prices of substitutes are likely to be P = $18.
Find Qd by substituting in predictions for P, Y, and Ps
Hence Qd = 36

35. 14. Stochastic Time Series
A little more advanced methods incorporate into time series the fact that economic data tends to drift
yt = a + byt-1 + et
In this series, if a is zero and b is 1, this is essentially the naïve model. When a is zero, the pattern is called a random walk.
When a is positive, the data drift. The Durbin-Watson statistic will generally show the presence of autocorrelation, or AR(1), integrated of order one.
One solution to variables that drift, is to use first differences.

36. Cointegrated Time Series
Some econometric work includes several stochastic variable, each which exhibits random walk with drift
Suppose price data (P) has positive drift
Suppose GDP data (Y) has positive drift
Suppose the sales is a function of P & Y
Salest = a + bPt + cYt
It is likely that P and Y are cointegrated in that they exhibit comovement with one another. They are not independent.
The simplest solution is to change the form into first differences as in: DSalest = a + bDPt + cDYt