Let's assume to have a panel including observations for 88 individuals over 18 years (1584 observations). The panel is now populated with a broad set of 50 possible regressors that I would like to now reduce by applying a variable selection algorithm. Among the regressors, I also included the spatial and temporal lags. One of the possible options would be represented by the application of the general-to-specific (GETS) modeling procedure.
As I understand from the literature (for instance Sucarrat and Escribano 2011), GETS starts from a large unrestricted model (GUM) and then removes the features by means of a step-wise regression. So basically, it removes a regressor and then performs a misspecification and a backtest (BaT) against the GUM. In this way, it verifies whether the removal added autocorrelation and/or heteroscedasticity or the performance increased respect to the GUM. It stops when no insignificant regressors are identified.
As reported Pretis et al 2018,"It should be underlined, however, that gets is not limited to time series models: Static models (e.g., cross-sectional or panel) can be estimated by specifying the regression without dynamics."
What does this "without dynamics" mean? Should I get the average values of the variables of each of the 88 individuals over the 18 years? How would this eventually deal with time trends and spatial correlation? is there any other procedure that is more suitable for this case?