Chapter 11 Solved Problems 1. Exhibit 11.2 Example Linear and Nonlinear Trend Patterns 2.

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Presentation transcript:

Chapter 11 Solved Problems 1

Exhibit 11.2 Example Linear and Nonlinear Trend Patterns 2

Exhibit 11.3 Seasonal Pattern of Home Natural Gas Usage 3

Exhibit Extra Trend and Business Cycle Characteristics (each data point is 1 year apart) 4

Exhibit 11.4 Call Center Volume Example of a time series with trend and seasonal components: 5

Exhibit 11.5 Chart of Call Volume 6

Basic Concepts in Forecasting Forecast error is the difference between the observed value of the time series and the forecast, or A t – F t. Mean Square Error (MSE) Mean Absolute Deviation Error (MAD) Mean Absolute Percentage Error (MAPE) Σ ( A t – F t ) 2 MSE = [11.1] T ׀A t – F t ׀ MAD = [11.2] T Σ׀ ( A t – F t )/A t ׀ X 100 MAPE = [11.3] T 7

Exhibit 11.6 Forecast Error of Example Time Series Data 8

Solved Problem Develop three-period and four-period moving-average forecasts and single exponential smoothing forecasts with a = 0.5. Compute the MAD, MAPE, and MSE for each. Which method provides a better forecast? PeriodDemandPeriodDemand

Based on these error metrics (MAD, MSE, MAPE), the 3-month moving average is the best method among the three. Solved Problem 10

Exhibit 11.7 Summary of 3-Month Moving-Average Forecasts 11

Exhibit 11.8 Milk-Sales Forecast Error Analysis 12

Single Exponential Smoothing Single Exponential Smoothing (SES) is a forecasting technique that uses a weighted average of past time-series values to forecast the value of the time series in the next period. F t+1 =  A t + (1 –  )F t = F t +  (A t – F t ) [11.5] 13

Exhibit 11.9 Summary of Single Exponential Smoothing Milk-Sales Forecasts with α =

Exhibit Graph of Single Exponential Smoothing Milk-Sales Forecasts with α =

Regression as a Forecasting Approach Regression analysis is a method for building a statistical model that defines a relationship between a single dependent variable and one or more independent variables, all of which are numerical. Y t = a + bt(11.7)  Simple linear regression finds the best values of a and b using the method of least squares.  Excel provides a very simple tool to find the best-fitting regression model for a time series by selecting the Add Trendline option from the Chart menu. 16

Exhibit Factory Energy Costs 17

Exhibit Format Trendline Dialog Box 18

Exhibit Least-Squares Regression Model for Energy Cost Forecasting 19

Exhibit Gasoline Sales Data 20

Exhibit Chart of Sales versus Time 21

Exhibit Multiple Regression Results 22