1 Doing Statistics for Business Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sandifer Chapter 13 Time Series and Forecasting

2 Doing Statistics for Business A qualitative model for forecasting relies on experience and expert opinion. A quantitative model uses past data to predict future values.

3 Doing Statistics for Business Causal models exploit the relationship between the dependent and other related variables in predicting future values for the dependent variable.

4 Doing Statistics for Business Time series models use only data on the variable of interest. They exploit patterns, repetitive or systematic behavior and/or trends in the data to predict future values for the dependent variable.

5 Doing Statistics for Business Figure 13.1 Sample Scatter Plot of Loaves Sold by Time

6 Doing Statistics for Business A Time Series is a set of observations of a variable at regular time intervals, such as yearly, monthly, weekly, daily, etc.

7 Doing Statistics for Business A stationary time series is one with no significant upward or downward trend. A non-stationary time series has some type of trend.

8 Doing Statistics for Business Chapter 13 Objectives Ü Getting Started with Time Series Data Ü Components of the Multiplicative Model Ü Simple Moving Average Models Ü Weighted Moving Average Models Ü Exponential Smoothing Models

9 Doing Statistics for Business Chapter 13 Objectives Ü Regression Models Ü Seasonal Indices Ü Other Forecasting Techniques

10 Doing Statistics for Business TRY IT NOW! Baseball Attendance Scatter Plot of NC Time Series Display the NC time series as a scatter plot. Do you see any patterns or trends? If so, what are they?

11 Doing Statistics for Business Discovery Exercise 13.1 Looking for Patterns and Trends Examine the time series displayed in the graphs below and identify any patterns and trends that you see. Use what you know about the particular data being collected to help you identify why the data look the way they do. A. The chart on the next slide shows the average monthly price (cents per kilowatt-hour) of electricity across the United States from 1988 to 1999.

12 Doing Statistics for Business Discovery Exercise 13.1 Looking for Patterns and Trends (con’t)

13 Doing Statistics for Business Discovery Exercise 13.1 Looking for Patterns and Trends (con’t) B. The Bureau of Labor Statistics (BLS) reports data on commodity prices on a monthly basis. These data are reported on a regional and national basis. The following graph displays the monthly average price (cents per pound) of white bread (pan) in the United States for the years

14 Doing Statistics for Business Discovery Exercise 13.1 Looking for Patterns and Trends (con’t)

15 Doing Statistics for Business Discovery Exercise 13.1 Looking for Patterns and Trends (con’t) C. The number of electric ranges shipped annually from 1987 to 1996 is collected by the appliance industry.

16 Doing Statistics for Business The multiplicative model says that any observation in the time series can be written as the product of 4 components: y t = T * S * C * R

17 Doing Statistics for Business The trend component, T, describes the systematic long-term tendency of the data to increase or decrease over time. The seasonal component, S, describes a systematic pattern that repeats itself year after year.

18 Doing Statistics for Business The cyclical component, C, models the systematic ups and downs in the time series which repeat every 2 to 10 years and are typically tied to the business economy. The random component, R, describes the irregular, unsystematic “bumps” in the values in the time series.

19 Doing Statistics for Business TRY IT NOW! Components of a time series Reconsider the time series showing the average monthly price of electricity. Which of the four components are present in this time series?

20 Doing Statistics for Business TRY IT NOW!(con’t) Components of a time series

21 Doing Statistics for Business Figure 13.2 FWC Time Series with Average Displayed

22 Doing Statistics for Business A k-period Moving Average is the average of the most recent k observations.

23 Doing Statistics for Business TRY IT NOW! Baseball Attendance A 2-Period MA Model Find the 2-period MA forecast for the number of people in families with children for Complete the following table to find the MSE for the 2- period MA model for the FWC time series.

24 Doing Statistics for Business TRY IT NOW! Baseball Attendance A 2-Period MA Model (con’t) How does the MSE for the 2-period MA model compare to the MSE for the 3-period MA?

25 Doing Statistics for Business Figure 13.3 FWC Time Series with 2-period MA Model and 3-period MA Model

26 Doing Statistics for Business A Simple Moving Average uses the simple average of the most recent k observations to predict for the next time period.

27 Doing Statistics for Business A Weighted Moving Average is a moving average model with unequal weights.

28 Doing Statistics for Business TRY IT NOW! Baseball Attendance A 2-Period Weighted MA Model Find the 2-period weighted MA forecast for the number of people in families with children for Weight the most recent observation by 0.75 and the second most recent observation by Complete the following table to find the MA model for the FWC time series.

29 Doing Statistics for Business TRY IT NOW! Baseball Attendance A 2-Period Weighted MA Model (con’t) Is this model better than the simple 2-period moving average?

30 Doing Statistics for Business An Exponential Smoothing Model is an averaging technique that uses unequal weights. The weights applied to past observations decline in an exponential manner.

31 Doing Statistics for Business Figure 13.4 Weights for Exponential Smoothing Model with  = 0.70

32 Doing Statistics for Business The Smoothing Constant, , is the weight assigned to the most recent observation in an exponential smoothing model.

33 Doing Statistics for Business TRY IT NOW! Baseball Attendance Exponential Smoothing Model Find the forecast for the number of people in families with children for 2001 using an exponential smoothing model with a smoothing constant of 0.6. Complete the following table to find the MSE for the exponential smoothing model (  = 0.06) for the FWC time series.

34 Doing Statistics for Business TRY IT NOW! Baseball Attendance Exponential Smoothing Model (con’t) Is this a better model than the model with a 0.7 smoothing constant?

35 Doing Statistics for Business TRY IT NOW! Baseball Attendance Regression Model Find the regression model and forecast for the number of people with no children (NC) for 2001 (time t = 11). The data are shown below:

36 Doing Statistics for Business TRY IT NOW! Baseball Attendance Evaluating the Regression Model for the NC Time Series Evaluate the regression model for the number of people in families with no children (NC). Find the MSE, the value of R 2 and test for the significance of the slope term.

37 Doing Statistics for Business Figure 13.5 Examples of Seasonal Time Frames

38 Doing Statistics for Business Steps for Modeling the Seasonal Component

39 Doing Statistics for Business TRY IT NOW! Finding Centered Moving Averages Verify the centered MA’s for the year 1996

40 Doing Statistics for Business TRY IT NOW! Finding Raw Seasonalities Verify the raw seasonality for Q1 for the year 1996.

41 Doing Statistics for Business TRY IT NOW! Finding Seasonal Indices Verify the seasonal indices for Q3 and Q4.

42 Doing Statistics for Business TRY IT NOW! Deseasonalize the data Verify the deasonalized value for quarter 1 of 1999.

43 Doing Statistics for Business TRY IT NOW! Predict the deseasonalized values Verify the deasonalized predicted value for quarter 1 of 2000.

44 Doing Statistics for Business TRY IT NOW! Predict the values Verify the prediction for quarter 2 of 2000.

45 Doing Statistics for Business Moving Average Models in Excel Use the Add Trendline option to analyze a moving average forecasting model in Excel. You must first create a graph of the time series you want to analyze. Select the range that contains your data and make a scatter plot of the data. Once the chart is created, follow these steps” 1. Click on the chart to select it, and click on any point on the line to select the data series. When you click on the chart to select it, a new option, Chart, s added to the menu bar. 2. From the Chart menu, select Add Trendline.

46 Doing Statistics for Business Moving Average Models in Excel (con’t) 3. Click on the Trend/Regression type box for Moving average. Specify the number of periods you want to use in the model by entering the value in the textbox labeled Period:

47 Doing Statistics for Business Figure 13.8 Scatter plot of FWC Population Data

48 Doing Statistics for Business Figure 13.9 The AddTrendline Dialog Box

49 Doing Statistics for Business Figure Chart with Moving Average Trendline

50 Doing Statistics for Business Figure 13.9 Moving Average Dialog Box

51 Doing Statistics for Business Figure Output from Moving Average Tool

52 Doing Statistics for Business Exponential Smoothing Models in Excel The simplest way to analyze a timer series using an Exponential Smoothing model in Excel is to use the data analysis tool. This tool works almost exactly like the one for Moving Average, except that you will need to input the value of  instead of the number of periods, k. Once you have entered the data range and the damping factor, 1- , and indicated what output you want and a location, the analysis is the same as the one for the Moving Average model.

53 Doing Statistics for Business Figure The Exponential Smoothing Dialog Box

54 Doing Statistics for Business Chapter 13 Summary In this chapter you have learned: 4 Time series data contains information on patterns and trends that can be used to forecast the behavior of the variable for the future. 4 Some basic terminology & techniques of Forecasting. 4 The multiplicative time series model

55 Doing Statistics for Business Chapter 13 Summary 4 The components of a time series 4 How to handle the seasonal component 4 How to use Moving Averages Weighted Moving Averages, and Exponential smoothing to predict future values of a numeric variable. 4 How to evaluate the model in order to choose the “best” model.