2 Responses to extrapolations

1. hypergeometric says:

   8 December 2014 at 17:56

   Thanks for your comment, Mark.

   Agreed, some understanding of dynamics is needed. In some cases, however, there is not a lot of dynamics needed, at least for short-run forecasts, even for some complicated systems. Sure, tracking an aircraft with radar is relatively simple because kinematics are relatively simple, even if modeling the sensor might not be in that case. But simple models can forecast well for complicated systems.

   The following figure is take from Hyndman and Khandakar’s write-up of their forecast package:
   

   These use exponential smoothing state-space models leading up to the forecast. Hyndman and colleagues have a couple of textbooks out describing these, primarily oriented towards business and financial forecasting.

   The same kinds of models can be applied to climate-related series, although I prefer Bayesian forecasting methods. Consider, for instance,
   
   The model here is a Gaussian random walk, one anticipating a step change. The fit is done using a Kalman filter forward, and then a Rauch-Tung-Striebel reverse smoother. The state variance is set to be a tenth of the observational. (The code is available, but it’s not very well documented, and intertwingled with a bunch of other calculations devised for a expository purpose other than this.)

   The reason for such complexity is that if trends are addressed using things like polynomials, or their generalizations, splines, and differing window sizes are tried, the result is a mess
   

   without a good way to discriminate among the choices.

   Loading...

   Reply
2. Mark says:

   8 December 2014 at 15:56

   The thing is, when you and I look at that we see a smooth exponential increase with some modest-sized oscillations. But someone else could come along and fit it with, say, a polynomial, in which case that flattish bit at the end turns into a rapid runaway just outside the data period, switching from positive or negative with the even or odd polynomial degree.

   To extrapolate successfully you always need an understanding of the underlying dynamics of the system. In other words a climate model, fancy or otherwise.

   Loading...

   Reply