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Centred Moving Average

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<ul><li><p>Nayland College Mathematics - 'More than just a school'</p><p>Excel: Smoothing data 3.8 Time Series HOME | Achievement Objectives | Overview | The Statistics CycleReport Writing: Summary | Introduction | Trend | Decompose | Recompose | Seasonal Effect | Predictions | Robustness | Comparing | Combining | Conclusion | Practice Assessment | Using iNZight: Getting Started | Importing Data | Using EXCEL: Smoothing | Trend | Seasonal Effects | Graphing | Predictions | Seasonal Adjustment | Non-Linear models | Comparing Excel & iNZight</p><p>15 Smoothing Raw Data</p><p>Smoothing the data is the process in which the seasonal cycle are removed (averaged out)</p><p>How this is done in Excel?What is the moving mean? </p><p>What is the order of the moving mean?What should the order of the moving mean be?The order of the time series data is the number of data values that cover one seasonal cycle. eg 2 monthly data has an order of 6 if the seasonal cycle is one year. </p><p>How do we handle data with an even order of the moving mean?How to find a centred moving mean. </p><p>Abel Tasman smoothed data p7 Road Casualities</p><p>You-Tube Video overview of concept of smoothing data using Excel and making Indivivual seasonal effects</p><p>X Network Access Message: Access Denied</p><p>Explanation:</p><p>Access to this site was blocked by system administrator. </p><p>Should this site be incorrectly blocked - Please Contact Granville Moolman 021 400 9059 - Please also consult following link http://cityweb.capetown.gov.za/en/isandt/Policies/Pages/SelfHelp.aspx</p><p>The page you are trying to browse to is categorized as "Online Communities" </p><p>If you believe you are getting this message by mistake, try contacting your administrator or Helpdesk. </p><p>Technical Information (for support personnel) Error Code: 403 Forbidden. Forefront TMG denied the specified </p><p>Uniform Resource Locator (URL). (12233) IP Address: 172.25.88.41 Date: 2014/12/05 01:12:17 PM [GMT] Server: CBD-CIVIC-PRX01.capetown.gov.za Source: proxy </p><p>Time series data often has some seasonal cycle.</p><p>To accurately predict the long term trend and determine the average seasonal variation we need to smooth the data.</p><p>To smooth the data we use a moving average.</p><p>The moving average lineshows the long term trend when the seasonal variation has been removed </p><p>Nayland Maths Home</p><p>Junior Maths Level 1 Level 2 L3 Statistics L3 Calculus L3 Maths</p><p>Page 1 of 5Smoothing seasonal effects</p><p>12/5/2014http://maths.nayland.school.nz/Year_13_Maths/3.8_Timeseries/3_smoothing.htm</p></li><li><p>Notice that the moving average line does not continue to the limits of the data range.</p><p>It is important the graph of the moving average does NOT look like this...</p><p>Calculate the Moving Mean (centre if needed)If the moving mean has an ODD order then just take the moving average of a group of data which covers one 'season' - ensuring that the moving average value is placed in the CENTRE of the data group.Example</p><p>The value of the moving average must be placed in the MIDDLE of the group </p><p>The formula to use in excel is... =average(click and drag over the first 7 data cells)</p><p>eg =AVERAGE(B2:B8)</p><p>Here the order of the data is 7 so we average the first 7 data values to smooth the 'seasonal' effect. This gives a value of 8464 which is placed in the cell lined up with the middle data value 8859</p><p>To find the next moving average we move down the data set</p><p>The first data value is dropped and the next added to calculate the next moving average.</p><p>Page 2 of 5Smoothing seasonal effects</p><p>12/5/2014http://maths.nayland.school.nz/Year_13_Maths/3.8_Timeseries/3_smoothing.htm</p></li><li><p>By copying the moving average formula down we can calculate all moving averages.</p><p>Remember NOT to copy to the moving average to the bottom of the data column. You must stop when the moving average reaches the last data value.</p><p>If the moving mean has an EVEN order then make an interim moving average then CENTRE the moving average to position it back in line with a data value - ensuring that the moving average value is placed JUST BELOW the CENTRE of the data group. Example</p><p>Because the moving average should be in the middle of an even group, it can either be placed above or below its correct position.</p><p>Copy down the moving average - remember not to go to the bottom of the data set.</p><p>By averaging each pair of moving averages we centre the moving average.</p><p>Notice that the centred moving average CMM lines up with the first data value after the midpoint of the quarterly data</p><p>And when we graph the data the centred moving average points line up with data value</p><p>Page 3 of 5Smoothing seasonal effects</p><p>12/5/2014http://maths.nayland.school.nz/Year_13_Maths/3.8_Timeseries/3_smoothing.htm</p></li><li><p>Here is an example with monthly data - order 12</p><p>In this example the moving average has been placed just above the midpoint of the 12 data values</p><p>However the centred moving mean still lines upwith the first data value below the midpoint of the 12 data values</p><p>Page 4 of 5Smoothing seasonal effects</p><p>12/5/2014http://maths.nayland.school.nz/Year_13_Maths/3.8_Timeseries/3_smoothing.htm</p></li><li><p>back to top</p><p>Page 5 of 5Smoothing seasonal effects</p><p>12/5/2014http://maths.nayland.school.nz/Year_13_Maths/3.8_Timeseries/3_smoothing.htm</p></li></ul>