Business Statistics: Communicating with Numbers By Sanjiv Jaggia and Alison Kelly

1. Business Statistics: Communicating with Numbers By Sanjiv Jaggia and Alison Kelly

2. Chapter 18 Learning Objectives (LOs) LO 18.1:Distinguish between the various models used in forecasting. LO 18.2:Use smoothing techniques to make forecasts. LO 18.3:Use trend regression models to make forecasts. LO 18.4:Calculate and interpret seasonal indices and use them to seasonally adjust a time series. LO 18.5:Use decomposition analysis to make forecasts. LO 18.6:Use trend regression models with seasonal dummy variables to make forecasts. LO 18.7:Use causal forecasting models to make forecasts.

3. Forecasting Nike Revenue • Here are Nike’s quarterly revenues from 1999 through 2008. We will use this historical data to make forecasts for the future. • During these years, revenue grew by 75 million per quarter. Some analysts, however, think growth will slow because of poor economic conditions at the end of the decade.

4. 18.1Choosing a Forecasting Model LO 18.1 Distinguish between the various models used in forecasting.

5. Forecasting Methods LO 18.1 • We focus on quantitative rather than qualitative forecasting models. • Qualitativeprocedures are based on the judgment of the forecaster. • Quantitativeprocedures use a formal model along with historical data. • Quantitative models can be further classified as causal and noncausal. • Causalmethods are based on a regression framework, where the variable of interest is related to a single or multiple explanatory variables. • Noncausal models do not present any explanation of the mechanism generating the variable of interest, but rather try simply to project historical data.

6. Model Selection Criteria LO 18.1

7. Model Selection Criteria LO 18.1

8. 18.2 Smoothing Techniques LO 18.2 Use smoothing techniques to make forecasts. • Forecasters often assume that time series consist of both systematic and unsystematic patterns. • A systematic pattern could be caused by a persistent trend or seasonal fluctuation. • Unsystematic patterns are caused by the presence of a random (irregular) error term. • In order to get a better estimate of the trend or seasonality, it might help to first smooth away these irregularities.

9. Moving Average Methods LO 18.2 • Due to its simplicity, the moving average method ranks among the most popular techniques for processing a time series. • The m-period moving average computed at time t is the average of the m most recent observations. • Here, we focus on odd-numbered moving averages, such as 3-period, 5-period, and so on. Later, we use even-numbered moving averages to extract the seasonal component of a time series.

10. Example 18.1 LO 18.2 • The United States consumes about 21 million barrels of petroleum a day, about half in the form of gasoline. The table below shows a portion of weekly gas production (in 1,000s of barrels per day) for the first 21 weeks in 2009:

11. Example 18.1 LO 18.2

12. 3-Period Moving Average LO 18.2 • After computing the 3-period moving average for weeks 2 through 20, we can see graphically how the moving average dampens the fluctuations in the time series.

13. Forecasts LO 18.2

14. MSE and MAD LO 18.2 • This table shows the MSE and the MAD computations: • MSE equals the total of column 6 divided by the number of observations with residuals (18), so MSE=52,973. MAD equals the total of column 7 divided by 18, so MAD=184.

15. Exponential Smoothing LO 18.2

16. Exponential Smoothing LO 18.2

17. Example 18.2 LO 18.2

18. LO 18.2

19. 18.3 Trend Forecasting Models LO 18.3 Use trend regression models to make forecasts.

20. Example 18.3 LO 18.3 • Hispanics are the fastest-growing minority in the U.S., comprising about one-sixth of the population. • The file Hispanic Characteristics, found on the text website,contains yearly United States’ data on the number of Hispanic households and the median income of Hispanic households. • We want to use the sample data to estimate two linear trend models, one for the number of Hispanic households and one for the median income of Hispanic households.

21. Trend Regression Results LO 18.3 In order to estimate the linear trend model for either data set, we first create the time variable, t.

22. Coefficient Interpretation LO 18.3

23. The Exponential Trend Model LO 18.3

24. Example 18.4 LO 18.3 Let’s return to the Hispanics Characteristics data. The number of Hispanic households seems to follow an exponential trend more closely than a linear one.

25. Example 18.4 LO 18.3 For the median income of Hispanic households, the linear trend model appears to work better.

26. MSE and MAD LO 18.3 • In this example the time series plots with the estimated trends provide useful insights. Goodness-of-fit measures can help us confirm our initial intuition. • When predicting the number of households, the exponential model performs better. But when predicting the median income, the linear trend is preferred.

27. Polynomial Trend Models LO 18.3

28. 18.4 Trend and Seasonality LO 18.4 Calculate and interpret seasonal indices and use them to seasonally adjust a time series.

29. Extracting Seasonality LO 18.4

30. Centered Moving Average CMA LO 18.4

31. The Ratio-to-Moving Average LO 18.4

32. The Seasonal Indices LO 18.4 • The table shows some of the Ratio-to-Moving Average values plus the average of these ratios for each quarter. These averages are called the unadjusted seasonal indices. • For quarterly data, the seasonal indices should add up to 4, so in order to ensure this requirement, we multiply each unadjusted seasonal index by 4 and divide by the sum of the four unadjusted indices. After performing these calculations, we arrive at the adjusted seasonal indices.

33. Extracting the Trend LO 18.4

34. Forecasting with Decomposition Analysis LO 18.5 Use decomposition analysis to make forecasts.

35. Nike Revenue Forecasts LO 18.5

36. Seasonal Dummy Variables LO 18.6 Use trend regression models with seasonal dummy variables to make forecasts.

37. Exponential Trend LO 18.6

38. Interpretation and Comparison LO 18.6

39. Causal Forecasting Methods LO 18.7 Use causal forecasting models to make forecasts. • So far we have discussed noncausal, or purely time series models. These models do not attempt to explain the mechanism generating the variable of interest. • Causal forecasting models are based on a regression framework, where the explanatory variables influence the outcome of the response variable. Here, we try to also understand the data-generating mechanism.

40. A Variety of Models LO 18.7

41. Example 18.7 LO 18.7 • The file Housing Units contains data on private housing units sold and per-capita GDP for 1981 to 2008. • The text discusses the estimation of three models to predict the amount of housing units sold: one with a lagged value for housing units, one with lagged GDP, and one with both variables.

42. Example 18.7 LO 18.7