Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-1 Chapter 7: Forecasting

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-2 Forecasting Techniques Qualitative and judgmental Statistical time series models Explanatory/causal models

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-3 Qualitative and Judgmental Methods Historical analogy – comparative analysis with a previous situation Delphi Method – response to a sequence of questionnaires by a panel of experts

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-4 Indicators and Indexes Indicators – measures believed to influence the behavior of a variable we wish to forecast Leading indicators Lagging indicators Index – a weighted combination of indicators Indicators and indexes are often used in economic forecasting

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-5 Time Series A time series is a stream of historical data Components of time series Trend Short-term seasonal effects Longer-term cyclical effects

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-6 Examples of Time Series

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-7 Statistical Forecasting Methods Moving average Exponential smoothing Regression analysis

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-8 Simple Moving Average Average random fluctuations in a time series to infer short-term changes in direction Assumption: future observations will be similar to recent past Moving average for next period = average of most recent k observations

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-9 Example: Moving Average Forecast With k = 3

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-10 Time Series Data and Moving Averages

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-11 Excel Tool: Moving Averages Tools > Data Analysis > Moving Average Enter range of data Enter value of k Select output options Select options

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-12 Excel Results Caution: chart aligns forecasts for next period with current period data

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-13 Weighted Moving Average Weight the most recent k observations, with weights that add to 1.0 Higher weights on more recent observations generally provide more responsive forecasts to rapidly changing time series

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-14 Computing Forecast Errors

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-15 Error Metrics and Forecast Accuracy Mean absolute deviation (MAD) Mean square error (MSE) Mean absolute percentage error (MAPE)

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-16 Summary of Error Metrics for Burglary Data

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-17 Exponential Smoothing Exponential smoothing model: F t+1 = (1 –  )F t +  A t = F t +  (A t – F t ) F t+1 is the forecast for time period t+1, F t is the forecast for period t, A t is the observed value in period t, and  is a constant between 0 and 1, called the smoothing constant.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-18 Excel Tool: Exponential Smoothing Tools > Data Analysis > Exponential Smoothing Enter data range Damping factor = 1 -  Select output range and options

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-19 Exponential Smoothing Example

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-20 Exponential Smoothing Forecasts (  = 0.6)

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-21 Forecasting Models With Linear Trends Double Moving Average Double Exponential Smoothing Based on the linear trend equation

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-22 Double Moving Average M t = [ A t-k+1 + A t-k+2 + … A t ]/k D t = [M t-k+1 + M t-k+2 + … M t ]/k a t = 2M t – D t b t = (2/(k-1))[M t – D t ] Use a T and b T in the linear trend equation to forecast k periods beyond period T:

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-23 Double Exponential Smoothing a t =  y t + (1-  ) (a t-1 + b t-1 ) b t =  (a t – a t-1 ) + (1-  )b t-1 Initialize: a 1 = A 1 b 1 = A 2 – A 1

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-24 Forecasting Models With Seasonality Additive model Multiplicative model

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-25 Additive Seasonality Level and seasonal factors: Forecast for next period a t =  ( A t - S t-s ) + (1-  ) a t-1 S t =  (A t - a t ) + (1-  ) S t-s

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-26 Initialization a s = a t = a s t = 1,2,…s S t = A t - a t t = 1,2,…s

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-27 Models for Trend and Seasonality Holt-Winters Additive Model Holt-Winters Multiplicative Model

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-28 Holt-Winters Additive Model Smoothing equations: Forecast for period t + 1: a t =  ( A t - S t-s ) + (1-  ) (a t-1 + b t-1 ) b t =  (a t – a t-1 ) + (1-  )b t-1 S t =  (A t - a t ) + (1-  ) S t-s

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-29 Initialization b t = b s, for t = 1,2,…s b s = [ (A s+1 – A 1 )/s + (A s+2 – A s )/s + ….(A s+s – A s )/s] / s

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-30 CB Predictor Excel add-in for forecasting Integrated with Crystal Ball software Example: Burglary Data

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-31 CB Predictor Input Data Dialog

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-32 CB Predictor Data Attributes Dialog

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-33 CB Predictor Method Gallery Dialog

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-34 CB Predictor Results Dialog

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-35 CB Predictor Output: Methods Table Durbin-Watson statistic: check for autocorrelation; a value of 2 indicates no autocorrelation Theil’s U statistic: comparison to naïve forecast. U 1, worse than guessing

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-36 CB Predictor Output: Results Table

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-37 Example: Gas and Electric Usage

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-38 CB Predictor Results

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-39 Regression-Based Forecasting Models

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-40 CB Predictor Regression Forecasting Results

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-41 Autoregressive Models First-order autoregressive model Y i = a 0 + a 1 Y i-1 +  i Second-order autoregressive model Y i = a 0 + a 1 Y i-1 + a 2 Y i-2 +  i

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-42 Portion of Coal Production File for Autoregessive Modeling

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-43 Second Order Autoregressive Model

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-44 First Order Autoregressive Model

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-45 Incorporating Seasonality into Regression Models Use ordinal variables. Example: Gas Usage =  0 +  1 Time +  2 January +  3 February +  4 March +  5 April +  6 May +  7 June +  8 July +  9 August +  10 September +  11 October +  12 November The forecast for December of the first year will be  0 +  1 (12). The forecast for January (Time = 1) would be  0 +  1 (1) +  2 (1).

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-46 Data Matrix

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-47 Regression ANOVA Results

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-48 Regression Forecasting With Causal Variables Sales (week 11) = (11) = 13,733 gallons

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall7-49 Causal Model Sales =  0 +  1 Week +  2 Price/Gallon Sales = Week – Price/Gallon Sales (week 11) = (11) (3.80) = 13,733 gallons