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- 1. IBS Statistics Year 1 Dr. Ning DING
- 2. Table of content <ul><li>Review </li></ul><ul><li>Learning Goals </li></ul><ul><li>Chapter 16: Time Series and Forecasting </li></ul><ul><li>Exercises </li></ul>
- 3. Chapter 3: Describing Data Review Chapter 3 Why Dispersion? Central Tendency?
- 4. Chapter 3: Describing Data Review Chapter 3 Dispersion Range Variation Standard Deviation
- 5. Chapter 3: Describing Data Review Chapter 3 Dispersion
- 6. Chapter 4: Describing Data P42 Example Ch2 The distribution is skewed to __________ because the mean is __________the median. the right larger than Mean =23.06 Review Chapter 4 Interquartile Range
- 7. Review Chapter 4 Chapter 4: Describing Data 2 3 4 5 6 7 8 9 2 3 4 5 6 7 10 13 2 3 4 4.25 4.75 7 8 9 2 3 3.25 3.50 3.75 4 5 9 Mean= 5.5 6.25 5.25 4.19 Median= 5.5 5.5 4.5 3.38
- 8. Review Chapter 4 Chapter 4: Describing Data Mean= 5.5 6.25 5.25 4.19 Median= 5.5 5.5 4.5 3.38 Most skewed? http://qudata.com/online/statcalc/
- 9. Chapter 12: Sim Reg & Corr Sample Exam P.4 Ŷ = a + b X a = -1.8181 Review Chapter 12
- 10. Chapter 12: Sim Reg & Corr Review Chapter 12 Negative Correlation Positive Correlation
- 11. Exercise Chapter 12: Sim Reg & Corr Sample Exam P.4 Ŷ = -1.8182 + 0.1329X a = -1.8181
- 12. Applicable when time series follows fairly linear trend that have definite rhythmic pattern Chapter 16: Time Series & Forecasting Review Chapter 16
- 13. 1+2+3+4+5+4+3= 22 / 7 = 3.143 Seven-Year Moving Total Moving Average 2+3+4+5+4+3+2= 23 / 7 = 3.286 3+4+5+4+3+2+3= 24 / 7 = 3.429
- 14. Learning Goals <ul><li>Chapter 16: </li></ul><ul><ul><li>Define the components of a time series </li></ul></ul><ul><ul><li>Compute a moving average </li></ul></ul><ul><ul><li>Determine a linear trend equation </li></ul></ul><ul><ul><li>Compute a trend equation for a nonlinear trend </li></ul></ul><ul><ul><li>Use a trend equation to forecast future time periods and to develop seasonally adjusted forecasts </li></ul></ul><ul><ul><li>Determine and interpret a set of seasonal indexes </li></ul></ul><ul><ul><li>Desearsonalize data using a seasonal index </li></ul></ul><ul><ul><li>Test for autocorrelation </li></ul></ul>
- 15. Exercise Chapter 16: Time Series & Forecasting Ŷ = a + b t = 1.73 a = 22.67 -1.73*4 = 15.75 P152 N6 Ch16 a = Y - b X
- 16. 3. Linear Trend Chapter 16: Time Series & Forecasting Ŷ = a + b t = 1.73 Ŷ = 22.67 + 1.73 t a = 22.67 = 22.67 a = Y - b X
- 17. 3. Linear Trend Chapter 16: Time Series & Forecasting Ŷ = a + b t Odd-numbered Even-numbered a = Y - b X
- 18. 4. Seasonal Variation Understanding seasonal fluctuations help plan for sufficient goods and materials on hand to meet varying seasonal demand Chapter 16: Time Series & Forecasting
- 19. 4. Seasonal Variation Chapter 16: Time Series & Forecasting Seasonal variations are fluctuations that coincide with certain seasons and are repeated year after year
- 20. 4. Seasonal Variation Chapter 16: Time Series & Forecasting Seasonal Index: A number, usually expressed in percent, that expresses the relative value of a season with respect to the average for the year (100%) Sales for December are 26.8% above an average month. Sales for July are 14% below an average month.
- 21. 4. Seasonal Variation Chapter 16: Time Series & Forecasting 2005 2006 2007 2008 2009 2010 Sales Report: in $ millions
- 22. 4. Seasonal Variation Chapter 16: Time Series & Forecasting Step 1: Re-organize the data 2005 2006 2007 2008 2009 2010
- 23. 6.7+4.6+10.0+12.7=34 /4=8.50 4.6+10.0+12.7+6.5=33.8 /4=8.45 Step 2: Moving Average
- 24. Step 3: Centered Moving Average
- 25. Step 4: Specific Seasonal Index
- 26. 10/8.475=1.180 12.7/8.45=1.503 6.5/8.425=0.772 Step 4: Specific Seasonal Index
- 27. + + + = Step 5: Typical Quarterly Index 2005 2006 2007 2008 2009 2010 *(0.9978) *(0.9978) *(0.9978) *(0.9978)
- 28. Step 6: Interpret Sales for the Fall are 51.9% above the typical quarter. Sales for the Winter are 23.5% below the typical quarter. 2005 2006 2007 2008 2009 2010
- 29. Appliance Center sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in $ millions) were reported. Determine a typical seasonal index for each of the four quarters. Exercise Chapter 16: Time Series & Forecasting P161 No.10 Ch16
- 30. Exercise Chapter 16: Time Series & Forecasting P161 No.10 Ch16 Step 1: Reorganize the data Step 2: Moving Average Step 3: Centered Moving Average Step 4: Specific Seasonal Index
- 31. Exercise Chapter 16: Time Series & Forecasting P161 No.10 Ch16 Step 5: Reorganize the data Step 6: Calculate the mean for each quarter Step 7: Sum up the four means Step 8: Divide 4 by Total of four means to get Correction Factor Step 9: Mean * Correction Factor
- 32. 5. Deseasonalizing Data Chapter 16: Time Series & Forecasting To remove the seasonal fluctuations so that the trend and cycle can be studied. Ŷ = a + b X Ŷ = a + b t
- 33. 5. Deseasonalizing Data Chapter 16: Time Series & Forecasting 76.5 57.5 114.1 151.9 / 0.765 = 8.759 / 0.575 = 8.004 / 1.141 = 8.761 / 1.519 = 8.361 / 1.519 / 0.765 / 0.575 / 1.141 / 0.765 / 0.575 / 1.141 / 1.519 = 8.498 = 8.004 = 8.586 = 8.953 = 9.021 = 8.700 = 9.112 = 9.283
- 34. Ŷ = a + b t Ŷ = 8.1096 + 0.0899 t Sale increased at a rate of 0.0899 ($ millions) per quarter. Ŷ = 8.1096 + 0.0899 * 25 = 10.3571 $ millions 10.3571*0.765 = 7.9232 $ millions Chapter 16: Time Series & Forecasting 76.5 57.5 114.1 151.9
- 35. Exercise Chapter 16: Time Series & Forecasting 1. Calculate the seasonal indices for each quarter, express them as a ratio and not as a %. You may round to 4 dec. places. 2. Interpret the seasonal index quarter II. 3. Deseasonalized the original revenue for 2008 quarter I. 4. For 2011 quarter II the forecasted revenue from the trend line was 55. Calculate the seasonalized revenue for 2011 quarter II. Friday Oct 22, 2010 Pigeon hole Ning Ding
- 36. Summary <ul><li>Chapter 16: </li></ul><ul><ul><li>A seasonal factor can be estimated using the ratio-to-moving-average method. </li></ul></ul><ul><ul><li>The six-step procedure yields a seasonal index for each period. </li></ul></ul><ul><ul><li>The seasonal factor is used to adjust forecasts, taking into account the effects of the season. </li></ul></ul>Chapter 16: Time Series & Forecasting
- 37. Step 1: Reorganize the data Step 2: Moving Average Step 3: Centered Moving Average Step 4: Specific Seasonal Index Step 5: Reorganize the data Step 6: Calculate the mean for each quarter Step 7: Sum up the four means Step 8: Divide 4 by Total of four means to get Correction Factor Step 9: Mean * Correction Factor Hint

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