Transcript No Slide Title

Business and Economic Forecasting
Chapter 5
Business and Economic Forecasting is a
critical managerial activity which comes in
two forms:
Quantitative Forecasting +2.1047%
Gives the precise amount
or percentage
 Qualitative Forecasting
Gives the expected direction
Up, down, or about the same
2008 Thomson * South-Western
Slide 1
Managerial Challenge
Excess Fiber Optic Capacity
• High-speed data installation
grew exponentially
100%
• 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
1940
demand properly
Color TVs
Internet
Access
1960
1980 2000
2020
Slide 2
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.
Slide 3
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)
Slide 4
Forecasting Criteria
The choice of a particular forecasting method
depends on several criteria:
1.costs of the forecasting method compared with
its gains
2.complexity of the relationships among
variables
3.time period involved
4.lead time between receiving information and
the decision to be made
5.accuracy needed in forecast
Slide 5
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
^
}
Slide 6
Quantitative Forecasting
• Deterministic Time
Series
» Looks For Patterns
» Ordered by Time
» No Underlying Structure
Like technical
security analysis
• Econometric Models
» Explains relationships
» Supply & Demand
» Regression Models
Like fundamental
security analysis
Slide 7
Time Series
Examine Patterns in the Past
Dependent Variable
X
X
X
Forecasted Amounts
To
TIME
The data may offer secular trends, cyclical variations, seasonal
variations, and random fluctuations.
Slide 8
Time Series
Examine Patterns in the Past
Dependent Variable
Secular Trend
X
X
X
Forecasted Amounts
To
TIME
The data may offer secular trends, cyclical variations, seasonal
variations, and random fluctuations.
Slide 9
Time Series
Examine Patterns in the Past
Dependent Variable
Secular Trend
Cyclical Variation
X
X
X
Forecasted Amounts
To
TIME
The data may offer secular trends, cyclical variations, seasonal
variations, and random fluctuations.
Slide 10
Elementary Time Series Models
for Economic Forecasting
NO Trend
1. 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
Slide 11
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.
Slide 12
3. Linear Trend & 4. Constant rate of growth
Linear Trend Growth
• 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
Uses a Semi-log Regression
• Used when trend is a
constant
PERCENTAGE rate
Log Yt = a + b•T,
where b is the
continuously
compounded growth
rate
Slide 13
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
Slide 14
Numerical Examples: 6 observations
MTB > Print c1-c3.
Sales Time Ln-sales
100.0
109.8
121.6
133.7
146.2
164.3
1
2
3
4
5
6
4.60517
4.69866
4.80074
4.89560
4.98498
5.10169
Using this sales
data, estimate
sales in period 7
using a linear and
a semi-log
functional
form
Slide 15
The linear regression equation is
Sales = 85.0 + 12.7 Time
Predictor Coef
Constant
84.987
Time
12.6514
s = 2.596
Stdev
2.417
0.6207
R-sq = 99.0%
t-ratio p
35.16 0.000
20.38 0.000
R-sq(adj) = 98.8%
The semi-log regression equation is
Ln-sales = 4.50 + 0.0982 Time
Predictor Coef
Stdev
Constant 4.50416 0.00642
Time
0.098183 0.001649
s = 0.006899
R-sq = 99.9%
t-ratio
p
701.35 0.000
59.54 0.000
R-sq(adj) = 99.9%
Slide 16
Forecasted Sales @ Time = 7
• Linear Model
• Sales = 85.0 + 12.7 Time
• Sales = 85.0 + 12.7 ( 7)
• Sales = 173.9
• Semi-Log Model
• Ln-sales = 4.50 + 0.0982
Time
• Ln-sales = 4.50 +
0.0982 ( 7 )
• Ln-sales = 5.1874
• To anti-log:
linear
» e5.1874 = 179.0


Slide 17
Sales Time Ln-sales
Semi-log is
exponential
100.0
109.8
121.6
133.7
146.2
164.3
179.0
173.9
1
2
3
4
5
6
4.60517
4.69866
4.80074
4.89560
4.98498
5.10169
7 semi-log
7 linear
7
Which prediction
do you prefer?
Slide 18
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
Slide 19
6. Seasonal Adjustments: The Ratio to Trend Method
 Take ratios of the actual to
12 quarters of data
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
I II III IV I II III IV I II III IV
» If average ratio is 1.02, adjust
forecast upward 2%
Quarters designated with roman numerals.
Slide 20
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 = 300 + 10•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
Slide 21
Soothing Techniques
8. Moving Averages
Dependent Variable
• 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
*
Forecast
Line is
Smoother
TIME
Slide 22
Smoothing Techniques
9. First-Order Exponential Smoothing
• A hybrid of the Naive • Each forecast is a function of
and Moving Average
all past observations
methods
• Can show that forecast is
^ t+1 = w•Yt +(1-w)Y
^t
• Y
based on geometrically
declining weights.
• A weighted average of ^Yt+1 = w .•Yt +(1-w)•w•Yt-1 +
^
2•w•Y
(1-w)
past actual and past
t-1 + …
forecast, with a weight
of w
Find lowest RMSE to pick the
best w.
Slide 23
First-Order Exponential
Smoothing Example for w = .50
1
2
3
4
5
Actual Sales
100
120
115
130
Forecast
100 initial seed required
.5(100) + .5(100) = 100
?
Slide 24
First-Order Exponential
Smoothing Example for w = .50
1
2
3
4
5
Actual Sales
100
120
115
130
Forecast
100 initial seed required
.5(100) + .5(100) = 100
.5(120) + .5(100) = 110
?
Slide 25
First-Order Exponential
Smoothing Example for w = .50
1
2
3
4
5
Actual Sales
100
120
115
130
?
Forecast
100 initial seed required
.5(100) + .5(100) = 100
.5(120) + .5(100) = 110
.5(115) + .5(110) = 112.50
.5(130) + .5(112.50) = 121.25
MSE = {(120-100)2 + (110-115)2 + (130-112.5)2}/3 = 243.75
RMSE = 243.75 = 15.61
Period 5
Forecast
Slide 26
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
Slide 27
Time given in months from change
LEADING INDICATORS*
COINCIDENT
» M2 money supply (-14.4)
INDICATORS
» S&P 500 stock prices (-11.1)
» Nonagricultural payrolls
» Building permits (-15.4)
(+.8)
» Initial unemployment claims
» Index of industrial
(-12.9)
production (-1.1)
» Contracts and orders for
» Personal income less
plant and equipment (-7.3)
transfer payment (-.4)
LAGGING INDICATORS
*Survey of Current Business, 1995
See pages 182-183 in the textbook
» Prime rate (+17.9)
» Change in labor cost per unit
of output (+6.4)
Slide 28
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
Slide 29
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
Survey Research Center
of U. of Mich. does repeat
surveys of households on
Big Ticket items (Autos)
• Ambiguous questions
• Respondents may lie on
questionnaires
Slide 30
Qualitative Forecasting
12. Expert Opinion
The average forecast from several experts
is a Consensus Forecast.
»
»
»
»
»
Mean
Median
Mode
Truncated Mean
Proportion positive or negative
Slide 31
EXAMPLES:
• IBES, First Call, and Zacks Investment -earnings forecasts of stock analysts of companies
• Conference Board – macroeconomic predictions
• Livingston Surveys--macroeconomic forecasts
of 50-60 economists
Individual economists tend to be less
accurate over time than the ‘consensus
forecast’.
Slide 32
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
Slide 33
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 = 2.4 + .03•T, and next period is T
= 17.
• Y = e2.910 = 18.357
» The prices of substitutes are likely to be
P = $18.
• Find Qd by substituting in predictions for P, Y,
and Ps
• Hence Qd = 430.31
Slide 34
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.
Slide 35
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
Slide 36