Q: Can I simply ignore the following warning (because it is about the posterior predictions, r_pred
, from the generated quantities block rather than about the estimated parameters)?
The following parameters had fewer than 0.001 effective samples per transition:
r_pred[1,1], r_pred[4,1], r_pred[5,1], r_pred[6,1], r_pred[8,1], r_pred[9,1], r_pred[10,1], r_pred[11,1], r_pred[12,1], r_pred[13,1], r_pred[14,1], r_pred[15,1], r_pred[16,1], r_pred[17,1], r_pred[18,1],
...
r_pred[67,48], r_pred[68,48], r_pred[69,48], r_pred[70,48], r_pred[72,48], r_pred[73,48], r_pred[74,48], r_pred[75,48], r_pred[76,48], r_pred[77,48], r_pred[78,48], r_pred[79,48]
Such low values indicate that the effective sample size estimators may be biased high and actual performance may be substantially lower than quoted.
The generated quantities block is like:
generated quantities {
vector[N2] r_pred[J];
...
for (j in 1:J) {
alpha[j,1] = mu_alpha;
for (n in 2:N2) {
alpha[j,n] = alpha[j,n1]  theta*Real2[j,n1];
}
u2[j,1:N] = u[j,1:N];
for (n in (N+1):N2) {
u2[j,n] = alpha[j,n] + beta*u2[j,n1] + sd_y*normal_rng(0,1);
}
r_pred[j] = u2[j] + Real2[j] + D2[j];
} //end of for (j in 1:J) {
} //end of generated quantities
where

J
is the number of entities (in my hierarchical latent AR1 model); 
N
is the training sample size (number of calendar quarters); 
N2
is the full sample size (incl. holdout); 
Real2
andD2
are deterministic transformations of both observed covariate data and estimated parameters; 
mu_alpha
,beta
,theta
, andsd_y
are estimated parameters; 
alpha
is a transformed parameter; 
r_pred
is the posterior prediction ofr
, which is the observed outcome; 
u
is the latent variable estimated from the training sample and 
u2
is its counterpart for the full sample.