Query regarding multiple one-step ahead forecasts

[adel-abou-jaber]

Hello Vaidotas,

I need some assistance with estimating a number of 1-step ahead forecasts using a direct MIDAS regression for h=1. The details are as follows:

• Data: I have observations on US GDP growth 1960Q1-2019Q4, and IP growth 1960.01-2019.12.
• MIDAS model I estimate is as such: midas<-midas_r(y~mls(x1,(3*h)+(0:12),3,nealmon),start=list(x1=rep(0,3))), where h=1.
• I want to forecast GDP growth for 2020Q1-2022Q4, using IP growth observations for 2020.01-2022.12
• I then want to retrieve the forecasts using the forecast() function, which is where I am confused:

1. I know that for a single one-step forecast (that of 2020Q1), you use the forecast() function as follows:
   fmidas<-forecast(midas,newdata=list(x1=rep(NA,3))), where I substitute 3 NA values for IP growth and get the one-step ahead forecast for 2020Q1, with 2019Q4 as the forecast origin.
2. For the forecasts from 2020Q2-2022Q4, what should I substitute in the "newdata" argument? Note that the forecast origin shifts: so for 2020Q2, the forecast origin is 2020Q1 and so on. The intuition here is to use the preceding 3 months of IP growth to forecast next quarter's GDP growth (so for 2020Q2 forecast, that would be using 2020.01-2020.03 IP growth observations).
3. In general, how do I use an h-step direct forecasting model I estimate over 1960.01-2019.12 to forecast in any forecasting sample of my choice? The question here is specifically about what to include in the "newdata" argument.

Please let me know if anything is unclear. Thank you for your prompt assistance.

Adel