May I ask a clarifying question? If my sample is between 2000-2015, back-casting means we want to backcast back to the periods before 2000, say 1990-1999. If we want to forecast 2000-2015, it actually implies nowcasting the periods between 2000-2015.

Another question is whether conditional_forecast command in Dynare indicates nowcasting?

Not sure I get the question. Backcasting involves inferring variables before the sample starts (in your case before 2000). Nowcasting usually involves inferring current values in the sample that are not (perfectly) observed (e.g. due to revisions, see for example https://www.frbatlanta.org/cqer/research/gdpnow.aspx). Forecasting would be out-of-sample, in your case after 2015.

conditional_forecast is not equal to nowcasting. Rather, it involves policy scenarios, i.e. asking what would happen if I fix particular variables at fixed values chosen by the researcher.

Thanks for clarifying my confusing. My question is can we do nowcasting in Dynare? I have an estimated model now and want to conduct nowcasting for my sample period, 2000-2015. But I am not sure what command can I use for nowcasting.

Thanks for the reply. Here are the updated variables I got after running the smoother command.
I am wondering how do we interpret these diagrams. I notice that some diagrams have green lines but some do not. What is the difference between them? For those without green lines, does it means the model performs well on nowcasting these variables? With green line implies there is a slight deviation on nowcasting the variables.