Demand Forecasting: Time Series Models Professor Stephen R. Lawrence College of Business and Administration University of Colorado Boulder, CO 80309-0419

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Demand ForecastingTime Series
ModelsProfessor Stephen R. LawrenceCollege
of Business and AdministrationUniversity of
ColoradoBoulder, CO 80309-0419
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Forecasting Horizons

• Long Term
• 5 years into the future
• RD, plant location, product planning
• Principally judgement-based
• Medium Term
• 1 season to 2 years
• Aggregate planning, capacity planning, sales
  forecasts
• Mixture of quantitative methods and judgement
• Short Term
• 1 day to 1 year, less than 1 season
• Demand forecasting, staffing levels, purchasing,
  inventory levels
• Quantitative methods

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Short Term ForecastingNeeds and Uses

• Scheduling existing resources
• How many employees do we need and when?
• How much product should we make in anticipation
  of demand?
• Acquiring additional resources
• When are we going to run out of capacity?
• How many more people will we need?
• How large will our back-orders be?
• Determining what resources are needed
• What kind of machines will we require?
• Which services are growing in demand? declining?
• What kind of people should we be hiring?

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Types of Forecasting Models

• Types of Forecasts
• Qualitative --- based on experience, judgement,
  knowledge
• Quantitative --- based on data, statistics
• Methods of Forecasting
• Naive Methods --- eye-balling the numbers
• Formal Methods --- systematically reduce
  forecasting errors
• time series models (e.g. exponential smoothing)
• causal models (e.g. regression).
• Focus here on Time Series Models
• Assumptions of Time Series Models
• There is information about the past
• This information can be quantified in the form of
  data
• The pattern of the past will continue into the
  future.

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Forecasting Examples

• Examples from student projects
• Demand for tellers in a bank
• Traffic on major communication switch
• Demand for liquor in bar
• Demand for frozen foods in local grocery
  warehouse.
• Example from Industry American Hospital Supply
  Corp.
• 70,000 items
• 25 stocking locations
• Store 3 years of data (63 million data points)
• Update forecasts monthly
• 21 million forecast updates per year.

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Simple Moving Average

• Forecast Ft is average of n previous
  observations or actuals Dt
  
• Note that the n past observations are equally
  weighted.
• Issues with moving average forecasts
• All n past observations treated equally
• Observations older than n are not included at
  all
• Requires that n past observations be retained
• Problem when 1000's of items are being forecast.

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Simple Moving Average

• Include n most recent observations
• Weight equally
• Ignore older observations

weight
1/n
...
1
2
n
3
today
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Moving Average
n 3
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ExampleMoving Average Forecasting
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Exponential Smoothing I

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
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Exponential Smoothing I

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
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Exponential Smoothing I

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
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Exponential Smoothing I

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
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Exponential Smoothing Concept

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
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Exponential Smoothing Math
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Exponential Smoothing Math
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Exponential Smoothing Math

• Thus, new forecast is weighted sum of old
  forecast and actual demand
• Notes
• Only 2 values (Dt and Ft-1 ) are required,
  compared with n for moving average
• Parameter a determined empirically (whatever
  works best)
• Rule of thumb ? lt 0.5
• Typically, ? 0.2 or ? 0.3 work well
• Forecast for k periods into future is

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Exponential Smoothing
a 0.2
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ExampleExponential Smoothing
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Complicating Factors

• Simple Exponential Smoothing works well with data
  that is moving sideways (stationary)
• Must be adapted for data series which exhibit a
  definite trend
• Must be further adapted for data series which
  exhibit seasonal patterns

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Holts MethodDouble Exponential Smoothing

• What happens when there is a definite trend?

Actual
Demand
Forecast
Month
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Holts MethodDouble Exponential Smoothing

• Ideas behind smoothing with trend
• De-trend'' time-series by separating base from
  trend effects
• Smooth base in usual manner using ?
• Smooth trend forecasts in usual manner using ?
• Smooth the base forecast Bt
• Smooth the trend forecast Tt
• Forecast k periods into future Ftk with base and
  trend

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ES with Trend
a 0.2, b 0.4
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ExampleExponential Smoothing with Trend
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Winters Method Exponential Smoothing w/ Trend
and Seasonality

• Ideas behind smoothing with trend and
  seasonality
• De-trend and de-seasonalizetime-series by
  separating base from trend and seasonality
  effects
• Smooth base in usual manner using ?
• Smooth trend forecasts in usual manner using ?
• Smooth seasonality forecasts using g
• Assume m seasons in a cycle
• 12 months in a year
• 4 quarters in a month
• 3 months in a quarter
• et cetera

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Winters Method Exponential Smoothing w/ Trend
and Seasonality

• Smooth the base forecast Bt
• Smooth the trend forecast Tt
• Smooth the seasonality forecast St

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Winters Method Exponential Smoothing w/ Trend
and Seasonality

• Forecast Ft with trend and seasonality
  
• Smooth the trend forecast Tt
• Smooth the seasonality forecast St

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ES with Trend and Seasonality
a 0.2, b 0.4, g 0.6
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ExampleExponential Smoothing withTrend and
Seasonality
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Forecasting Performance
How good is the forecast?

• Mean Forecast Error (MFE or Bias) Measures
  average deviation of forecast from actuals.
• Mean Absolute Deviation (MAD) Measures average
  absolute deviation of forecast from
  actuals.
• Mean Absolute Percentage Error (MAPE) Measures
  absolute error as a percentage of the
  forecast.
• Standard Squared Error (MSE) Measures variance
  of forecast error

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Forecasting Performance Measures
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Mean Forecast Error (MFE or Bias)

• Want MFE to be as close to zero as possible --
  minimum bias
• A large positive (negative) MFE means that the
  forecast is undershooting (overshooting) the
  actual observations
• Note that zero MFE does not imply that forecasts
  are perfect (no error) -- only that mean is on
  target
• Also called forecast BIAS

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Mean Absolute Deviation (MAD)

• Measures absolute error
• Positive and negative errors thus do not cancel
  out (as with MFE)
• Want MAD to be as small as possible
• No way to know if MAD error is large or small in
  relation to the actual data

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Mean Absolute Percentage Error (MAPE)

• Same as MAD, except ...
• Measures deviation as a percentage of actual data

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Mean Squared Error (MSE)

• Measures squared forecast error -- error variance
• Recognizes that large errors are
  disproportionately more expensive than small
  errors
• But is not as easily interpreted as MAD, MAPE --
  not as intuitive

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Fortunately, there is software...