centred moving average

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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

15 Smoothing Raw Data

Smoothing the data is the process in which the seasonal cycle are removed (averaged out)

How this is done in Excel?What is the moving mean?

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.

How do we handle data with an even order of the moving mean?How to find a centred moving mean.

Abel Tasman smoothed data p7 Road Casualities

You-Tube Video overview of concept of smoothing data using Excel and making Indivivual seasonal effects

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Time series data often has some seasonal cycle.

To accurately predict the long term trend and determine the average seasonal variation we need to smooth the data.

To smooth the data we use a moving average.

The moving average lineshows the long term trend when the seasonal variation has been removed

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Notice that the moving average line does not continue to the limits of the data range.

It is important the graph of the moving average does NOT look like this...

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

The value of the moving average must be placed in the MIDDLE of the group

The formula to use in excel is... =average(click and drag over the first 7 data cells)

eg =AVERAGE(B2:B8)

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

To find the next moving average we move down the data set

The first data value is dropped and the next added to calculate the next moving average.



By copying the moving average formula down we can calculate all moving averages.

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.

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

Because the moving average should be in the middle of an even group, it can either be placed above or below its correct position.

Copy down the moving average - remember not to go to the bottom of the data set.

By averaging each pair of moving averages we centre the moving average.

Notice that the centred moving average CMM lines up with the first data value after the midpoint of the quarterly data

And when we graph the data the centred moving average points line up with data value



Here is an example with monthly data - order 12

In this example the moving average has been placed just above the midpoint of the 12 data values

However the centred moving mean still lines upwith the first data value below the midpoint of the 12 data values



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