Applied Business Forecasting and Regression Analysis

Applied Business Forecasting and Regression Analysis

Applied Business Forecasting and Planning Introduction To Business Forecasting Chapter Overview Introduce Business Forecasting. Review Subjective Forecasting Methods. Introduce two simple Nave Forecasting Models. Develop Criteria for Evaluating Forecast Accuracy Introduction What is forecasting? Forecasting is an attempt to foresee the future by examining the past. Forecasts require judgment

Most estimates obtained in quality forecasting are derived in an objective and systematic fashion and do not depend solely on subjective guesses and hunches of the analyst. Forecasting and Decision Making Example: Decision to Whether to build a new factory Requires forecasts on Future demand, technological innovations, cost, prices, competitors plan, labor, legislation, etc. Most forecasting required for decision making is handled judgmentally in an intuitive fashion, often without separating the task of forecasting from that of decision making. Forecasting and Decision making

Systematic, explicit approaches to forecasting can be used to supplement the common sense and management ability of decision makers. All types and forms of forecasting techniques are extrapolation, that is, predicting within the existing data. Quantitative forecasting techniques should be used in with analysis, judgment, common sense, and business experience in order to produce an effective forecasting outcome. Advantages and Disadvantages of Subjective Methods Subjective (qualitative or judgmental) forecasting methods are sometimes considered desirable because they do not require any particular mathematical background of the individuals involved. Subjectivity is the most important advantage of this class of methods. There are often forces at work that cannot be captured by quantitative methods.

Advantages and Disadvantages of Subjective Methods The disadvantages of subjective methods are: 1. 2. 3. They are almost always biased They are not consistently accurate overtime. It takes yeas of experience for someone to learn how to convert intuitive judgment into good forecast. Who needs forecasts? Every organizations, large and small, private and public. Needs for forecasts cuts across all functional lines. It applies to problems such as:

How much this company worth? (Finance) Will a new product be successful? (Marketing) What level of inventories should be kept? (Production) How can we identify the best job candidates? (Personnel) Nave Method 1 It is based solely on the most recent information available. Suitable when there is small data set. Some times it is called the no change forecast. The nave forecast for each period is the immediately proceeding observation. Nave Method 1 The simplest nave forecasting model, in which the forecast value is equal to the previous observed value, can be described in algebraic form as follows:

y t yt 1 Since it discards all other observations, it tracks changes rapidly. Example:Sales of saws for Acme Tool Company,1994-2000 The following table shows the sales of saws for the Acme tool Company. These data are shown graphically ass well. In both forms of presentation you can see that the sales varied considerably throughout this period, from a low of 150 in 1996Q3 to a high of 850 in 2000Q1. The Fluctuations in most economic and business series (variables) are best seen after converting the data graphic form. Example:Sales of saws for Acme Tool Company,1994-2000 Year

Quarter 1994 1995 1996 1997 1998 1999 2000 t 1 2 3 4 1 2 3 4 1 2 3 4 1 2

3 4 1 2 3 4 1 2 3 4 1 2 3 sales 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23 24 25 26 27 500 350 250 400 450 350 200 300 350 200 150 400 550 350 250 550 550

400 350 600 750 500 400 650 850 600 450 Example:Sales of saws for Acme Tool Company,1994-2000 Sales of saws for the Acme Tool Company: 1994-2000 900 800 700 600 Saws 500 400 300

200 100 0 0 5 10 15 Year 20 25 30 Example:Sales of saws for Acme Tool Company,1994-2000 The forecast for the first quarter of 2000 , using the nave method is: t yt 1 y 25 y 24 y

25 650 y Example:Sales of saws for Acme Tool Company,1994-2000 Year 1994 1995 1996 1997 1998 1999 2000 Quarter 1 2 3 4 1 2 3 4 1

2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 t 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 sales 500 350 250 400 450 350 200 300 350

200 150 400 550 350 250 550 550 400 350 600 750 500 400 650 850 600 450 700 Forecast 500 350 250 400 450 350 200 300 350

200 150 400 550 350 250 550 550 400 350 600 750 500 400 650 850 600 450 Example:Sales of saws for Acme Tool Company,1994-2000 Quarterly Sales of Saws for Acm toll Company 1994-2000 900 800 700 Sales

600 500 sales Forecast 400 300 200 100 0 0 5 10 15 Quarters 20 25 30

Nave Method 2 One might argue that in addition to considering just the recent observation, it would make sense to consider the direction from which we arrived at the latest observation. That is: if the series dropped to the latest point, perhaps it is reasonable to assume further drop and if we have observed an increase, it may make sense to factor into our forecast some further increase. Nave Method 2 In general algebraic terms the model becomes y t yt 1 P( yt 1 yt 2 ) Where P is the proportion of the change between period t-2 and t-1 that we choose to include in the forecast. We call this Nave method(2).

Example:Sales of saws for Acme Tool Company,1994-2000 The forecast for the first quarter of 2000 using the Nave method(2) with P = 50% is: y 25 y25 1 0.5( y25 1 y25 2 ) y 25 y24 0.5( y24 y23 ) y 25 650 0.5(650 400) 775 Example:Sales of saws for Acme Tool Company,1994-2000 Year 1994 1995 1996 1997 1998 1999 2000 Quarter 1

2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 t 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 sales 500

350 250 400 450 350 200 300 350 200 150 400 550 350 250 550 550 400 350 600 750 500 400 650 850 600 450 700 Forecast (N2)

275 200 475 475 300 125 350 375 125 125 525 625 250 200 700 550 325 325 725 825 375 350 775 950 475 375 Example:Sales of saws for Acme Tool Company,1994-2000 Quarterlt sales of Saws for Acme Toll Company 1994-2000

1000 900 800 700 Sales 600 sales 500 Forecast (N2) 400 300 200 100 0 0 5 10 15 Quarters 20

25 30 Evaluating Forecasts We have looked at two alternative forecasts of the sales for the Acme Tool Company. Which forecast is best depends on the particular year or years you look at. It is not always possible to find one model that is always best for any given set of business or economic data. But we need some way to evaluate the accuracy of forecasting models over a number of periods so that we can identify the model that generally works the best. Evaluating Forecasts Among a number of possible criteria that could be used, five common ones are: 1. 2. 3.

4. 5. 6. Mean absolute error (MAE) Mean percentage error (MPE) Mean absolute percentage error (MAPE) Mean squared Error (MSE) Root Mean squared Error (RMSE) Theils U-statistic Evaluating Forecasts To illustrate how each of these is calculated, let yt = Actual value in period t yt = Forecast value in period t n = number of periods used in the calculation Mean Absolute Error

The mean absolute error (MAE) Measures forecast accuracy by averaging the magnitudes of the forecast errors. 1 n MAE yt y t n t 1 Mean Percentage Error The Mean Percentage Error (MPE) Can be used to determine if a forecasting method is biased (consistently forecasting low or high) Large positive MPE implies that the method consistently under estimates. Large negative MPE implies that the method consistently over estimates. Mean Percentage Error The forecasting method is unbiased if MPE

is close to zero. 1 n ( yt y t ) MPE n t 1 yt Mean absolute Percentage Error The Mean Absolute Percentage Error (MAPE) Provides an indication of how large the forecast errors are in comparison to actual values of the series. Especially useful when the yt values are large. Mean absolute Percentage Error Can be used to compare the accuracy of the same or different methods on two different time series data. 1 n yt y t MAPE n t 1

yt Mean Squared Error This approach penalizes large forecasting errors. 1 n MSE ( yt y t ) 2 n t 1 Root Mean Squared Error The RMSE is easy for most people to interpret because of its similarity to the basic statistical concept of a standard deviation, and it is one of the most commonly used measures of forecast accuracy. n RMSE (y t y t ) 2 t 1

n Theils U-statistic This statistic allows a relative comparison of formal forecasting methods with nave approaches and also squares the errors involved so that large errors are given much more weight than smaller errors. Mathematically, Theils U-statistic is defined as y y n 1 U ( t 1 t 1 )2 yt yt 1 yt 2 (

) yt t 1 t 1 n 1 Theils U-statistic U = 1 The nave method is as good as the forecasting technique being evaluated. U < 1 The forecasting technique being used is better than the nave method. U > 1 There is no point in using a formal forecasting method since using a nave method will produce better results Example:VCR data Data was collected on the number of VCRs sold last year for Vernons Music store. Month January

February March April May June July August September October November December t 1 2 3 4 5 6 7 8 9 10 11 12 Sales 123 130 125

138 145 142 141 146 147 157 150 160 Forecast(N1) At - Ft 123 130 125 138 145 142 141 146 147 157 150 7 -5 13 7

-3 -1 5 1 10 -7 10 Example:VCR data Monthly VCR Sales 180 160 140 VC R Sales 120 100 Sales Forecast(N1) 80 60 40 20

0 0 2 4 6 8 Months 10 12 14 Example:VCR data Month January February March April May June July August September

October November December t 1 2 3 4 5 6 7 8 9 10 11 12 Sales 123 130 125 138 145 142 141 146 147 157 150

160 Forecast (N2) At - Ft 133.5 122.5 144.5 148.5 140.5 140.5 148.5 147.5 162 146.5 -8.5 15.5 0.5 -6.5 0.5 5.5 -1.5 9.5 -12 13.5 Example:VCR data Monthly VCR Sales 180

160 140 VC R Sales 120 100 Sales Forecast (N2) 80 60 40 20 0 0 2 4 6 8 Months

10 12 14 Example:VCR data Error analysis: RMSE 7.24 8.97 Forecast (N1) Forecast (N2) Monthly VCR Sales 180 160 140 120 V C R S a le s 100

Sales Forecast(N1) Forecast (N2) 80 60 40 20 0 0 2 4 6 8 Months 10 12 14

Evaluating Forecasts We will focus on root-mean-squared error (RMSE) to evaluate the relative accuracy of various forecasting methods. All quantitative forecasting models are developed on the basis of historical data. When RMSE are applied to the historical data, they are often considered measures of how well various models fit the data (how well they work in the sample). Evaluating Forecasts To determine how accurate the models are in actual forecast (out of sample) a hold out period is often used for evaluation. It is possible that the best model in sample may not be the best in out of sample.

Using Multiple Forecasts When forecasting Sales or some other business economic variables, it is best to consider more than one model. In our example of VCR sales, using the two nave model, we could take the lowest forecast value as the most pessimistic, the highest as the most optimistic, and the average value as the most likely. This is the simplest way to combine forecasts. Sources of Data The quantity and type of data needed in developing forecasts can vary a great deal from one situation to another. Some forecasting techniques require only data series that is to be forecasted

Nave method, exponential smoothing, decomposition method. Some , like multiple regression methods require a data series for each variable included in the forecasting model. Sources of Data Sources of data Internal records of the organization. Outside of the organization Trade associations Governmental and syndicated services There is a wealth of data available on the internet.

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