Moving Average Method

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  • Hi there, Really struggling with working out the centered moving average trend. Ive been at this 5 full days trying to get the same answer as in an example i have found but know luck. I've been asked to work the moving average and then the centered moving average out, then the centered moving average trend, then Cyclic Factor which i understand to be the ratio between the CMA and the CMAtrend. Then working out the Seasonal Factor and the seasonal Index.I've been able to work out how to do the SF but also unsure on the index, if you are able to help at all i would be extremely greatful!
    Many Thanks
    Natalie
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Moving Average Method

  1. 1. Moving Average Method Time Series Secular Trend 3.Moving Average Method 4. Method Of Least Squares
  2. 2. Moving Averages <ul><li>Used for Smoothing </li></ul><ul><li>Series of Arithmetic Means Over Time </li></ul><ul><li>Result Dependent Upon Choice of L (Length of Period for Computing Means) </li></ul><ul><li>To Smooth Out Cyclical Component, L Should Be Multiple of the Estimated Average Length of the Cycle </li></ul><ul><li>For Annual Time Series, L Should Be Odd </li></ul>
  3. 3. Moving Averages <ul><li>Example: 3-Year Moving Average </li></ul><ul><ul><li>First average: </li></ul></ul><ul><ul><li>Second average: </li></ul></ul>(continued)
  4. 4. Moving Average Example Year Units Moving Ave 1994 2 NA 1995 5 3 1996 2 3 1997 2 3.67 1998 7 5 1999 6 NA John is a building contractor with a record of a total of 24 single family homes constructed over a 6-year period. Provide John with a 3-year moving average graph.
  5. 5. Moving Average Example Solution Year Response Moving Ave 1994 2 NA 1995 5 3 1996 2 3 1997 2 3.67 1998 7 5 1999 6 NA 94 95 96 97 98 99 8 6 4 2 0 Sales L = 3 No MA for the first and last ( L -1)/2 years
  6. 6. Exponential Smoothing <ul><li>Weighted Moving Average </li></ul><ul><ul><li>Weights decline exponentially </li></ul></ul><ul><ul><li>Most recent observation weighted most </li></ul></ul><ul><li>Used for Smoothing and Short-Term Forecasting </li></ul>
  7. 7. Exponential Weight: Example Year Response Smoothing Value Forecast (W = .2, (1-W)=.8) 1994 2 2 NA 1995 5 (.2)(5) + (.8)(2) = 2.6 2 1996 2 (.2)(2) + (.8)(2.6) = 2.48 2.6 1997 2 (.2)(2) + (.8)(2.48) = 2.384 2.48 1998 7 (.2)(7) + (.8)(2.384) = 3.307 2.384 1999 6 (.2)(6) + (.8)(3.307) = 3.846 3.307
  8. 8. Question No 1 <ul><li>Calculate the five yearly moving averages of a no of students studying in a commerce college as shown in by the following figures </li></ul>
  9. 9. Home work 1 <ul><li>Work out the trend values by centered 4 yearly moving average method for the following data and plot the given values and trend values on a graph </li></ul>
  10. 10. Question no 3 <ul><li>For the following Series of observation verify that 4 year centered moving averages is equivalent to a 5 year weighted moving average with weights 1,2,2,2,1 </li></ul><ul><li>ting </li></ul>

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