added alternative parameterization of ARMA(1,1) model

Author: Bob Carpenter

misc/moving-avg/arma11_alt.stan

@@ -0,0 +1,25 @@
+# ARMA(1,1) with Wayne Folta-style err encoding
+
+data {
+  int<lower=1> T;       // number of observations
+  real y[T];            // observed outputs
+}
+parameters {
+  real mu;              // mean term
+  real phi;             // autoregression coeff
+  real theta;           // moving avg coeff
+  real<lower=0> sigma;  // noise scale
+}
+model {
+  real err;
+  mu ~ normal(0,10);
+  phi ~ normal(0,2);
+  theta ~ normal(0,2);
+  sigma ~ cauchy(0,5);
+  err <- y[1] - mu + phi * mu;
+  err ~ normal(0,sigma);
+  for (t in 2:T) {
+    err <- y[t] - (mu + phi * y[t-1] + theta * err); 
+    err ~ normal(0,sigma);
+  }
+}