How generated quantities Moving Average Models?

Modeling
1 
data {
  int<lower=0> Q;  // num previous noise terms
  int<lower=3> T;  // num observations
  vector[T] y;     // observation at time t
}
parameters {
  real mu;              // mean
  real<lower=0> sigma;  // error scale
  vector[Q] theta;      // error coeff, lag -t
}
transformed parameters {
  vector[T] epsilon;    // error term at time t
  for (t in 1:T) {
    epsilon[t] = y[t] - mu;
    for (q in 1:min(t - 1, Q))
      epsilon[t] = epsilon[t] - theta[q] * epsilon[t - q];
  }
}
model {
  vector[T] eta;
  mu ~ cauchy(0, 2.5);
  theta ~ cauchy(0, 2.5);
  sigma ~ cauchy(0, 2.5);
  for (t in 1:T) {
    eta[t] = mu;
    for (q in 1:min(t - 1, Q))
      eta[t] = eta[t] + theta[q] * epsilon[t - q];
  }
  y ~ normal(eta, sigma);
}
2

Hi @dis, welcome to discourse! I don’t quite understand what your question is. What do you wish to compute in the generated quantities?

3

you can try generate the fitted values and residuals of a MA model in the bayesforecast package

library(bayesforecast)

Sf1 = stan_sarima(ts,c(0,0,q))
ft = posterior_predict(Sf1)

where ts is the time series and q the number of lags in the ma model

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