Welcome to MM305 Unit 5 Seminar Dr. Bob Forecasting

Eight Steps to Forecasting 1. Determine use of forecast - what objective are we trying to obtain? 2. Select items or quantities to be forecasted. 3.Determine time horizon of forecast: Short-range (less than three months) Medium-range (3 months to 3 years) Long-range (3+ years) 4. Select forecasting model or models. 5. Gather data needed to make forecast. 6. Validate forecasting model. 7. Make forecast. 8. Implement results.

Forecasting Models

Qualitative Models Attempts to incorporate judgmental or subjective factors into forecasting model. Opinions by experts, individual experiences and judgments, and other subjective factors may be considered. Especially useful when subjective factors are expected to be very important or when accurate quantitative data are difficult to obtain. Useful for long-term forecasting.

Time-Series and Causal Models 1.Time-series Models: Time-series models attempt to predict future by using historical data. Models make assumption that what happens in future is a function of what has happened in past. 2.Causal Models: As with time-series models, causal models also rely on quantitative data. Bivariate and multivariate regression models are examples of these models.

Components of a Time Series

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

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

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

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

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

Measures of Forecast Accuracy - Example using Excel

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

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

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)

Excel QM (page 174)

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 )

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

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

Comparison of MA and ES Similarities: Both methods are appropriate for stationary series Both methods depend on a single parameter Both methods lag behind a trend

Comparison of MA and ES Differences: ES carries all past history (forever!) MA eliminates “bad” data after N periods MA requires all N past data points to compute new forecast estimate ES only requires last forecast and last observation (data point) to continue

Moving Average and Exponential Smoothing -Example using Excel

Linear Trend, Regression, and Forecasting -Excel Data Analysis

Linear Trend, Regression, and Forecasting -Forecasting Trend Projection: Forecasting Period t = 17 F t =13970*(t) F t =13970*(16) = $516,157

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

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

Excel QM—Regression/Trend Analysis

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)= (8) = , or 141 generators (sales in 2009)= (9) = , or 152 generators

Using Technology Appendix C: Using POM-QM for Windows Appendix D: Using Excel QM Appendix 5.1 (Page 201)