I have a quick question regarding a smoothed variable after performing the estimation. The model is entered in a nonlinear fashion and then estimated on quadratically detrended data. The variable in question is the default probability of borrowers which is defined as:
default probability = 1 - (probability of non-default)
where the probability of non-default is characterised by a distribution and therefore the variable is bounded between 0 and 1. The default probability is not part of the data set which is used for the estimation. When looking at the smoothed path of the default probability there are values which are greater than 1 and smaller than 0 (e.g. 2 or -1). I’ve found the same result for the probability of non-default itself.
Does the graph in this case show the deviation from the level or is this a mistake in the model? Because by construction the values can’t be greater than 0 or 1. The way I made sense of this at the moment is that based on the estimation and smoothed shocks we obtain the smoothed series in deviation from its level rather than it’s steady state. Is my intuition correct?
Many thanks for your help.