I have about 60 macroeconomic and financial indicators; all of them stationary (logs and differencing), with monthly data for the last 25 years. I am trying to predict changes in a financial variable (Y) for the month and the quarter ahead.
I have processed the data through PCA (Principal Components Analysis) and CFA (Common Factor Analysis). I am now using the corresponding components and factors to create 2 OLS models that would allow me to forecast the change in the independent variable as per below.
I have used lasso in Stata to estimate models that use the best variables (Principal components and Common Factors) that have good in-sample and out-sample performance. However, lasso is not able to handle lag variables.
I wanted to ask the following:
- Is there any problem from a statistical point of view if I include lag variables of Principal Components or Common Factors? My understanding is that one of the benefits of PCA and CFA is that the new variables are not correlated for PCA, and almost not correlated for CFA. Hence, introducing the new variables could it add multicollinearity problems if one of the components has serial correlation? Is there any other reason to not do this, as I couldn't find any academic paper using lags on principal component regressions. The new model would look like below.
It seems that it is not possible to use lag variables in Stata when implementing Lasso. Do I need to select the model with lags by trial and error or is there any other tool.
What are the tests that I need to run in the data/model to check that the results are not biased:
3.a. Stationary test, has been completed before running PCA/CFA
3.b. Multicollinearity not required because of PCA/CFA? What about if I add the lag variables?
3.c. Do I need to check for autocorrelation within the independent and each of the dependent variables?
3.d. any other test?