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### Forecasting

Dr. Everette S. Gardner, Jr.

Judgment exercises

Exercise 1

Finished files are the result of years of scientific study combined with the experience of years.

How many times does the letter F appear in the sentence above? Count them only once; do not go back and count them again. ________

How confident are you in your answer? Rate your confidence on a scale of 0 to 100, where 0 means that you are sure you are wrong, and 100 means that you are sure you right. _________

Forecasting

Judgment exercises (cont.)

Exercise 2

Threatened by a superior enemy force, the general faces a dilemma. His intelligence officers say his soldiers will be caught in an ambush in which 600 of them will die unless he leads them to safety by one of two available routes. If he takes the first route, 200 soldiers will be saved. If he takes the second route, there’s a one-third chance that 600 soldiers will be saved and a two-thirds chance that none will be saved. Which route should he take? ________

Forecasting

Judgment exercises (cont.)

Exercise 3

The general again has to choose between two escape routes. But this time his aides tell him that if he takes the first, 400 soldiers will die. If he takes the second, there’s a one-third chance that no soldiers will die, and a two-thirds chance that 600 soldiers will die. Which route should he take? _______

Forecasting

Judgment exercises (cont.)

Exercise 4

Linda is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student, she was deeply concerned with discrimination and other social issues, and participated in anti-nuclear demonstrations. Which statement is more likely?

a. Linda is a bank teller.

b. Linda is a bank teller and active in the feminist

movement.

_______

Forecasting

Human biases in forecasting

Company Politics

● Forecast what the boss wants to hear

Overconfidence

● Confidence has no relation to accuracy

Wishful thinking

● Optimistic forecasts more probable

Success/failure attribution

● Good forecasts due to skill, bad due to chance

Forecasting

Human biases in forecasting

Gambler’s fallacy

● Bad luck and good luck will balance out

Data presentation

● Misleading graphs/tables easily accepted

Conservatism

● Refusal to accept drastic change

Forecasting

Forecasting methods

Human judgment

● Subject to bias and inconsistency

● Models usually beat humans

Time series forecasting

● Based on analysis of past history

● Cheap and easy

● On average, most accurate method

● Should always be attempted

Forecasting

Forecasting methods (cont.)

Regression modeling

● Based on causal relationships

● Expensive and difficult

● Must forecast independent variables

Growth or market development models

● Based on assumed growth patterns

● Cheap and easy

● Difficult to validate

Forecasting

Can your data be forecastedby a model?

Use common sense

● Abrupt turning points usually impossible to predict

Compare your accuracy to a naïve benchmark

● Forecast for next period is the same as the data

this period

● If you cannot beat a naïve benchmark, forecasting

is usually futile

Forecasting

Forecast profiles

Additive Multiplicative

Nonseasonal Seasonality Seasonality

Constant

Level

Linear

Trend

Exponential

Trend

Damped

Trend

Forecasting

Simple exponential smoothing

- Error in t = Actual data – Forecast for t

(2) Forecast for t+1 = Forecast for t + α(Error in t)

To get started:

Set first forecast equal to mean of first few data.

Smoothing weight (α):

In practice, α is usually 0.30 – 0.50.

Effects of extreme α values:

If α = 0, the forecast never changes.

If α = 1, this is a naïve or random walk model.

Forecasting

Simple.xls

Error measures forevaluating forecast models

● MAD = Mean absolute deviation (error)

● MSE = Mean squared error

● MAPE = Mean absolute percentage error

Forecasting

Smoothing a linear trend

(1) Error in t = Actual data - Forecast for t

(2) Level at end of t = Forecast for t + h1(Error in t)

(3) Trend at end of t = Trend at end of t–1 + h2(Error in t)

(4) Forecast for t+1 = Level at end of t + Trend at end of t

To get started, set:

Initial trend = Average growth in first four data

Initial level = First data observation – initial trend

Search for weights in the following ranges:

Level weight (h1)0.10 to 0.90, increments of .10

Trend weight (h2) 0.05 to 0.30, increments of .05

Forecasting

Trendsmooth.xls

The general trend model

(1) Error in t = Actual data – Forecast for t

(2) Level at end of t = Forecast for t + h1(Error in t)

(3) Trend at end of t = ø(Trend at end of t – 1) + h2(Error in t)

(4) Forecast for t+1 = Level at end of t + ø(Trend at end of t)

Long-term forecasting:

Forecast for t+2 = Forecast for t+1 + ø2(Trend at end of t)

Forecast for t+3 = Forecast for t+2 + ø3(Trend at end of t)

Trend possibilities:

- If ø < 1, the trend is damped.
- If ø = 1, the trend is linear.
- If ø > 1, the trend is exponential.
- If ø = 0, there is no trend (same as simple smoothing).

Forecasting

Starting up the general trend model

- Initial values
- Initial trend = Average growth in first four data
- Initial level = First data observation – Initial trend
- Search for parameters in the following ranges
- Level weight (h1) 0.10 to 0.90
- Trend weight (h2) 0.05 to 0.30
- Phi (ø) 0.60 to 1.00

Forecasting

Multiplicative seasonality

The seasonal index is the expected ratio of actual

data to the average for the year.

Actual data / Index = Seasonally adjusted data

Seasonally adjusted data x Index = Actual data

Forecasting

Multimon.xls

Multiplicative seasonal adjustment

- Compute moving average based on length of seasonality (4 quarters or 12 months).
- Divide actual data by corresponding moving average.
- Average ratios to eliminate randomness.
- Compute normalization factor to adjust mean ratios so they sum to 4 (quarterly data) or 12 (monthly data).
- Multiply mean ratios by normalization factor to get final seasonal indexes.
- Deseasonalize data by dividing by the seasonal index.
- Forecast deseasonalized data.
- Seasonalize forecasts from step 7 to get final forecasts.

Forecasting

Additive seasonality

The seasonal index is the expected difference between actual data and the average for the year.

Actual data - Index = Seasonally adjusted data

Seasonally adjusted data + Index = Actual data

Forecasting

Additmon.xls

Additive seasonal adjustment

- Compute moving average based on length of seasonality (4 quarters or 12 months).
- Compute differences: Actual data - moving average.
- Average differences to eliminate randomness.
- Compute normalization factor to adjust mean differences so they sum to zero.
- Compute final indexes: Mean difference – normalization factor.
- Deseasonalize data: Actual data – seasonal index.
- Forecast deseasonalized data.
- Seasonalize forecasts from step 7 to get final forecasts.

Forecasting

Forecasting simulations

Dynamic simulation

● Short-range (one-step-ahead) forecasting test

● Use data in fit periods to select model

● During forecast periods:

1. Make one forecast.

2. Observe error.

3. Adjust model.

4. Go to 1.

Static simulation

● Long-range forecasting test

● Use data in fit periods to select model

● Make all forecasts at once

Forecasting

Data transformations for forecasting

Deseasonalize

Isolates trend

% Change

Isolates trend

Natural log

Converts exponential trend to linear

Square root

Reduce variance

Aggregate

Quarterly or monthly data to annual

Forecasting

Forecasting management

Organize for forecasting

● Pinpoint responsibility

● Only one corporate forecast

● Separate forecasting and planning

Monitor accuracy

● Choose a standard measure

● Keep a track record

● Benchmark

● Hold performance reviews

Scrub the data

● Adjust outliers

● Throw out unique data

Forecasting

Forecasting management (cont.)

Compare alternative forecasts

● Top-down vs. bottom up

● Monthly vs. quarterly data

● Deseasonalized vs. raw data

● Percent change data

● Time series forecasts

● Regression forecasts

Simulate forecasting

● One-step-ahead

● Long-range

Estimate confidence limits

● What is the range of forecast errors in past?

Forecasting

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