Introduction to Business Analytics BADM3400 Forecasting Techniques Chapter 9 PDF

Introduction to Business Analytics BADM3400 Lecture Forecasting Techniques Chapter 9 Jason Chan, PhD 1 Forecasting Techniques Managers require good forecasts of future events. Three major ca...

Introduction to Business Analytics BADM3400 Lecture Forecasting Techniques Chapter 9 Jason Chan, PhD 1 Forecasting Techniques Managers require good forecasts of future events. Three major categories of forecasting approaches: 1. Qualitative and judgmental techniques 2. Statistical time-series models 3. Explanatory/causal models 2 Qualitative and Judgmental Forecasting Qualitative and Judgmental techniques rely on experience and intuition. The historical analogy approach obtains a forecast through comparative analysis with prior situations. The Delphi method questions an anonymous panel of experts 2-3 times in order to reach a convergence of opinion on the forecasted variable. 3 Practice Question Before launching a new line of toys, GH Toys Inc. used the method of historical analogy to obtain a forecast. In this scenario, GH Toys Inc.: A. noted the behavior of its current customers while they use their products. B. used a panel of experts, whose identities were kept confidential from one another, to respond to a sequence of questionnaires. C. noted the consumer response to similar previous products to marketing campaigns and used the responses as a basis to predict how the new marketing campaign might fare. D. used a brainstorming session among a group of experts to draw new ideas. E. A and C are correct 4 Practice Question The Delphi method used for forecasting: A. obtains forecasts through a comparative analysis with a previous situation. B. uses measures that are believed to influence the behavior of a variable that the researcher wishes to forecast. C. uses a single measure that weights multiple indicators and provides a measure of overall expectation. D. uses a panel of experts, whose identities are not typically kept confidential from one another, to respond to a sequence of questionnaires. E. None of the above 5 Example 1: Predicting the Price of Oil Early 1988 - oil price was about $22 a barrel Mid-1988 - oil price dropped to $11 a barrel because of oversupply, high production in non-OPEC regions, and lower than normal demand In the past, OPEC would raise the price of oil. Historical analogy would forecast a higher price. However, the price continued to drop even though OPPEC agreed to cut production. Historical analogies cannot always account for current realities! 6  Example 2: Economic Indicators GDP (Gross Domestic Product) measures the value of all goods and services produced. – GDP rises and falls in a cyclic fashion. Forecasting GDP is often done using leading indicators (series that change before the GDP changes) and lagging indicators (series that follow changes in the GDP) indicators. Examples – Leading : formation of business enterprises , percent change in money supply – Lagging : business investment expenditures , prime rate , inventories on hand 7 Example 3: Leading Economic Indicators An index is a single measure that weights multiple indicators and provides a measure of overall expectation. An Index of Leading Indicators was developed by the Department of Commerce. This index is related to the economic performance is available from www.conference-board.org. It includes measures such as: – average weekly manufacturing hours – new orders for consumer goods – building permits for private housing – S&P500 stock prices 8 Statistical Forecasting Models Time Series - a stream of historical data, such as weekly sales T = number of periods, t = 1, 2,…,T Time series generally have components such as: – random behavior – trends (upward or downward) – seasonal effects – cyclical effects Stationary time series have only random behavior. A trend is a gradual upward or downward movement of a time series. 9 Example 4: Identifying Trends in a Time Series Total Energy Production & Consumption – General upward trend with some short downward trends; the time series is composed of several different short trends. 10 Seasonal Effects A seasonal effect is one that repeats at fixed intervals of time, typically a year, month, week, or day. 11 Cyclical effects Cyclical effects describe ups and downs over a much longer time frame, such as several years. 12  Practice Question Time-series models may exhibit seasonal effects or cyclical effects. A seasonal effect differs from a cyclical effect in that a seasonal effect: A. has no trend, is relatively constant, and only exhibits random behavior. B. describes ups and downs over a time frame such as several years. C. is one that repeats at fixed intervals of time, typically a year, month, week, or day. D. is based on analysis of historical time-series data and are predicated on the assumption that the future is an extrapolation of the past. E. is based on analysis of historical time-series data and are predicated on the assumption that the future is an intrapolation of the past. 13 Forecasting Models for Stationary Time Series Moving average model Exponential smoothing model –These are useful over short time periods when trend, seasonal, or cyclical effects are not significant. 14 Moving Average Models The simple moving average method is a smoothing method based on the idea of averaging random fluctuations in the time series to identify the underlying direction in which the time series is changing. The simple moving average forecast for the next period is computed as the average of the most recent k observations. At + At −1 + + At − k +1 Ft +1 = (9.1) k Larger values of k result in smoother forecast models since extreme values have less impact. 15 Example5: Moving Average Forecasting The Tablet Computer Sales file contains the number of units sold over the past 17 weeks. 16 Example5: Moving Average Forecasting Three-period moving average forecast for week 18: ( A17 + A16 + A15 ) 82 + 71 + 50 F18 = = = 67.67 3 3 17 Spreadsheet : Moving Average Forecasting 18 Using Excel’s Moving Average Tool Data Analysis Option 19 Example 6: Moving Average Tool We do not recommend using the chart or error options because the forecasts generated by this tool are not properly aligned with the data. Generate your own chart. 20 Practice Question The data for the number of AI machines sold for the past 7 weeks are 16 units, 17 units, 18 units, 20 units, 18 units,22 units and 24 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 3 the three- period moving average forecast for a. week 8 b. week 6 c. week 9 21 Error Metrics and Forecast Accuracy 22 Practice Question The data for the number of AI machines sold for the past 6 weeks are 6 units, 8 units, 8 units, 10 units,14 units and 16 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 2 the two- period moving average forecast. Compute a. MAD b. MSE c. RMSE d. MAPE 23 Example7: Using Error Metrics to Compare Moving Average Forecasts Tablet Computer Sales data 2-, 3-, and 4-period moving average models 2-period model has smallest error metric values. 24 Example7: Using Error Metrics to Compare Moving Average Forecasts 25 Practice Question (T/F) 1) Time series models extrapolate historical data from the variable of interest. 2) An exponential forecasting method is a time series forecasting method. 3) The naïve forecast for the next period is the actual value observed in the current period. 4) Mean absolute deviation (MAD) is simply the sum of forecast errors. 26 Practice Question 5) A diagram for a time series may be plotted on a two- dimensional graph with the horizontal axis representing the variable to be forecast (such as sales). 6) When the smoothing constant α = 0, the exponential smoothing model is equivalent to the naïve forecasting model. 7) When the smoothing constant α = 1, the exponential smoothing model is equivalent to the naïve forecasting model. 8) Bias is the average error of a forecast model. 27 Exponential Smoothing Models 28 Example 8: Using Exponential Smoothing to Forecast Tablet Computer Sales 29 Example 8: Using Exponential Smoothing to Forecast Tablet Computer Sales Forecast for week 3 when  = 0.7 : (1 − 0.7 )( 88 ) + ( 0.7 )( 44 ) = 57.2 30 Example 9: Finding the Best Exponential Smoothing Model for Tablet Computer Sales 31 Example 9: Finding the Best Exponential Smoothing Model for Tablet Computer Sales The forecast using α =0.6 provides the lowest error metrics 32 Example 10: Using Excel’s Exponential Smoothing Tool Select Data Analysis from the Analysis group and then choose Exponential Smoothing. Note that Damping factor = 1−α The first cell of the Output Range should be adjacent to the first data point. 33 Example 10: Using Excel’s Exponential Smoothing Tool 34 Example 10: Using Excel’s Exponential Smoothing Tool Exponential Smoothing tool results 35 Forecasting Models for Time Series with a Linear Trend 36 Double Exponential Smoothing 37 Example 11: Double Exponential Smoothing First ten years of data in the Excel file Coal Production Choose α = 0.6 and β = 0.4 38 Regression-Based Forecasting for Time Series with a Linear Trend Simple linear regression can be applied to forecasting using time as the independent variable. 39 Example 12: Forecasting Using Trend-lines Coal Production data with a linear trend-line Note that the linear model does not adequately predict the recent drop in production after 2008. 40 Example 12: Forecasting Using Trend lines 41 Autocorrelation in Time Series When autocorrelation is present, successive observations are correlated with one another; for example, large observations tend to follow other large observations, and small observations also tend to follow one another. – In such cases, other approaches, called autoregressive models, are more appropriate. 42 Autocorrelation in Time Series 43 Forecasting Time Series with Seasonality When time series exhibit seasonality, different techniques provide better forecasts than the ones we have described: – Multiple regression models with categorical variables for the seasonal components – Holt-Winters models, similar to exponential smoothing models in that smoothing constants are used to smooth out variations in the level and seasonal patterns over time. 44 Example 13: Regression-Based Forecasting for Natural Gas Usage Gas & Electric Excel file Use a seasonal categorical variable with k = 12 levels. Construct the regression model using k − 1 dummy variables, with January being the reference month. gas usage = 0 + 1 time +  2 February + 3 March +  4 April + 5 May +  6 June +  7 July + 8 August + 9 September + 10 October + 11 November + 12 December 45 Example 13: Regression-Based Forecasting for Natural Gas Usage 46 Example 13: Regression-Based Forecasting for Natural Gas Usage Data matrix 47 Example13: Regression-Based Forecasting for Natural Gas Usage Final regression results (time and February were insignificant) gas usage = 236.75 − 36.75 March − 99.25 April − 192.25 May − 203.25 June − 208.25 July − 209.75 August − 208.25 September − 196.75 October − 149.75 November − 43.25 December 48 Example 16: Regression-Based Forecasting for Natural Gas Usage 49 Example 16: Forecasting Gasoline Sales Using Simple Linear Regression Excel file Gasoline Sales Simple trend line using week as the independent variable 50 Example 16: Forecasting Gasoline Sales Using Simple Linear Regression Predicted sales for week 11 = 812.99(11) + 4790.1 = 13, 733 gallons 51 Example17: Incorporating Causal Variables in a Regression-Based Forecasting Model The average price per gallon changes each week, and this may influence consumer sales. Average price per gallon is a causal variable. Develop a multiple linear regression model to predict gasoline sales using both time and price per gallon. 52 Example17: Incorporating Causal Variables in a Regression- Based Forecasting Model 53 Example17: Incorporating Causal Variables in a Regression- Based Forecasting Model 54 Example17: Incorporating Causal Variables in a Regression-Based Forecasting Model 55 Practice Question In the linear trend equation, Ft+k = at + btk, i. at is known as the ________. i. identify the term that signifies the trend 56 The Practice of Forecasting Judgmental and qualitative methods are used for forecasting sales of product lines and broad company and industry forecasts. Simple time-series models are used for short- and medium-range forecasts. Regression methods are typically used for long- term forecasts. 57 Practice Question In forecasting, what is an index? A. It is a stream of current data, such as weekly sales. B. It is a stream of historical data, such as weekly sales. C. It is a time series that does not have trend, seasonal, or cyclical effects but is relatively constant and only exhibits random behavior. D. It is a measure that provides a complete forecast. E. It is a single measure that weights multiple indicators and provides a measure of overall expectation. F. A and B are correct 58