Business Analytics Time Series Analysis and Forecasting PDF

Business Analytics © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Analysis and Forecasting...

Business Analytics © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Analysis and Forecasting Chapter 8 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Introduction (Slide 1 of 2) Forecasting methods can be classified as qualitative or quantitative. Qualitative methods generally involve the use of expert judgment to develop forecasts. Quantitative forecasting methods can be used when: Past information about the variable being forecast is available. The information can be quantified. It is reasonable to assume that past is prologue. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Introduction (Slide 2 of 2) The objective of time series analysis is to uncover a pattern in the time series and then extrapolate the pattern into the future. The forecast is based solely on past values of the variable and/or on past forecast errors. Modern data-collection technologies have enabled individuals, businesses, and government agencies to collect vast amounts of data that may be used for causal forecasting. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns Horizontal Pattern Trend Pattern Seasonal Pattern Trend and Seasonal Pattern Cyclical Pattern © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 1 of 20) Time series: A sequence of observations on a variable measured at successive points in time or over successive periods of time. The measurements may be taken every hour, day, week, month, year, or any other regular interval. The pattern of the data is important in understanding the series’ past behavior. If the behavior of the times series data of the past is expected to continue in the future, it can be used as a guide in selecting an appropriate forecasting method. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 2 of 20) Horizontal Pattern: Exists when the data fluctuate randomly around a constant mean over time. Stationary time series: It denotes a time series whose statistical properties are independent of time: The process generating the data has a constant mean. The variability of the time series is constant over time. A time series plot for a stationary time series will always exhibit a horizontal pattern with random fluctuations. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 3 of 20) Table 8.1: Gasoline Sales Time Week Sales (1,000s of gallons) Series 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 4 of 20) Figure 8.1: Gasoline Sales Time Series Plot © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 5 of 20) Sales Sales Table 8.2: Gasoline Sales Time (1,000s of (1,000s of Series after Obtaining the Week gallons) Week gallons) Contract with the Vermont State 1 17 12 22 Police 2 21 13 31 3 19 14 34 4 23 15 31 5 18 16 33 6 16 17 28 7 20 18 32 8 18 19 30 9 22 20 29 10 20 21 34 11 15 22 33 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 6 of 20) Figure 8.2: Gasoline Sales Time Series Plot after Obtaining the Contract with the Vermont State Police © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 7 of 20) Trend Pattern: A trend pattern shows gradual shifts or movements to relatively higher or lower values over a longer period of time. A trend is usually the result of long-term factors such as: Population increases or decreases. Shifting demographic characteristics of the population. Improving technology. Changes in the competitive landscape. Changes in consumer preferences. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 8 of 20) Table 8.3: Bicycle Sales Time Series Year Sales (1,000s) 1 21.6 2 22.9 3 25.5 4 21.9 5 23.9 6 27.5 7 31.5 8 29.7 9 28.6 10 31.4 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 9 of 20) Figure 8.3: Bicycle Sales Time Series Plot © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 10 of 20) Table 8.4: Cholesterol Drug Year Revenue ($ millions) Revenue Times 1 23.1 2 21.3 3 27.4 4 34.6 5 33.8 6 43.2 7 59.5 8 64.4 9 74.2 10 99.3 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 11 of 20) Figure 8.4: Cholesterol Drug Revenue Times Series Plot ($ millions) © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 12 of 20) Seasonal Pattern: Seasonal patterns are recurring patterns over successive periods of time. Example: A retailer that sells bathing suits expects low sales activity in the fall and winter months, with peak sales in the spring and summer months to occur every year. The time series plot not only exhibits a seasonal pattern over a one-year period but also for less than one year in duration. Example: daily traffic volume shows within-the-day “seasonal” behavior, with peak levels occurring during rush hour, moderate flow during the rest of the day, and light flow from midnight to early morning. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 13 of 20) Table 8.5: Umbrella Sales Time Year Quarter Sales Series 1 1 125 2 153 3 106 4 88 2 1 118 2 161 3 133 4 102 3 1 138 2 144 3 113 4 80 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 14 of 20) Table 8.5: Umbrella Sales Time Year Quarter Sales Series (cont.) 4 1 109 2 137 3 125 4 109 5 1 130 2 165 3 128 4 96 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 15 of 20) Figure 8.5: Umbrella Sales Time Series Plot © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 16 of 20) Trend and Seasonal Pattern: Year Quarter Sales ($1,000s) Some time series include both a 1 1 4.8 trend and a seasonal pattern. 2 4.1 3 6.0 4 6.5 2 1 5.8 2 5.2 Table 8.6: Quarterly Smartphone 3 6.8 Sales Time Series 4 7.4 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 17 of 20) Table 8.6: Quarterly Smartphone Year Quarter Sales ($1,000s) Sales Time Series (cont.) 3 1 6.0 2 5.6 3 7.5 4 7.8 4 1 6.3 2 5.9 3 8.0 4 8.4 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 18 of 20) Figure 8.6: Quarterly Smartphone Sales Time Series Plot © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 19 of 20) Cyclical Pattern: A cyclical pattern exists if the time series plot shows an alternating sequence of points below and above the trendline that lasts for more than one year. Example: Periods of moderate inflation followed by periods of rapid inflation can lead to a time series that alternates below and above a generally increasing trendline. Cyclical effects are often combined with long-term trend effects and referred to as trend-cycle effects. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Time Series Patterns (Slide 20 of 20) Identifying Time Series Patterns: The underlying pattern in the time series is an important factor in selecting a forecasting method. A time series plot should be one of the first analytic tools. We need to use a forecasting method that is capable of handling the pattern exhibited by the time series effectively. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 1 of 10) Table 8.7: Computing Forecasts and Measures of Forecast Accuracy Using the Most Recent Value as the Forecast for the Next Period Absolute Absolute Time Value of Squared Value of Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 1 17 2 21 17 4 4 16 19.05 19.05 −10.5 3 19 21 −2 2 4 3 10.53 4 23 19 4 4 16 17.39 17.39 −27.7 5 18 23 −5 5 25 8 27.78 −12.5 6 16 18 −2 2 4 0 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 12.50 Forecast Accuracy (Slide 2 of 10) Table 8.7: Computing Forecasts and Measures of Forecast Accuracy Using the Most Recent Value as the Forecast for the Next Period (cont.) Absolute Absolute Time Value of Squared Value of Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 7 20 16 4 4 16 20.00 20.00 −11.1 8 18 20 −2 2 4 1 11.11 9 22 18 4 4 16 18.18 18.18 −10.0 10 20 22 −2 2 4 0 10.00 −33.3 11 15 20 −5 5 25 3 33.33 12 22 15 7 7 49 31.82 31.82 Totals 5 41 179 1.19 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 211.69 Forecast Accuracy (Slide 3 of 10) Naïve forecasting method: Using the most recent data to predict future data. The key concept associated with measuring forecast accuracy is forecast error. Measures to determine how well a particular forecasting method is able to reproduce the time series data that are already available. Forecast error. Mean forecast error (MFE). Mean absolute error (MAE). Mean squared error (MSE). Mean absolute percentage error (MAPE). © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 4 of 10) Forecast Error: Difference between the actual and the forecasted values for period t. Mean Forecast Error: Mean or average of the forecast errors. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 5 of 10) Mean Absolute Error (MAE): Measure of forecast accuracy that avoids the problem of positive and negative forecast errors offsetting one another. Mean Squared Error (MSE): Measure that avoids the problem of positive and negative errors offsetting each other is obtained by computing the average of the squared forecast errors. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 6 of 10) Mean Absolute Percentage Error (MAPE): Average of the absolute value of percentage forecast errors. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 7 of 10) Table 8.8: Computing Forecasts and Measures of Forecast Accuracy Using the Average of All the Historical Data as the Forecast for the Next Period Absolute Absolute Value of Squared Value of Time Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 1 17 2 21 17.00 4.00 4.00 16.00 19.05 19.05 3 19 19.00 0.00 0.00 0.00 0.00 0.00 4 23 19.00 4.00 4.00 16.00 17.39 17.39 5 18 20.00 −2.00 2.00 4.00 −11.11 11.11 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 8 of 10) Table 8.8: Computing Forecasts and Measures of Forecast Accuracy Using the Average of All the Historical Data as the Forecast for the Next Period (cont.) Absolute Absolute Value of Squared Value of Time Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 6 16 19.60 −3.60 3.60 12.96 −22.50 22.50 7 20 19.00 1.00 1.00 1.00 5.00 5.00 8 18 19.14 −1.14 1.14 1.31 −6.35 6.35 9 22 19.00 3.00 3.00 9.00 13.64 13.64 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 9 of 10) Table 8.8: Computing Forecasts and Measures of Forecast Accuracy Using the Average of All the Historical Data as the Forecast for the Next Period (cont.) Absolute Absolute Value of Squared Value of Time Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 10 20 19.33 0.67 0.67 0.44 3.33 3.33 11 15 19.40 −4.40 4.40 19.36 −29.33 29.33 12 22 19.00 3.00 3.00 9.00 13.64 13.64 Totals 4.52 26.81 89.07 2.75 141.34 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Forecast Accuracy (Slide 10 of 10) The average of past values provides more accurate forecasts for the next period than using the most recent observation. Average of Naïve Method Past Values MAE 3.73 2.44 MSE 16.27 8.10 MAPE 19.24% 12.85% Compare the accuracy of the two forecasting methods by comparing the values of MAE, MSE, and MAPE for each method. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing Moving Averages Exponential Smoothing © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 1 of 16) Moving Averages: Moving averages method: Uses the average of the most recent k data values in the time series as the forecast for the next period. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 2 of 16) Table 8.9: Summary of Three-Week Moving Average Calculations Absolute Absolute Value of Squared Value of Time Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 1 17 2 21 3 19 4 23 19 4 4 16 17.39 17.39 5 18 21 −3 3 9 −16.67 16.67 6 16 20 −4 4 16 −25.00 25.00 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 3 of 16) Table 8.9: Summary of Three-Week Moving Average Calculations (cont.) Absolute Absolute Value of Squared Value of Time Series Forecast Forecast Forecast Percentage Percentage Week Value Forecast Error Error Error Error Error 7 20 19 1 1 1 5.00 5.00 8 18 18 0 0 0 0.00 0.00 9 22 18 4 4 16 18.18 18.18 10 20 20 0 0 0 0.00 0.00 11 15 20 −5 5 25 −33.33 33.33 12 22 19 3 3 9 13.64 13.64 Totals 0 24 92 −20.79 129.21 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 4 of 16) Figure 8.7: Gasoline Sales Time Series Plot and Three-Week Moving Average Forecasts © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 5 of 16) Figure 8.8: Data Analysis Dialog Box © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 6 of 16) Figure 8.9: Moving Average Dialog Box © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 7 of 16) Figure 8.10: Excel Output for Moving Average Forecast for Gasoline Data © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 8 of 16) Forecast Accuracy: The values of the three measures of forecast accuracy for the three-week moving average calculations in Table 8.9. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 9 of 16) Exponential Smoothing: Exponential smoothing uses a weighted average of past time series values as a forecast. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 10 of 16) Illustration of Exponential Smoothing: Hence, the forecast for period 2 is: © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 11 of 16) Time Squared Series Forecast Forecast Week Value Forecast Error Error 1 17 17.0 16.0 2 21 0 4.00 0 17.8 3 19 0 1.20 1.44 18.0 24.6 4 23 4 4.96 0 19.0 −1.0 5 18 3 3 1.06 18.8 −2.8 6 16 3 3 8.01 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 12 of 16) Time Squared Series Forecast Forecast Week Value Forecast Error Error 7 20 18.26 1.74 3.03 8 18 18.61 −0.61 0.37 9 22 18.49 3.51 12.32 10 20 19.19 0.81 0.66 11 15 19.35 −4.35 18.92 12 22 18.48 3.52 12.39 Totals 10.92 98.80 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 13 of 16) © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 14 of 16) Figure 8.13: Exponential Smoothing Dialog Box © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 15 of 16) Figure 8.14: Excel Output for Exponential Smoothing Forecast for Gasoline Data © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Moving Averages and Exponential Smoothing (Slide 16 of 16) Forecast Accuracy: If the time series contains substantial random variability, a small value of the smoothing constant is preferred and vice-versa. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting Linear Trend Projection Seasonality without Trend Seasonality with Trend Using Regression Analysis as a Causal Forecasting Method Combining Causal Variables with Trend and Seasonality Effects Considerations in Using Regression in Forecasting © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 1 of 19) Linear Trend Projection: Regression analysis can be used to forecast a time series with a linear trend. Simple linear regression analysis yields the linear relationship between the independent variable and the dependent variable that minimizes the MSE. Use this approach to find a best-fitting line to a set of data that exhibits a linear trend. Trend variable (time period t) is the independent variable. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 2 of 19) Linear Trend Projection (cont.): Equation for the trendline: Trend equation for the bicycle sales time series: Thus, the linear trend model yields a sales forecast of 32,500 bicycles for the next year. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 3 of 19) Figure 8.15: Excel Simple Linear Regression Output for Trendline Model for Bicycle Sales Data © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 4 of 19) Linear Trend Projection (cont.): We can also use more complex regression models to fit nonlinear trends: Autoregressive models: Regression models in which the independent variables are previous values of the time series. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 5 of 19) Seasonality without Trend: We can model a time series with a seasonal pattern by treating the season as a dummy variable. Illustration: Consider the data on the number of umbrellas sold in Table 8.5. The time series plot corresponding to this data in Figure 8.5 does not suggest any long-term trend in sales. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 6 of 19) Illustration (cont.): Closer inspection of the time series plot suggests that a quarterly seasonal pattern is present. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 7 of 19) Seasonality without Trend Illustration (cont.): The three dummy variables can be coded as follows: General form of the equation relating the number of umbrellas sold to the quarter the sales take place: © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 8 of 19) Table 8.11: Umbrella Sales Time Series with Dummy Variables Period Year Quarter Qtr1 Qtr2 Qtr3 Sales 1 1 1 1 0 0 125 2 2 0 1 0 153 3 3 0 0 1 106 4 4 0 0 0 88 5 2 1 1 0 0 118 6 2 0 1 0 161 7 3 0 0 1 133 8 4 0 0 0 102 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 9 of 19) Table 8.11: Umbrella Sales Time Series with Dummy Variables (cont.) Period Year Quarter Qtr1 Qtr2 Qtr3 Sales 9 3 1 1 0 0 138 10 2 0 1 0 144 11 3 0 0 1 113 12 4 0 0 0 80 13 4 1 1 0 0 109 14 2 0 1 0 137 15 3 0 0 1 125 16 4 0 0 0 109 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 10 of 19) Table 8.11: Umbrella Sales Time Series with Dummy Variables (cont.) Period Year Quarter Qtr1 Qtr2 Qtr3 Sales 17 5 1 1 0 0 130 18 2 0 1 0 165 19 3 0 0 1 128 20 4 0 0 0 96 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 11 of 19) Seasonality with Trend: The time series contains both seasonal effects and a linear trend. Consider the data for the smartphone time series in Table 8.6. The time series plot corresponding to this data (Figure 8.6) indicates that there is both linear trend and seasonal pattern. The general form of the regression equation takes the form. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 12 of 19) Table 8.12: Smartphone Sales Time Series with Dummy Variables and Time Period Period Year Quarter Qtr1 Qtr2 Qtr3 Sales (1,000s) 1 1 1 1 0 0 4.8 2 2 0 1 0 4.1 3 3 0 0 1 6.0 4 4 0 0 0 6.5 5 2 1 1 0 0 5.8 6 2 0 1 0 5.2 7 3 0 0 1 6.8 8 4 0 0 0 7.4 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 13 of 19) Table 8.12: Smartphone Sales Time Series with Dummy Variables and Time Period (cont.) Period Year Quarter Qtr1 Qtr2 Qtr3 Sales (1,000s) 9 3 1 1 0 0 6.0 10 2 0 1 0 5.6 11 3 0 0 1 7.5 12 4 0 0 0 7.8 13 4 1 1 0 0 6.3 14 2 0 1 0 5.9 15 3 0 0 1 8.0 16 4 0 0 0 8.4 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 14 of 19) Seasonality with Trend (cont.): The dummy variables in the equation for Smartphone Sales time series provide four equations given time period t corresponds to quarters 1, 2, 3, and 4. Quarter 1: Sales = 4.71 + 0.146t. Quarter 2: Sales = 4.04 + 0.146t. Quarter 3: Sales = 5.77 + 0.146t. Quarter 4: Sales = 6.07 + 0.146t. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 15 of 19) Using Regression Analysis as a Causal Forecasting Method: The relationship of the variable to be forecast with other variables may also be used to develop a forecasting model. Advertising expenditures when sales are to be forecast. The mortgage rate when new housing construction is to be forecast. Grade point average when starting salaries for recent college graduates are to be forecast. The price of a product when the demand for the product is to be forecast. The value of the Dow Jones Industrial Average when the value of an individual stock is to be forecast. Daily high temperature when electricity usage is to be forecast. Causal models: Models that include only variables that are believed to cause changes in the variable to be forecast. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 16 of 19) Student Population Quarterly Sales Restaurant (1,000s) ($1,000s) Table 8.13: Student Population 1 2 58 and Quarterly Sales Data for 10 2 6 105 Armand’s Pizza Parlors 3 8 88 4 8 118 5 12 117 6 16 137 7 20 157 8 20 169 9 22 149 10 26 202 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 17 of 19) Figure 8.16: Scatter Chart of Student Population and Quarterly Sales for Armand’s Pizza Parlors © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 18 of 19) © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Using Regression Analysis for Forecasting (Slide 19 of 19) Combining Causal Variables with Trend and Seasonality Effects: Regression models are very flexible and can incorporate both causal variables and time series effects. Considerations in Using Regression in Forecasting: Whether a regression approach provides a good forecast depends largely on how well we are able to identify and obtain data for independent variables that are closely related to the time series. Part of the regression analysis procedure should focus on the selection of the set of independent variables that provides the best forecasting model. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Determining the Best Forecasting Model to Use © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Determining the Best Forecasting Model to Use (Slide 1 of 2) A visual inspection can indicate whether seasonality appears to be a factor and whether a linear or nonlinear trend seems to exist. For causal modeling, scatter charts can indicate whether strong linear or nonlinear relationships exist between the independent and dependent variables. If certain relationships appear totally random, this may lead you to exclude these variables from the model. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Determining the Best Forecasting Model to Use (Slide 2 of 2) While working with large data sets, it is recommended to divide your data into training and validation sets. Based on the errors produced by the different models for the validation set, you can pick the model that minimizes some forecast error measure, such as MAE, MSE or MAPE. There are software packages that will automatically select the best model to use. Ultimately, the user should decide which model to use based on the software output and his managerial knowledge. © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  End of Chapter 8 © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.