In this post I wanted to expand on one of the findings from post no. 2. Here I’ve looked at best fit models from the persepective of different points in time, at ten year intervals, to see if at that point we might have been able to predict the future behaviour of the GDP data.
The first set of graphs show two examples, that appear to straddle a significant change in the data’s behaviour sometime in the middle of the 70’s. It is the transition between the models from before 1975, which seemed to predict mean behaviour before but not after. and subsequent best fit models which continued to predict mean behaviour up until 2010.
Some things can we see :
- The first two models of the data set (1955-1964 then 1955-1974 (shown)) allow for what seems to be typical oscillation around the mean model for those periods (mean best fit exponential model)
- The first two models beyond about 1975 can no longer continue to predict mean oscillation behaviour, and the actual % deviation take a new course.
- Once a new model is recalculated for 1955-1985 period, the new and subsequent oscillations come back into line,
- Their amplitude is also seems to be larger and less noisey than before.
- The pre-’75 deviations now appear more like a positive “mountain range” (remember that this data is still used in subsequent models)
- The most recent deviation, from 2008 onwards, does seem to be “breaking away” from the existing model, as happened in the mid-70’s, as the system begins to find a new mean behaviour. If this is the case, then there is no point using the previous models to predict future behaviour, other than learning from the earlier “break-away”. The data will take on new characteristics and parameters.
- I will however speculated that it will take on the form of an exponential curve, around which oscillations will take place
- In it’s simplest form could be modelled by something like an underdamped 3rd order differential equation : a 1st order response [the exponential component], with underdamped oscillation on top[2nd order, boom-bust cycle].
- Whatever form the equation actually takes, the patterns suggest that GDP seems to have classical linear feedback behaviour at it’s heart (in this case positive feedback appears dominant), and particularly during what we might term “stable” predictable periods.
- If there are chaotic or non-linear components, they could be coming into play during the unstable periods where the parameters of the model are “re-adjusting themselves”. Almost by definition the shorter-term outcomes would be unpredictable.
I’m sure that there’s nothing ground-breaking here, but I’m pleased that there seem to be some strong linear components to the GDP output statistics, which suggests that we might be able to extract some simple dominant components (or causal loops) from what could be a very complex model (see Causal Diagram example below). It’s probably some of the minor causal components that become more significant during “uncertain” periods, where trust breaks down or the system “givens” are less “trustworthy” (read predictable).
P.S. Below is a fuller set of graphs for comparison:
Left to Right: 1) 1955-1965 Data; 2) 1955-1975 Data; 3) 1955-1985 Data; 4) 1955-1995 Data; 5) 1955-2005 Data; 6) 1955-2010 Data. Top to Bottom: 1) Data and best fit exponential model; 2) Deviation from model by data, as % of GDP for the period; 3) Deviation from model extended forward to whole 1955-2010 data set.