I am running a VAR model to predict the flow of consumer loans (dependent variable). I have three independent variables (consumption of durables goods, employment rate and households GFCF). Each variable has 76 quarterly observations. My four series are stationary in difference. Results are confirmed by ADF and PP test. I tried to run several VAR with different specifications (add and change in the independent variables, tried different p order, add a dummy variable to capture an outline in 2020 because of the pandemic crisis). Nonetheless, my residuals are still highly autocorrelated. I can't understand why. I do maybe miss something. My residuals are also non-normally distributed (which seems to be not very important for forecasting as I have understood). I am using R.
If anyone has some suggestions and recommendations, I would be very grateful!
The existence of autocorrelation and a failure of normality tests is very often an indication of misspecification. Have you done any stability tests (recursive estimation)? Have you a missing variable? For example, real interest rates tend to be persistent and this persistence might show up as autocorrelation if the variable was relevant and excluded. You would know far more about this subject and select relevant variables that might be included.
I would also expect some of your variables to be seasonal. Are they seasonally adjusted? If so has the adjustment process changed the stochastic nature of the series? Have you tried to model the unadjusted series (if available) using a VAR and seasonal dummies?
A model with autocorrelation will not forecast well. Guy Mélard 's suggestion of a VARMA model, or even a univariate ARMAX model, models the autocorrelation and might help.
I should mention that all four variables in your current VAR are dependent variables.
I presume that you have read https://www.pfaffikus.de/rpacks/vars/files/vignette-vars.pdf
Most residual autocorrelation can be resolved by introducing the past value of the variable of interest as an explanatory variable. As I understand it, consumer loans have some kind of seasonality. It is necessary to look at the ACF or spectrum of the loan data to see whether peaks appear periodically, and if so, it is necessary to introduce a seasonal lags.
Have you tried estimating a vector error correction model (VECM) that adds the lagged levels of the variables to the difference VAR that you have estimated. The levels variables may be the omitted variables that are causing the evident autocorrelation. You could test for cointegration to see if you need a VECM and/or VEC to forecast from. Consideration of structural breaks, seasonality, other omitted variables, VARMA as well as univariate ARIMA models (as suggested by Guy and John above) are also good avenues to pursue.
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