I am trying to run ARMA to extract signal chronology for hydrological analysis. Now, where I am stuck in time series analysis is in "USE OF BACKSHIFT OPERATOR". I have stationary data of tree ring. I want to extract signal from tree ring to use in the hydrological analysis. In general field of dendrochronology (tree ring), people use
Yt = [θ (B) / ϕ (B)] et for extracting chronology for climate signal.
[D1t+Et ] = [ϕ (B)/ θ (B)] It - et , for extracting chronology for endogenous disturbance signal.
I have little knowledge on the use of back-shift operator. I am a SAS user and I have used PROC ARIMA too. But, I don't know how to use back-shift operator (B). For the above formula, I want to calculate the Yt and [D1t+Et ] using back-shift operator. So, I was wondering if I could get your help to figure out how we can obtain these operators, θ (B) / ϕ (B) separately to use in the above formula. Can we request SAS for backshift operator for the fitted model and use those operators in the way we want? Is there any way to ask SAS to get output for above formula?
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