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DEMAND FORECASTING

The firm must decide on several variables such as:

- How much of each product to produce
- What price to charge
- How much to spend on advertising
- What is the future growth of the firm
- etc.

Answers depend on:

- The level of future economic activity (macro forecasts)
- The level of the demand for the firm’s products (micro forecasts)

Forecasting techniques range from very naive to very sophisticated ones.

Which forecasting method the firm should use depends on:

1 - the cost of preparing the forecast and the benefit that results from it.

2 - the lead time in decision making (short or long).

3 - the time period of the forecast (short or long)

4 - the level of accuracy required (high or low)

5 - the quality and availability of the data (good or bad)

6 - the level of complexity of the relationships to be forecasted (complex or simple)

THE GREATER THE LEVEL OF ACCURACY REQUIRED AND THE MORE COMPLEX THE RELATIONSHIPS, THE MORE SOPHISTICATED AND EXPENSIVE WILL BE THE FORECASTING EXERCISE.

QUALITATIVE METHODS

- can be helpful in supplementing quantitative forecasts.

- invaluable in cases of new products (video phone).

1 - Survey Techniques.

- They provide general information. Surveys of economic intentions e.g.,:

- businesses usually plan to add to plant and equipment long before expenditures are actually incurred

- consumers decisions to purchase major consumption items are made months (cars, TVs) or years (houses) in advance of actual purchase.

Some of the best known surveys in USA are:

a - Surveys of business executives’ plant and equipment expenditure plans. These are conducted by:

* McGraw-Hill, Inc. (Twice a year. Accounts for more than 50% of new plant expenditures)

* The Department of Commerce (4 times a year, more comprehensive)

* Securities and Exchange Commission

* National Industrial Conference Board

b - Surveys of plans for inventory changes and sales expectations. Conducted by:

* US Department of Commerce

* McGraw-Hill Inc.

* Dunn and Bradstreet

* National Association of Purchasing Agents

c - Surveys of consumer expenditure plans. conducted by:

* The Bureau of the Census

* The Survey Research Center of the University of Michigan

2 - Opinion polls

Suitable for specific forecasts of the firm’s own sales. This is made by polling experts within and outside the firm, e.g.,

a - Executive polling. The firm Polls its top management from sales, production, finance, and personnel departments on their views on the sales outlook for the firm during next quarter or year. Outside market experts can also be polled.

To avoid bandwagoning, DELPHI METHOD can be used.

b - Sales force polling. The people closest to the market, their views can be very valuable to the firm.

c - Consumer intentions polling.

3 - Soliciting a foreign perspective

- Suitable for exporters. Solicit the ideas of government and business leaders living abroad, e.g.,

* GM’s European Advisory Council

* IBM’s Advisory councils in Europe and Latin America

TIME SERIES ANALYSIS

- The most frequently used forecasting methods.

- Attempts to forecast future values by examining past observations of the data only.

- Assumption: time series will continue to move in the future as in the past.

Reasons for fluctuations in time series data.

Time series vary over time. These variations are caused by secular trends, cyclical fluctuations, seasonal variations, and irregular or random influences.

a - Secular Trends: Long run increase of decrease in the data series e.g., population, PCI, leaded gasoline, …etc.

b - Cyclical Fluctuations: major expansions and contractions in most time series that seems to recur every several years.

c - Seasonal Variation: regularly recurring fluctuations in economic activity during each year, e.g., because of weather and social customs.

d - Irregular or random influences: variations in the data series resulting from wars, natural disasters, strikes, or other unique events

TREND PROJECTION.

- Projecting a straight line to the data either visually or by regression analysis.

a - Absolute amount of growth.

- The linear regression model will take the form of :

Dt = Do + b.T; (1)

- Do = the estimated demand at time period T = 0 (i.e., demand in the base year).
- b = the absolute amount of growth.

Fitting a regression line to estimate the trend

- Form a trend variable (starting from 1 – 16
- Enter the data into Excel
- Estimate the OLS using Excel

R-squared = .533452

- Adjusted R-squared = .500127
- F-statistic (zero slopes) = 16.0076

Estimated Standard

Variable Coefficient Error t-statistic P-value

+++++++++++++++++++++++++++++++++++++++++++++

C 11.9000 .952507 12.4934 ** [.000]

TIME .394118 .098506 4.00096 ** [.001]

+++++++++++++++++++++++++++++++++++++++++++++

- (interpretation of results)
- Forecasting:
- D17 = 11.90 + 0.394(17) = 18.60 1st Q of 2006
- D18 = 11.90 + 0.394(18) = 18.99 2nd Q of 2006
- D19 = 11.90 + 0.394(19) = 19.39 3rd Q of 2006
- D20 = 11.90 + 0.394(20) = 19.78 4th Q of 2006

b - constant percentage rate of growth

- In many cases it may be appropriate to use the constant percentage growth rate model:
- Dt = Do(1+g)t; (2)
- where g is the constant percentage growth rate to be estimated.
- transform eq.2 into the linear logarithmic form:
- ln Dt = ln Do + t ln(1+g);
- Using the same data set;

R-squared = .540843

- Adjusted R-squared = .508047
- F-statistic (zero slopes) = 16.4907

Estimated Standard

Variable Coefficient Error t-statistic P-value

+++++++++++++++++++++++++++++++++++++++++++++++++++

C 2.48691 .062793 39.6049 ** [.000]

TIME .026371 .649391E-02 4.06087 ** [.001]

+++++++++++++++++++++++++++++++++++++++++++++++++++

taking the antilog of

- ln Do = 2.49 is Do = 12.06
- and ln (1+g) = 0.026 is (1+g) = 1.026 ( note g = 0.26 or 2.6% )

by substitution:

- Do = 12.06 x (1.026)t;
- Using this equation to forecast the demand in 2006 gives:
- D17 = 12.06 x (1.026)17 = 18.66
- D18 = 12.06 x (1.026)18 = 19.14
- D19 = 12.06 x (1.026)19 = 19.64
- D20 = 12.06 x (1.026)20 = 20.15

A – Seasonal Variations

- The data presented above shows a strong seasonal variation. by incorporating this seasonal variation we can improve the forecasts.

Methods of Adjustment

- 1 - Ratio-to-Trend

steps:

1 - use the estimated regression to forecast demand for the whole period, ( we have both actual and forecasted data for the same period of time ).

2 - rearrange the data by quarter groups

3 - take the ratio of actual to forecasted data

4 - calculate the average of these ratios

5 - use the average ratio to adjust forecasts for seasonal variation

Forecasting

- D17 = 11.90 + 0.394(17) = 18.60(0.887) = 16.50
- D18 = 11.90 + 0.394(18) = 18.99(1.165) = 22.12
- D19 = 11.90 + 0.394(19) = 19.39(0.907) = 17.59
- D20 = 11.90 + 0.394(20) = 19.78(1.042) = 20.61

B - Dummy Variables

- create dummy variables for each quarter

- the dummy variable takes the value 1 in its own quarter and zero otherwise.

- take one quarter as a base period quarter (usually quarter 4)

- add the created (3) dummy variables to the demand function. It becomes:

Qt = ao + a1 t + a2 D1t + a3 D2t + a4 D3t; (3)

- estimate the new demand function

- use the estimated regression function to forecast demand

Regression Results

estimated Standard

Variable Coefficient Error t-statistic P-value

C 12.7500 .226134 56.3826 ** [.000]

TIME .375000 .016855 22.2486 ** [.000]

D1 -2.37500 .219115 -10.8391 ** [.000]

D2 1.75000 .215849 8.10751 ** [.000]

D3 -2.12500 .213866 -9.93613 ** [.000]

using these estimates to forecast the demand gives the following:

D17 = 12.75 - 2.375(17)-2.372(1)+1.75(0)-2.125(0)= 16.75

D17 = 12.75 - 2.375(18)-2.372(0)+1.75(1)-2.125(0)= 21.25

D17 = 12.75 - 2.375(19)-2.372(0)+1.75(0)-2.125(1)= 17.75

D17 = 12.75 - 2.375(20)-2.372(0)+1.75(0)-2.125(0)= 20.25

Smoothing Techniques

- Predict future values of a time series on the basis of some average of its past values only.

- Useful when the time series exhibit little trend or seasonal variations. Irregular of random variation in the time series is then smoothed, and future values are forecasted based on some average of past observations.

2 - Moving Averages

- Forecast value is equal to the average value of the time series in a number of previous periods.

- We select several moving averages, and forecast demand using each of these moving averages.

- To decide which of these moving averages forecasts better (closer to actual data) calculate the root-mean-square error RMSE.

RMSE = ;

where:

A = actual value of the time series in period t.

F = forecast value

n=number of forecasts

We have two forecasts for the demand; 21.33 and 20.6. To decide which is better, calculate RMSE

RMSE3 = = 2.95

RMSE5 = = 2.99

The three quarter moving average is marginally a better forecast.

2 - Exponential Smoothing

- Simple moving averages give equal weight to all observations in computing the average.
- Exponential smoothing overcomes this objection and is used more frequently than simple averages
- The forecast of period t+1 is a weight average of actual and forecasted values of the time series in period t

- A weight w is given to the actual value and (1-w) to the forecast such that

Ft+1 = wAt + (1-w) Ft; 0 w 1;

- A= Actual F = Forecast

(w + (1-w)) =1).

- To start forecasts we have to assign a value for Ft, one way is to take the average of the whole period.

- Since we can use different weights, we use RMSE to decide which of forecast is better.

e.g. use the same data from the above table to calculate forecasts using w=0.3 and w=0.5;

- RMSE = = 2.70
- RMSE = = 2.91
- the exponential forecast 21.0 is better.

Seasonal Fluctuations: Barometric Methods

- To forecast cyclical swings or turning points in business cycles we use an index of leadingindicators. Just as the barometer indicates changes in the weather, leading indicators are used to forecast turning points.
- leading indicators used to forecast an increase in general business activity and vice versa.

Recession Warning Rules

- To illustrate the historical performance of an operational version of this recession-warning rule, Chart 1 shows six-month annualized percent changes in the leading index, along with a disjointed line denoting periods when more than half of its component series were falling (i.e., the diffusion index over the same six-month period was below 50 percent).
- The chart also shows that a recession has usually just begun, or is imminent, when the following two criteria are met simultaneously across a six-month span:
- The annualized rate of change in the leading index falls below –3.5 percent over a six-month span;
- and (2) the diffusion index is below 50 percent.
- (Note that -3.5 percent corresponds roughly to the -2 percent level previously reported by The Conference Board. As of the 2001 revision

Diffusion Index. A simple methodology

- An index gives the percentage of the indicators move up.
- if we have 12 indicators, 7 of them moved up

DI = No of indicators which rise up / total No. of indicators

In general if:

- DI > 50% expansion
- DI < 50% contraction
- DI = 7/12 = 58.33

if they move upward for several months expansion

Diffusion Index. standard methodology

Diffusion Index = 100 x

(1.0 x “substantially more” +

0.75 x “more” +

0.50 x “same” +

0.25 x “less” +

0.0 x “substantially less” )

Weights:

- substantially more (percent of the sample) = 1
- More (percent of the sample) = .75
- Same (percent of the sample) = .5
- less (percent of the sample) = .25
- substantially less (percent of the sample) = 0
- Note:
- “Percents of the sample” of all of the responses sum to 100% of the sample.
- Consequently, the index values are bounded by 0% and 100%.

Cumulative Diffusion Indexes

- In addition to the One-Month Diffusion Indexes, there are the Cumulative Diffusion Indexes which track current conditions.
- The cumulative diffusion indexes are calculated based on the following formula:

Current observation = prior period + diffusion index – 50

- A diffusion index above 50 indicates growth,
- A diffusion index below 50 indicates the opposite.

Econometric Models

- Incorporates the best features other forecasting techniques, such as trend, seasonal, smoothing techniques and barometric methods.

Single Equation models.

Q = a0 + a1 P + a2 Y + a3 N + a4 Ps + a5 Pc + a6 A + e

steps:

- collect data about the variables

- estimate your model

- predict the values for independent variables in the coming period

- use your estimated model to forecast the demand in the future

Example; (the demand for New York-London passengers)

ln Qt = 2.737 - 1.247 ln Pt + 1.905 ln GNPt R2 = 0.97

Suppose that Pt+1 = 550; GNPt+1 = 1480

To forecast take the log. of Pt+1 and GNPt+1

ln 550 = 6.31 ln 1480 = 7.3

Hence:

Qt+1 = 2.737 - 1.247 ( 6.310) + 1.905 (7.3) = 8.775

take the antilog of 8.775

Qt+1 = 6 470 000

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