I have some time series data that is auto-correlated, and I am trying to account for in my correlation analysis. I have found out how to calculate the effective DoF based on Bretherton et al. (1999), which is:

DoFeff = N * ((1-(r1*r2)) / ((1+(r1*r2)) , eq. 1

where r1 and r2 are the first order autocorrelation coefficients for the two variables. My main question is how exactly do I account for this in my analysis? In correlation, the DoF is pairs-2, so for a simple bivariate correlation with two variables, there is 0 DoF. Now if I do regression this is different again, and I get t values that are influenced by DoF that I can use to assess the significance of the correlation coefficients. I worked out the DoF_eff and used that to assess significance based on t-values that SPSS gave me in the linear regression output, but I guess that is probably pointless as the t-values in the regression output are based on the DoF in the model ( n-1 ).

But, how can I use the information from eq. 1 in a statistical package? I have access to Matlab, SPSS, Minitab and Origin. I am thinking that I may have to do something with ARIMA...but I honestly am not sure. Any help would be greatly appreciated!

The Bretherton et al. (1999) paper is: "The Effective Number of Spatial Degrees of Freedom of a Time-Varying Field" (section 5).