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What would the formula for a 95% prediction interval for an ARMA(2,2) model be?

The specific model I am using is: an ARIMA(2,0,2) with non-zero mean, with the following parameter estimates:

Coefficients: 

      ar1      ar2      ma1      ma2       mean
      1.3421  -0.6738  -0.2027  -0.2564  1544.4039    
s.e.  0.0984   0.0801   0.1261   0.1097   131.9242

sigma^2 estimated as 761965:  log likelihood=-932.08
AIC=1876.17   AICc=1876.95   BIC=1892.58
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    $\begingroup$ Are you looking for a confidence-interval or for a prediction-interval? There is a difference. $\endgroup$
    – Stephan Kolassa
    Commented Nov 13, 2019 at 19:44
  • $\begingroup$ I am looking for a prediction interval. I just realized I wrote confidence in the original question. My mistake, sorry! $\endgroup$
    – Sean
    Commented Nov 13, 2019 at 20:01

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you have to generate the psi weights which can be obtained by expressing the model as a pure long-lagged ma model https://rdrr.io/cran/tswge/man/psi.weights.wge.html . You also need the estimate of the variance. If you have identified anomalies in the data set you need to employ monte-carlo procedures and re-sample the error process.

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