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rtime-seriesgammgcvautocorrelation

Adding an Moving Average component in GAMs model

I have a simple model, for which the residuals exhibit auto-correlation beyond one order.

I have a simple model for which I want to include a moving average component up to a third order.

My model is this: 

m1<-gamm(y~s(x,k=5), data = Training)

the time series properties of y, shows that this follows an ARMA(0,0,3)

because the residuals of m1 are auto-correlated I want to include a moving average component in m1

The answers for similar questions talk only about an AR(1) process, which is not my case.

Solution

  • You can use the corARMA(p, q) function in package nlme for this. corAR1(p) is just a special case function as there are certain efficiencies for that particular model.

    You have to pass q and/or p for the order of the ARMA(p, q) process with p specifying the order of the AR terms and q the order of the MA terms. You also need to pass in a variable that orders the observations. Assuming you have a single time series and you want the MA process to operate at the entire time series level (rather than say within a years but not between) then you should crate a time variable that indexes the order of the observations; here I assume this variable is called time.

    Then the call is: 

    m1 <- gamm(y ~ s(x, k = 5), data = Training,
           correlation = corARMA(q = 3, form = ~ time))

    When looking at the residuals, be sure to extract the normalised residuals as those will include the effect of the estimated MA process:

    resid(m1, type = "normalised")