What is Degree of Freedom in ARIMA?
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Answers ( 3 )
suppose you have an ARIMA(3,0,0) model and the time series you are operating on
has around 100 data points then, you have 97 degrees of freedom.
Degrees of freedom is basically the amount of values in a system that are free to vary.
suppose , you have 10 numbers whose mean is 25. Now, if you are asked to guess these
10 numbers then can have a random guess at 9 of these numbers but you will have to choose the
10th number in such a way that the mean comes out to be 25. So, you don’t have control over that
one value but the rest of the 9 values are free to vary.
In continuation with swaplaw007 answer, DOF is the number of values in a system that are free to vary.
With respect to the time series model
For a Gaussian (white) time series with N independent numbers, the DOF is equal to N-2, the loss of 2 degrees of freedom is to account for the specification of the mean and standard deviation. However, the DOF for nonwhite time series is smaller than N-2 given to the fact that the sampled values are not completely independent of each other.
Let’s say you have an ARIMA(2,0,0), and the length n=100, then you have 98 degrees of freedom. Then the first two values of the variable you are modelling are “used”, and you will have 98 fitted values, and 98 degrees of freedom.