# Brooks-Gelman(1998) statistics in Dynare

Hi.
Brooks and Gelman have three different statistics including \hat R_{interval} and second and third moments for investigation of univariate and multivariate convergence in distribution.

Dynare shows these graphs by red and blue colors for interval and second and third moments.

\hat R_{interval}=\frac{Length \ \ of \ \ total \ \ sequence \ \ intervals}{mean \ \ length \ of \ \ the \ within \ sequence \ intervals }

My question is what is numerator and denominator colors in Dynare ?

The other question is that suppose we have 3 chains and number of iterations is 100000.
Therefore we must have confidence intervals for 100000 in denominator but 300000 in numerator!!! because we calculate intervals in numerator for m \times n sample.

Although we have two other moments including second and third moments graphs.

1. From Pfeifer (2014): An Introduction to Graphs in Dynare at sites.google.com/site/pfeiferecon/dynare:
“The blue line shows the 80% interval/quantile range based on the pooled draws from all sequences, while the red line shows the mean interval range based on the draws of the individual sequences.”
2. Interval here is not a confidence interval.

How Dynare calculates length of total sequence?? For example in intervals we have two different values such as 0.1 and 0.8
How dynare calculates length of this interval??

\hat R_{interval}=\frac{Length \ \ of \ \ total \ \ sequence \ \ intervals}{mean \ \ length \ of \ \ the \ within \ sequence \ intervals }

What do you mean? If you have different chains, you pool the values and then compute the cutoff values for the respective percentiles. Say the 10th percentile of \beta is 0.97 and the 90th percentile is 0.99. Then the length of the interval is 0.99-0.97=0.02

Thank you so much professor.