Clarification with Mixed Frequency estimation

Estimation ML/Bayesian estimation
1

To Dr Pfeifer,

I am currently running a Bayesian estimation, where the model is in quarterly frequency, but some observed variables are only able in an annual frequency.

Following Pfeifer (2013), observation equations, section 7.3,
if my variable of annual frequency is obs_A,
I created a variable obs_A_annual ( which looks something like A + A(-1) + A(-2) + A(-3) ).

I question that I had from your example, in Listing 15, was that when declaring ‘varobs’, you use ‘y_tilde’ instead of ‘y_tilde_quarterly’.
It feels like the data, with NaNs for months without observations, should correspond to ‘y_tilde_quarterly’ instead of ‘y_tilde’.

Is my interpretation correct?

Further, if ‘y_tilde_quarterly’ is reported in January, April, July, and October,
would it be correct to construct the data so that the reported values are positioned in January, April, July, and October, and the remaining is left as NaN?

Thank you for your time in advance.

2
  1. Yes, you are correct. I uploaded a correct version of the document.
  2. What do you mean with “reported in January”? If you define quarterly GDP as the sum of monthly GDPs, then the quarterly value is observed in the last month of the quarter. The statistical agency only reporting it in January does not matter for the agents in the model who observe that object (the value is contained in their information set for that last month). It’s only us econometricians that do not observe that data in real time.