Transform forecasted data back to original

My requirement is to forecast gdp using a simple DSGE. The final expected outcome is to predict the real GDP growth for next 5 years from the Q4 2020 GDP (I have a dataset with real GDP figures upto Q4 2020) . For eg;

Q1 2021 5.5%
Q2 2021 4.3%
and so on.

I can use the estimation to estimate the relevant parameters. The dataset is deseasoned, logged, and detrended (using one-side HP filter). The forecasted data is in a specific form (deseasoned and detrended). My question is how to transform these output data back to the real gdp data so that I can calculated quarter to quarter GDP growth rates.

In your setup that is not possible. You are interested in forecasting the level of GDP. But you decomposed the level into a trend and a cycle and only forecasted the cyclical component. For that reason, you cannot back out the level as you don’t have a forecast of the trend component.

Thanks prof. Pfeifer. What sort of data transformations plus modifications for observational equations in the mod file are required in order to achieve this? Your advice is much appreciated.

Your problem is not explicitly modeling the trend. You could do that by assuming a unit root with drift in your model and estimate the model in growth rates. Ferroni’s work may also be an option:

Thanks professor. I will refer both Ch.5 “A Guide to Specifying Observation Equations for the
Estimation of DSGE Models” and Ferroni’s.

Hi Prof. Pfeifer,

As per your instructions, I’ve modified the mod. file to capture a trend in the observed data. sl_gdp_est_4.mod (1.9 KB) data_sl.csv (605 Bytes) . y_obs is the log difference of annual gdp per capita. The mod.file is a slightly modified version of the example (Listing 9) provided in Ch.5 “A Guide to Specifying Observation Equations for the Estimation of DSGE Models .

My questions are;

  1. I have only 10 data points in the dataset for the estimation. Does this in anyway undermine the accuracy of the estimation results?
  2. Does the forecast option in estimation take the fluctuations in observed data (i.e. my dataset) as shocks and perform the forecast?
  3. Kindly highlight any shortcomings and points to improve if you spot any.
  1. See Sufficient number of observation for an estimation and Sufficient sample size to estimate DSGE model
  2. Yes, the forecast option will take the data into account via the Kalman smoother.
  3. As far as I can see, things look ok.

Many thanks professor.