FORECASTING

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• FORECASTING

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Types of Forecasts

• Qualitative
• Time Series
• Causal Relationships
• Simulation

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Qualitative Forecasting Approaches

• Historical Analogy
• Panel Consensus
• Delphi
• Market Research

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Quantitative Approaches

• Naïve (time series)
• Moving Averages (time series)
• Exponential Smoothing (time series)
• Trend Projection (time series)
• Linear Regression (causal)

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Naïve Method

• This periods forecast Last periods
  observation
• Crude but effective
• August sales 1000 September sales ??
• 1000!

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Moving Averages

• This periods forecast Average of past n
  periods observations
• Example for n 3 Sales for Jan through March
  were 100, 110, 150
• April forecast (100110150)/3 120

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Example
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Evaluating Forecasts

• Concept Forecast worth function of how close
  forecasts are to observations
• Mean Absolute Deviation (MAD)
• MAD sum of absolute value of forecast errors /
  number of forecasts (e.g. periods)
• MAD is the average of the absolute value of all
  of the forecast errors.

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Weighted Moving Averages

• This periods forecast Weighted average of past
  n periods observations
• Example for n 3 Sales for Jan through March
  were 100, 110, 150
• Suppose weights for last 3 periods are .5
  (March), .3 (Feb), and .2 (Jan)
• April forecast .5150.3110.2100 128

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Exponential Smoothing

• New Forecast Last periods forecast alpha
  (Last periods actual observation - last periods
  forecast)
• Mathematically F(t) F(t-1) alpha A(t-1)
  - F(t-1), where F is the forecast A is the
  actual observation, and alpha is the smoothing
  constant -- between 0 and 1
• Example F(t-1) 100 A(t-1) 110 alpha 0.4
  -- Find F(t)
• F(t) 104
• Can add parameters for trends and seasonality

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Trend Projections

• Use Linear regression
• Model yhat a b x
• a y-intercept forecast at period 0
• b slope rate of change in y for each period x
• Example Sales 100 10 t, where t is period
• For t 15, Find yhat --
• yhat 250
• Can find and a and b via Method of Least Squares

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Linear Regression

• Model yhat a b1 x1 b2 x2 bk
  xk
• a y-intercept
• bi slope rate of change in y for each increase
  in xi, given that other xjs are held constant
• Example College GPA 0.2 0.5 HS GPA 0.001
  HS SAT
• For a HS student with a 3.0 GPA and 1200 SAT -
  what is the forecast?
• The forecast college GPA 2.90
• Can find a, b1, and b2 via Method of Least Squares