The time series thing looks good.
If that sig2v is a variance add a sqrt:
v[i] ~ normal(0, sqrt(sig2v));
If you parameterize it in terms of standard deviation (sigv or something), then you can easily switch between centered and non-centered parameterization using:
vector[N] v; // centered
And
vector<multiplier = sigv>[N] v; // non-centered
(Updated non-centered parametrization with offset and multiplier - #3 by daniel_h)