Welcome to MM305

Unit 5 Seminar

Prof Greg

Forecasting

What is forecasting?What is forecasting?

• An attempt to predict the future using data.

• Generally an 8-step process1. 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 data6. Validate your forecasting model7. Make the forecast8. Implement the results (make use of it)

Regression Analysis

Multiple Regression

MovingAverage

Exponential Smoothing

Trend Projections

Decomposition

Forecasting ModelsForecasting Models

Figure 5.1

Delphi Methods

Jury of Executive Opinion

Sales ForceComposite

Consumer Market Survey

Time-Series Methods

Qualitative Models

Causal Methods

Forecasting Techniques

Forecasting MethodsForecasting 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

Components of a Time Series

Measures of Forecast AccuracyMeasures of Forecast Accuracy

• Mean Absolute Deviation (MAD):MAD = |forecast error| / T

= |At - Ft| / T

• Mean Squared Error (MSE):MSE = (forecast error)2 / T

= (At – Ft)2 / T

• Mean Absolute Percent Error (MAPE):

MAPE = 100 (|At - Ft|/ At) / T

General Forms of Time-Series ModelsGeneral 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 ModelsCausal 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 VariationsSeasonal 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

Moving Average (MA)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

n

YYYF ntttt

111

...

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

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

Weighted Moving Averages (WMA)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)

n

ntnttt www

YwYwYwF

...

...

21

11211

Excel QM Excel QM

Exponential Smoothing (ES)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:

Ft= Ft-1 + ( At-1 - Ft-1 )

)- tperiodfor forecast - - tperiodin value(actual - tperiodfor forecast

t periodfor Forecast

111

Selecting the Smoothing Constant 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)

Excel QM: Port of Baltimore Example (page 177)

Program 5.2B

Time-Series Forecasting ModelsTime-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

Decomposition of a Time SeriesDecomposition 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

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 = b0 +b1X

Excel QM—Regression/Trend AnalysisExcel QM—Regression/Trend Analysis

Midwestern Manufacturing Company ExampleMidwestern 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

XY 54107156 ..ˆ

(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

Month Ending

Rating 3-mo Moving Average Weighted 3-mo Moving Average (1st mo=3, 2nd mo=2, 3rd mo=1)

3-mo Absolute Deviation

3-mo Weighted Absolute Deviation

1 2.0

2 2.2

3 2.5

4 1.9 (2.0+2.2+2.5)/3 = 2.23 (6.0+4.4+2.5)/6 = 2.15 0.33 0.25

5 2.3 (2.2+2.5+1.9)/3 = 2.20 (6.6+5.0+1.9)/6 = 2.25 0.10 0.05

6 2.0 (2.5+1.9+2.3)/3 = 2.23 (7.5+3.8+2.3)/6 = 2.27 0.23 0.27

Total Deviations 0.66 0.57

MAD 0.22 0.19

Hour Lottery Ticket Sales

8 am 150

10 am 142

12 noon 190

2 pm 223