Sugihara: Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series

Heard about this paper from a short bio of the author, Sugihara

He, along with Robert May, coauthored several papers on chaos theory and financial markets. This lead to him being given a huge pile of money by Deutsche Bank.

Robert May ended up as Baron of Oxford, among other honors. Baron May also wrote the landmark Infectious Diseases of Humans: Dynamics and Control (Oxford Press, 1992).

This paper presents an approach for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.

---

Two sources of uncertainty in forecasting natural systems: additive noise (ie measurement error) and complex dynamics. The prediction error for additive noise should be constant regardless of how many time steps ahead one is predicting. Prediction error for chaotic dynamics should increase sharply the more timesteps ahead one looks.

To create the C.D. predictor:
Lag series by E steps
To predict outcome of sample t,
find t's E+1 nearest neighbors in the lagged data
predicted outcome is exponetially weighted mean of n.neighbor's outcomes, with
weight == distance between t and the neighbor
E is related to the number of attractor by E_min < 2D +1. You can (given enough data) estimate D using i.e. the Grassberer-Procaccia algorithm. One can also test for changes in system dynamics by comparing accuracy of 1) predict second half using first half 2) randomly select training data over entire series

---

Possible follow-ups:
Can we describe the E-dimensional space? Do the points cluster, or are they diffuse?

Given that we can test for changes in the system dynamics, can we detect these change-points?

How does this relate to the resilience of cities paper, and its concept of slow trends pushing the city off a cliff; leading to sudden and drastic state changes

How does this relate to the nature and structure of human dynamics (thinking of the insurgency paper, which I will post soon).