1. Welcome to MM305 Unit 5 Seminar Prof Greg Forecasting

2. What is forecasting? An attempt to predict the future using data. Generally an 8-step process 1.Why are you forecasting? 2.What are you forecasting? 3.When are you forecasting to? 4.How you are going to forecast. 5.Gather the needed data 6.Validate your forecasting model 7.Make the forecast 8.Implement the results (make use of it)

3. Regression Analysis Multiple Regression Moving Average Exponential Smoothing Trend Projections Decomposition Forecasting Models Figure 5.1 Delphi Methods Jury of Executive Opinion Sales Force Composite Consumer Market Survey Time-Series Methods Qualitative Models Causal Methods Forecasting Techniques

4. Forecasting Methods  Qualitative  Qualitative models incorporate judgmental or subjective factor  Useful when subjective factors are thought to be important or when accurate quantitative data is difficult to obtain  Time Series  Time-series models attempt to predict the future based on the past  Causal Models  Causal models use variables or factors that might influence the quantity being forecasted

5. Components of a Time Series

6. Measures of Forecast Accuracy Mean Absolute Deviation (MAD): MAD =  |forecast error| / T =  |A t - F t | / T Mean Squared Error (MSE): MSE =  (forecast error) 2 / T =  (A t – F t ) 2 / T Mean Absolute Percent Error (MAPE): MAPE = 100  (|A t - F t |/ A t ) / T

7. General Forms of Time-Series Models There are two general forms of time-series models: Most widely used is multiplicative model, which assumes forecasted value is product of four components. Forecast = (Trend) *(Seasonality) *(Cycles) *( Random) Additive model adds components together to provide an estimate. Forecast = Trend + Seasonality + Cycles + Random

8. Causal Models Goal of causal forecasting model is to develop best statistical relationship between dependent variable and independent variables. Most common model used in practice is regression analysis. In causal forecasting models, when one tries to predict a dependent variable using: a single independent variable -simple regression model more than one independent variable -multiple regression model

9. Trend Projection Fits a trend line to a series of historical data points The line is projected into the future for medium- to long-range forecasts Several trend equations can be developed based on exponential or quadratic models The simplest is a linear model developed using regression analysis

10. Seasonal Variations Recurring variations over time may indicate the need for seasonal adjustments in the trend line A seasonal index indicates how a particular season compares with an average season When no trend is present, the seasonal index can be found by dividing the average value for a particular season by the average of all the data

11. Moving Average (MA) MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of data over time Equation: MA = (Actual value in previous k periods) / k

12. Excel QM: 3-Year Moving Average (Page 172)

13. Weighted Moving Averages (WMA) Used when trend is present Older data usually less important Weights based on intuition Equation: WMA =  (weight for period i) (actual value in period i)  (weights)

14. Excel QM

15. Exponential Smoothing (ES) A form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant ()  ranges from 0 to 1 is subjectively chosen Equation: F t = F t-1 +  ( A t-1 - F t-1 )

16. Selecting the Smoothing Constant  Selecting the appropriate value for  is key to obtaining a good forecast The objective is always to generate an accurate forecast The general approach is to develop trial forecasts with different values of  and select the  that results in the lowest MAD

17. Excel QM: Port of Baltimore Example (page 177) Program 5.2B

18. Time-Series Forecasting Models A time series is a sequence of evenly spaced events Time-series forecasts predict the future based solely of the past values of the variable Other variables are ignored

19. Decomposition of a Time Series Trend (T) -- upward and downward movement Seasonality (S) -- Demand fluctuations Cycles (C) -- Patterns in annual data Random Variation s (R) – “Blips” caused by chance

20. Trend Projection Trend projection fits a trend line to a series of historical data points The line is projected into the future for medium- to long-range forecasts The simplest is a linear model developed using regression analysis  Ŷ = b 0 +b 1 X

21. Excel QM—Regression/Trend Analysis

22. Midwestern Manufacturing Company Example The forecast equation is To project demand for 2008, we use the coding system to define X = 8 Likewise for X = 9 (sales in 2008)= 56.71 + 10.54(8) = 141.03, or 141 generators (sales in 2009)= 56.71 + 10.54(9) = 151.57, or 152 generators

23. Month Ending Rating3-mo Moving Average Weighted 3-mo Moving Average (1 st mo=3, 2 nd mo=2, 3 rd mo=1) 3-mo Absolute Deviation 3-mo Weighted Absolute Deviation 12.0 22.2 32.5 41.9(2.0+2.2+2.5)/3 = 2.23(6.0+4.4+2.5)/6 = 2.150.330.25 52.3(2.2+2.5+1.9)/3 = 2.20(6.6+5.0+1.9)/6 = 2.250.100.05 62.0(2.5+1.9+2.3)/3 = 2.23(7.5+3.8+2.3)/6 = 2.270.230.27 Total Deviations0.660.57 MAD0.220.19

33. Hour Lottery Ticket Sales 8 am150 10 am142 12 noon190 2 pm223