Phase Space Reconstruction from Time Series Data: Where History Meets Theory
In ‘dissipative’ dynamical systems, variables evolve asymptotically toward low‐dimensional ‘attractors’ that define their dynamical properties. Unfortunately, real‐world dynamical systems are generally too complex for us to directly observe these attractors. Fortunately, there is a method—‘phase space reconstruction’—that can be used to indirectly detect attractors in real‐world dynamical systems using time series data on a single variable (Broomhead and King, 1985; Schaffer and Kott, 1985; Kott et al, 1988; Williams,1997). Armed with this knowledge, we can formulate more accurate and informative models of real‐world dynamical systems. We begin by introducing the concept of phase space attractors within the context of a dynamic ISLM model. We next demonstrate how phase space reconstruction faithfully reproduces one of the model’s attractors. Finally, we discuss how phase space reconstruction fits into a more general ‘diagnostic’ modeling approach that relies on historical data to guide and test the deterministic formulation of theoretical dynamical models. As an example of diagnostic modeling, we test how closely the attractor generated by the dynamic ISLM model visually approximates the attractor reconstructed from time series data on real‐world interest rates.
|Date of creation:||Oct 2010|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.fooddynamics.org/|
When requesting a correction, please mention this item's handle: RePEc:ags:iefi10:100455. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (AgEcon Search)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.