How to obtain trace plots after a Metropolis-Hastings

It can be useful to plot iterations vs. sampled values for each variable (parameter) in a chain. If the Metropolis-Hastings converges to a stable distribution, the trace plot has to be stable (e.g. no trend in the sampled values).

After a metropolis (that is after the estimation command in the mod file) you just have to write:



After the estimation of the model in fs2000.mod if we want to build a trace plot for parameter alp, we write:


and the following plot will pop up:


where the black curve is a moving average of the sampled values. That is, if the sampled values are $\{\alpha_i\}_{i=1}^N$ where $N$ is the number of simulations in the Metropolis Hastings chain, the moving average curve is defined as:

a_{j}=\frac{1}{2q+1}\sum_{k=-q}^{q} \alpha_{j+k}

for all $j$ between $q+1$ and $N-q$. The default value of $q$ is 200. The value of $q$ may be changed by writing:

options_.trace_plot_ma = 2222;

before the call to trace_plot. A value of $q$ roughly equal to $10 \%$ of $N$ seems to be reasonable. In our example, we see that the moving average curve is slightly downward slopping, meaning that the Metropolis Hastings did not reach the ergodic distribution after 22000 draws.

DynareWiki: TracePlots (last edited 2009-03-25 17:12:09 by localhost)