currently I am working on creating an index that describes the development of main monetary variables in R. Yet, I don't really know how to efficiently create the index such that the weights are based on the historical correlations of the included variables after conducting a dynamic factor model.
The setting: My time series has 18 variables and 408 time periods. I estimated a dynamic factor model (DFM command) for which I used 4 factors and 1 lag following the recommended information criteria. The data is stationary and standardized. My code looks like this:
DFM1 = DFM(time_series, r=4, p=1, em.method = "BM")
After the estimation, I now have access to the following statistical properties:
- eigenvalues (18x1) and eigenvector (18x18)
- factor estimates (408 x 4)
- covariance matrices of factor estimates (4x4x408)
- factor transition matrix (4x4)
- observation matrix (18x4)
- State (error) covariance matrix (4x4)
- observation (error) covariance matrix (4x4)
The question: How can I now create an index that is weighted according to the impact of the different factors over time? My goal is to track the development of the monetary policy index over time and use it as a proxy.
I would be most thankful for your help!! I am currently a newbie at coding and econometrics and would be thankful if anyone has an idea or experience in this.