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Week5- Omis Lecture Notes.pdf

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Department
Marketing
Course
MKTG 2030
Professor
Ben Kelly
Semester
Winter

Description
Quantitative Analysis for Management Decisions Lecture 5 Forecasting What  is  Forecasting?   - Forecasting is the art and science of predicting future events - Underlying basis of all business decision - production, inventory, personnel, facilities "It is far better to foresee even without certainty than not to foresee at all. " --Henri Poincare in The Foundations of Science , page 129. Department  Uses  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 Time  Series  Data   • Numerical data obtained at regular time intervals • The time intervals can be annually, quarterly, daily, hourly, etc. • Example: Year: 1999 2000 2001 2002 2003 Sales: 75.3 74.2 78.5 79.7 80.2 A time series plot is a two-dimensional plot of time series data • The vertical axis measures the variable of interest • The horizontal axis corresponds to the time periods Page 1 of 37 Quantitative Analysis for Management Decisions Lecture 5 Introduction  to  Time  Series  Analysis   • A time-series is a set of observations on a quantitative variable collected over time. • Examples − Dow Jones Industrial Averages − Historical data on sales, inventory, customer counts, interest rates, cos ts, etc • Businesses are often very interested in forecasting time series variables. • Often, independent variables are not available to build a regression model of a time series variable. • In time series analysis, we analyze the past behavior of a variable in order to predict its future behavior.  Forecast based only on past values, no other variables are important Assumes that factors influencing past and present will continue influence in future Time  Series  Components   • Trend can be upward or downward • Trend can be linear or non-linear Page 2 of 37 Quantitative Analysis for Management Decisions Lecture 5 Page 3 of 37 Quantitative Analysis for Management Decisions Lecture 5 Some  Time  Series  Terms   • Stationary Data - a time series variable exhibiting no significant upward or downward trend over time. • Nonstationary Data - a time series variable exhibiting a significant upward or downward t rend over time. • Seasonal Data - a time series variable exhibiting a repeating patterns at regular intervals over time. Example  -­‐  Consumers'  Expenditure   Page 4 of 37 Quantitative Analysis for Management Decisions Lecture 5 Approaching  Time  Series  Analysis   • There are many, many different time series techniques. • It is usually impossible to know which technique will be best for a particular data set. • It is customary to try out several different techniques and select the one that seems to work best. • To be an effective time series modeler, you need to keep several time series tec hniques in your “tool box.”   Time  Series  Models   A. Stationary Models 1. Moving Average 2. Weighted Moving Average 3. Exponential Smoothing 4. Seasonality a. Additive b. Multiplicative B. Trend Models 1. Double Moving Average 2. Double Exponential Smoothing (Holt’s) 3. Seasonality (Holt-Winter’s) a. Additive b. Multiplicative C. Regression Models (Trend and/or Seasonality) How do you know if it’s a good forecast? How will you use these results to evaluate the quality of forecast? Measuring  Accuracy   Page 5 of 37 Quantitative Analysis for Management Decisions Lecture 5 Common  Measures  of  Error  (Evaluating  the  Forecast)   Computing  MAD,  MSE   1) Use the desired forecasting method to forecast BACK IN TIME for time period for which you have actual data. 2) Compare the model’s forecast to the actual historical values -> calculate the MAD and MSE based on the differences between forecast and actual values. 3) Repeat for each method you would like to evaluate. 4) Compare resulting MAD’s and MSE’s. Page 6 of 37 Quantitative Analysis for Management Decisions Lecture 5 Have student come up to compute MAD from the data. Tell them about ABS function in Excel for computing absolute values. Suggest use of a full period of seasonality (e.g. 4 quarters) to eliminate seasonal effects and focus on any trends that may be present. Note the results on the graph (plot also historical predictions for MA). Large errors have more impact in the MSE calculation Ask students what they’d do to compute MSE. Tell them about SUMXMY2 function to compute numerator for MSE. Show the computation. Page 7 of 37 Quantitative Analysis for Management Decisions Lecture 5 A  Comment  on  Comparing  MSE  Values   • Care should be taken when comparing MSE values of two different forecasting techniques. • The lowest MSE may result from a technique that fits older values very well but fits recent values poorly. • It is sometimes wise to compute the MSE using only the most recent values. The  Simplest  Forecast:  A  Naive  Approach   • Assumes demand in next period is the same as demand in most recent period • e.g., If January sales were 68, then February sales will be 68 • Sometimes cost effective and efficient • Can be good starting point Extrapolation  Models   • Extrapolation models try to account for the past behavior of a time seri es variable in an effort to predict the future behavior of the variable.  We’ll first talk about several extrapolation techniques that are appropriate for stationary data. Smoothing  Techniques… If we can determine which components actually exist in a ti me series, we can develop better forecasts. We can reduce random variation by smoothing the time series. Two methods to smooth the data are:  Moving averages and  Exponential smoothing. Time  Series  Models   A. Stationary Models 1. Moving Average 2. Weighted Moving Average 3. Exponential Smoothing 4. Seasonality a. Additive b. Multiplicative B. Trend Models 1. Regression Models Moving  Average  Method   • A forecasting technique that uses an average of the most recent periods of the data to forecast the next period • Looks back at history for a fixed period of time Page 8 of 37 Quantitative Analysis for Management Decisions Lecture 5 Moving  Averages  (Textbook  Notation)    No general method exists for determining k.  We must try out several k values to see what works best. • Example: Four-quarter moving average – First average: – Second average: – etc… • The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are asfollows: Forecast the mileage for the next year usin g 2-year moving average. Page 9 of 37 Quantitative Analysis for Management Decisions Lecture 5 Moving  Average  Example   In Excel: Tools > Data Analysis… > Moving Average Page 10 of 37 Quantitative Analysis for Management Decisions Lecture 5 Graph  of  Moving  Average   Moving  Average   • What is the effect of choosing a larger value for n? What happens when n matches the period of the data? Try n=2, n=4 and n=6 for “Clothing and Footwear”. Page 11 of 37 Quantitative Analysis for Management Decisions Lecture 5 • How does the forecast compare to actual values? • What happens to the forecast as you forecast further into the future? Evaluating  the  Forecast   • How do you know if it’s a good forecast? • MAD • MSE Page 12 of 37 Quantitative Analysis for Management Decisions Lecture 5   Time  Series  Models   A. Stationary Models 1. Moving Average 2. Weighted Moving Average 3. Exponential Smoothing 4. Seasonality a. Additive b. Multiplicative B. Trend Models 1. Regression Models Weighted  Moving  Average   • Used when trend is present • Older data usually less important • Weights based on experience and intuition Weighted  Moving  Average  (Textbook  Notation)   • The moving average technique assigns equal weight to all previous observations Page 13 of 37 Quantitative Analysis for Management Decisions Lecture 5  The weighted moving average technique allows for different weights to be assigned to previous observa tions.  We must determine values for k and the w i Weighted  Moving  Average    Carbondale  Hospital  Example  Revisited   Page 14 of 37 Quantitative Analysis for Management Decisions Lecture 5   Graph  of  Weighted  Moving  Average   MA  and  Seasonality?   Is it possible to assign weights to capture effects due to seasonality? How might you do this? Potential  Problems  With  Moving  Average   • Increasing the size of n (the number of periods averaged) does smooth out the forecast but makes it less sensitive to real changes in the data Page 15 of 37 Quantitative Analysis for Management Decisions Lecture 5 • Does not forecast trends well -> used for short term forec asting   Time  Series  Models
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