How to model a series with a shock in all independent variables

Question

My problem is a small sample of quarterly macro data with only about 55 observations. During the observed period there were several shocks, one of which happened four years ago and was rather huge, affecting all variables. Now I am trying to forecast GDP growth based on 20 other macro/financial variables, but the forecasts are simply anticipating the huge plunge.

Introducing a break does not solve the problem, as it would only make sense in the case where the independent variables were not so severely affected. I tried combination forecasts using quadratic optimization, MSFE and DMSFE, I even tried restricting the lag structure of ADL or introducing a cubic Hermite term, but each time there was a downward trend after the 4th or 5th step ahead. The data seems to beg for smoothing, only I cannot use a simple mean/median over the problematic period for all the variables as it would mean losing a lot of information.

Would a spline term be a good solution? I am not looking for an opinion, but for an advice based on experience with modelling shocks.

• Richard Hardy: 55 observations and 20 variables? If you do not do any regularization, you will have very high estimation variance and thus likely erratic forecasts.
• Roux: I do combination forecasts and introduce up to two independent variables at a time, keeping it quite parsimonious.
• Richard Hardy: Could you show some of the models you use? It could be easier to comment on a specific model than on the generic problem. Once you have a good solution to a specific problem, hopefully it would generalize nicely to your broader problem.
• Roux: I use ADL with up to 4 quarterly lags of the dependent variable and up to 2 lags of 1 independent variable. There are also some monthly data, so I use up to 6 monthly lags and/or 2 monthly leads of those. In other words, ADL(p,q,m,l), where: p indicates the lag structure of the autoregressive part, p=1 to 4; q is the number of lags of a quarterly independent variable, q=0 to 2; m is the number of lags of a monthly independent variable, m=0/3/6 and l is the number of leads of a monthly independent variable, l=0/2. Each model has up to 1 quarterly and up to 1 monthly independent variable.
• mlofton: I didn't read the paper so maybe it gets into the explanation of my question but I've never seen an ADL with different variables that had different frequencies ( the response is quarterly, I think, and some of the independents are monthly ? ) .. Maybe the data are such that somehow the frequency mixing doesn't matter but I would take a look at the MIDAS literature if you haven't already. MIDAS is the econometric framework developed by Ghysels that handles multiple frequencies but that's the extent of my knowledge on it.

Answer 1

I used the methodology developed in Banbura, Marta and Modugno, Michele, (2014), MAXIMUM LIKELIHOOD ESTIMATION OF FACTOR MODELS ON DATASETS WITH ARBITRARY PATTERN OF MISSING DATA, Journal of Applied Econometrics, 29, issue 1, p. 133-160.

The factor extracted from the data helped capture the co-movement of the series.