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

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.

• 55 observations and 20 variables? If you do not do any regularization, you will have very high estimation variance and thus likely erratic forecasts. Jun 2, 2017 at 8:25
• I do combination forecasts and introduce up to two independent variables at a time, keeping it quite parsimonious.
– Roux
Jun 2, 2017 at 8:47
• 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. Jun 2, 2017 at 8:54
• 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.
– Roux
Jun 2, 2017 at 9:20