Assumes causal system past future

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• Assumes causal systempast gt future
• Forecasts rarely perfect because of randomness
• Forecasts more accurate forgroups vs.
  individuals
• Forecast accuracy decreases as time horizon
  increases

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Time Series Forecasts

• Trend - long-term movement in data
• Seasonality - short-term regular variations in
  data
• Irregular variations - caused by unusual
  circumstances
• Random variations - caused by chance

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Forecasting Time Line
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Forecast Variations
Figure 1
Irregularvariation
Trend
Cycles
Cycle
90
89
88
Seasonal variations
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Seasonal Variations

• Regular repeatring movements in time series
  values that can be tied to recurring events
• Annual variations weather, summer/winter sports
  equipment
• Vacations/holidays airline travel, greeting
  cards, resort

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• Daily, Weekly, Monthly rush traffic hours,
  theaters and restaurants, banks, mail volume,
  sales of toys, beer, automobiles, turkeys,
  highway usage, hotel registrations, gardening,
  public transportations, electric power plants

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Multiplicative Seasonal Model

• Forecast Trend x SI x Random Components
• SI Seasonal Index or Relatives or Percentages
• SI 1.20 for May - Sales in May are 20 above
  the monthly average
• SI 0.90 for July - Sales in July are only 90
  of the monthly average

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Forecasting Procedures

• Determine the purpose and time level of details,
  resources (manpower, computing times, etc), level
  of accuracy
• Establish a time horizon
• Select a forecasting technique
• Collect and analyze the data, and prepare the
  forecast, identify any assumptions
• Monitor the forecast

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Quantitative Forecasting Models

• Naive Forecasts
• Moving Average Method
• Weighted Moving Average method
• Exponential Smoothing Method
• Exponential Smoothing with Trend (Double)
• Associative methods
• Simple Linear regression
• Multiple Linear regression

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Example 1, Shopping Carts
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Naïve Forecasts

• Strengths
• Weaknesses
• Variations of Naïve Forecasts
• Weekly Restaurant
• Yearly Hotel

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Discussions on Naive Forecasts

• No cost
• Easy to use
• Not accurate
• Seasonal and trend data
• ForecastLast seasons actual obs

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Simple Moving Average
Figure 2
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Simple Moving Average
How to choose n ? Smoothness vs.
Responsiveness Naïve Forecast is special case of
MA
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Discussions on Moving Average Method

• n1, MAActual obs Naive Forecast
• ngt1, MA-more smooth-lag of changes
• n up, MA-more smooth/not responsive
• n - balance costs of responding to data changes
  versus random variations
• easy to use and understand
• require more data and equal weights for each datum

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Weighted Moving Average

• MA is a special case of WMA
• Choice of weights Ws
• Choice of n

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Exponential Smoothing
Ft Ft-1 ?(At-1 - Ft-1) ?At-1 (1-?)Ft-1 F2
F1 ?(A1 - F1) ?A1 (1-?)F1 Assume F1 A1
42, ? 0.10 F2 F1 ?(A1 - F1) 42 0.10(42
- 42) 42 F3 F2 ?(A2 - F2) 42 0.10(40 -
42) 41.8

• Premise--The most recent observations might have
  the highest predictive value.
• Therefore, we should give more weight to the more
  recent time periods when forecasting.
• Strengths
• Weaknesses
• WMA is a special case of Exponential smoothing

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Picking a Smoothing Constant ?
????.2
????.05
Choice of ? Smoothness Responsiveness
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Discussions on Exponential Smoothing

• alpha - positively related to responsiveness
• alpha -(0.05-0.50) and trial and error
• easy to calculate and need minimum of data
• widely used
• alpha up - more weight on recent obs
• not useful if trend exists

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Linear Trend Equation
Yt a bt

• Meanings of a and b
• a is the intercept or Y value as t 0 (e.g.
  Fixed cost)
• b is the slope or marginal change in Y with unit
  change in t
• b is similar to the slope. However, since it is
  calculated with the variability of the data in
  mind, its formulation is not as straight-forward
  as our usual notion of slope.

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Calculating a and b
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Linear Trend Equation Example
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Linear Trend Calculation
812
-
6.3(15)
a




143.5

5
y 143.5 6.3t
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Forecast Accuracy

• Error - difference between actual value and
  predicted value
• Mean absolute deviation (MAD)
• Average absolute forecasting error
• Mean squared error (MSE)
• Average of squared forecasting error
• Mean absolute percent error (MAPE)
• Average of relative absolute forecasting error
• Tracking signal
• Ratio of cumulative error and MAD

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Comparisons of Forecasting Accuracy

• none is superior to others
• choice of MAD, MSE or MAPE
• choice of forecasting techniques
• monitoring forecasting performance overtime
• Artificial intelligence and expert systems