Degrees of freedom for a moving average?

Joz

New Member
#1
Can someone please help me to determine the correct number of degrees of freedom used when calculating a moving average?
For example, with annual time series data values from 1900-2000 I would like to correlate both annual and 5-yr moving average values to another independent data set.
The degrees of freedom for a correlation analysis using the original series is n-2=99, but I’m not sure about the degrees of freedom when using the averaged series.
I realize it cannot just be n-4, because the observations are used multiple times in calculating the moving average. (n-8 values are used 5 times in calculating the moving average).
I’ve included a short example below to illustrate how the moving averages were calculated.

Any help will be greatly appreciated-


Obs 5-yr MA
1 -
2 -
3 ave(1,2,3,4,5)
4 ave(2,3,4,5,6)
5 ave(3,4,5,6,7)
6 ave(4,5,6,7,8)
7 ave(5,6,7,8,9)
8 ave(6,7,8,9,10)
9 -
10 -