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BUAD306 Chapter 3 – Forecasting
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Everyday Forecasting Weather Time Traffic Other examples???
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Forecasting What is forecasting? How is it used in business?
Approaches to forecasting Forecasting techniques
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What is Forecasting? Forecast: A statement about the future
Used to help managers: Plan the system Plan the use of the system
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Use of Forecasts Accounting Cost/profit estimates Finance
Cash flow and funding Human Resources Hiring/recruiting/training Marketing Pricing, promotion, strategy MIS IT/IS systems, services Operations Schedules, MRP, workloads Product/service design New products and services
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Forecasting Basics Assumes causal system past ==> future
Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases
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Elements of a Good Forecast
Timely – feasible horizon Reliable – works consistently Accurate – degree should be stated Expressed in meaningful units Written – for consistency of usage Easy to Use - KISS
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Approaches to Forecasting
Judgmental – subjective inputs Time Series – historical data Associative – explanatory variables
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Judgmental Forecasts Executive Opinions Accuracy??
Sales Force Feedback Bias??? Consumer Surveys Outside Opinions Industry experts
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What would you rather evaluate?
Period A B C 1 30 18 46 2 34 17 26 3 32 19 27 4 23 5 35 22 6 48 7 29 8 36 25 20 9 24 14 10 31 11 47 12 28 13 37 15 33 16
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Time Series Forecasts Based on observations over a period of time
Identifies: Trend – LT movement in data Seasonality – ST variations Cycles – wavelike variations Irregular Variations – unusual events Random Variations – chance/residual Examples on the board
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Forecast Variations Trend Cycles Irregular variation 90 89 88
Seasonal Variations 90 89 88 Cycles
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Examples on the board & HW#1…
Naïve Forecasting Simple to use Minimal to no cost Data analysis is almost nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy Examples on the board & HW#1…
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HW Problem 1 Day Muffins Buns Cupcakes 1 30 18 46 2 34 17 26 3 32 19
27 4 23 5 35 22 6 48 7 29 8 36 25 20 9 24 14 10 31 11 47 12 28 13 37 15 33 16
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HW Problem 1 Muffins Buns Cupcakes
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Techniques for Averaging
Moving average Weighted moving average Exponential smoothing
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Simple Moving Average MAn = n Ai Where:
i = index that corresponds to periods n = number of periods (data points) Ai = Actual value in time period I MA = Moving Average Ft = Forecast for period t
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Example 1: Moving Average
Four period moving average for period 7: Four period moving average for period 8: Four period moving average for period 9 if actual for 8 = 5025: Period Sales 1 3520 2 2860 3 4005 4 3740 5 4310 6 5001 7 4890 8 ??
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Weighted Moving Average
Similar to a moving average, but assigns more weight to the most recent observations. Total of weights must equal 1.
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Example 2: Weighted Moving Average
Period Sales 1 3520 2 2860 3 4005 4 3740 5 4310 6 5001 7 4890 8 ?? Compute a weighted moving average forecast for period 8 using the following weights: .40, .30, .20 and .10:
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HW #2 – Let’s Discuss Month Sales Feb 19 Mar 18 Apr 15 May 20 June
July 22 Aug
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Calculating Error et = At - Ft Mathematically:
Let’s discuss examples on board…
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Exponential Smoothing
Premise--The most recent observations might have the highest predictive value…. Therefore, we should give more weight to the more recent time periods when forecasting.
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Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1) Next forecast = Previous forecast + (Actual -Previous Forecast) Smoothing Constant
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About = Smoothing constant selected by forecaster
It is a percentage of the forecast error The closer the value is to zero, the slower the forecast will be to adjust to forecast errors (greater smoothing) The higher the value is to 1.00, the greater the responsiveness to errors and the less smoothing READ TEXT
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Example 3: Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1) Assume a starting forecast of 4030 for period 3. Given data at left and = .10, what would the forecast be for period 8? Period Sales 1 3520 2 2860 3 4005 4 3740 5 4310 6 5001 7 4890 8 ??
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Example 3: Exponential Smoothing
Period Act Forecast Calc Fore 3 4005 4030 4 3740 5 4310 6 5001 7 4890 8
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HW #2 – Let’s Discuss Month Sales Feb 19 Mar 18 Apr 15 May 20 June
July 22 Aug
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Techniques for Seasonality
Seasonal Variations – regularly repeating movements in series values that can be tied to recurring events Computing Seasonal Relatives: READ THE TEXT Look at HW #12 – don’t have to know this for exam
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Using Seasonal Relatives
Allows you to incorporate seasonality or deseasonalize data Incorporate: Useful when trend and seasonality are apparent Deseasonalize – Remove seasonal components to get a clearer picture of non-seasonal components
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Example 4: Using Seasonal Relatives
A publisher wants to predict quarterly demand for a certain book for periods 9 and 16, which happen to be in the 3rd and 2nd quarters of a particular year. The data series consists of both trend and seasonality. The trend portion of demand is projected using the equation: yt=12, t. Quarter relatives are Q1= 1.3, Q2=.8, Q3=1.4, Q4=.9 Use this information to predict demand for periods 9 and 16. The trend values: Applying the relatives:
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HW #11 – Let’s Discuss Ft = 40 – 6.5t + 2t2
The following equation summarizes the trend portion of quarterly sales of condos over a long cycle. Prepare a forecast for each Q of 2014 and 1Q15. Ft = 40 – 6.5t + 2t2 Ft = unit sales t= 0 at 1Q 2012 Quarter Relative 1 1.1 2 3 .6 4 1.3
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Assoc. Forecasting Technique: Simple Linear Regression
Predictor variables - used to predict values of variable interest Regression - technique for fitting a line to a set of points Least squares line - minimizes sum of squared deviations around the line
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Linear Regression Assumptions
Variations around line are random No patterns are apparent Deviations around the line should be normally distributed Predictions are being made only in the range of observed values Should use minimum of 20 observations for best results
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Suppose you analyze the following data...
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y c = a + bx b = n (xy) - (x)(y) a = y - bx n n(x2) - (x)2
The regression line has the following equation: y c = a + bx Where: y c = Predicted (dependent) variable x = Predictor (independent) variable b = slope of the line a = Value of y c when x=0 b = n (xy) - (x)(y) n(x2) - (x)2 a = y - bx n
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Example 5 - Linear Regression:
Suppose that a manufacturing company made batches of a certain product. The accountant for the company wished to determine the cost of a batch of product given the following data: Size of batch 20 30 40 50 70 80 100 120 150 Cost of batch (in 1000s) $1.4 3.4 4.1 3.8 6.7 6.6 7.8 10.4 11.7 Question… which is the dependent (y) and which is the independent (x) variable?
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We are now ready to determine the values of b and a:
b = n (xy) - (x)(y) = 9 (5264) - (660)(55.9) n(x2) - (x) (63600) - (660)2 = = = a = y - bx = (660) = n 9
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y c = a + bx y c = y c = Our linear regression equation:
What is the cost of a batch of 125 pieces? y c =
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Problem #7 Freight car loadings at a busy port are as follows: Week #
1 220 10 380 2 245 11 420 3 280 12 450 4 275 13 460 5 300 14 475 6 310 15 500 7 350 16 510 8 360 17 525 9 400 18 541 Freight car loadings at a busy port are as follows:
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Problem #7 b = n (xy) - (x)(y) n(x2) - (x)2 a = y - bx n
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Correlation (r) A measure of the relationship between two variables
Strength Direction (positive or negative) Ranges from to +1.00 Correlation close to 0 signifies a weak relationship – other variables may be at play Correlation close to +1 or -1 signifies a strong relationship
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Calculating a Correlation Coefficient
r = n( xy) - ( x)( y) n( x2)- ( x)2 * n( y2) - ( y)2
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r = 9 (5264) - (660)(55.9) 9(63600)- (660)2 * 9(439.11) - (55.9)2
Example 6: Continued r = n( xy) - ( x)( y) n( x2)- ( x)2 * n( y2) - ( y)2 r = (5264) - (660)(55.9) 9(63600)- (660)2 * 9(439.11) - (55.9)2 r = = = * * 28.76
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Coefficient of Determination (r2)
How well a regression line “fits” the data Ranges from 0.00 to 1.00 The closer to 1.0, the better the fit
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Example 6: Continued r = .985 r2 = = .97
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Conclusion of Example R = .985 R2 = .9852 = .97 Positive, close to one
Closer to one, the better the fit to the line
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Forecast Accuracy Error - difference between actual value and predicted value Mean absolute deviation (MAD) Average absolute error Mean squared error (MSE) Average of squared error Why can’t we simply calculate error for each observed period and then select the technique with the lowest error?
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Does the # of errors calculated impact the "accuracy" comparison???
Error Example Period Actual 3PMA 5PMA 3P WMA .6, .3, .1 EX SM .2 LR 1 55 55.69 2 60 60.66 3 75 56 65.63 4 58 68.5 59.8 70.6 5 80 63.3 59.44 75.57 6 90 71 65.6 72.9 63.552 80.54 7 70 76 72.6 83.8 85.51 8 92 74.6 77 90.48 9 100 84 78 85.2 95.45 10 86.4 94.6 100.42 #errors? Does the # of errors calculated impact the "accuracy" comparison???
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Calculating Error et = At - Ft Mathematically:
What do the negative errors mean? How do they affect total error? et = At - Ft
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Calculating MAD and MSE
= Actual forecast n MSE = Actual forecast) - 1 2 n (
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Conclusions with MAD & MSE
The MAD and MSE can be used as a comparison tool for several forecasting techniques. The forecasting technique that yields the lowest MAD and MSE is the preferred forecasting method.
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Which technique would you select for your forecast approach?
MAD & MSE Comparison Tech MAD MSE 3 Period MA 3.6 8.1 Exp Sm .02 2.2 5.6 Exp Sm .04 2.6 6.1 Which technique would you select for your forecast approach?
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