The basis of the choice of methods of analysis are:
researcher preferences;
analysis conditions;
data structure.
What are the most common methods for the analysis of economic dynamics?
Your experience in the application of fuzzy sets theory, chaos theory, econophysics analysis of economic dynamics.
As an engineer in the field of automation and control, I can suggest You many approaches, as some were already given. But, MIT paper by Sergey Paltsev "Moving from Static to Dynamic General Equilibrium Economic Models..." is fine reading for an issue.Also, stability issues are relevant!
http://test2-globalchange.mit.edu/files/document/MITJPSPGC_TechNote4.pdf
I think best analyzer for economical topologies is optimal control theory which consist of NLP(non-linear programming) and CV(calculus of variation) .the best and most optimized answer to a economic problem obtained by optimal control.in that you have a problem which is object to some constraints fully simulated like real world.
My friend Vyacheslav, the problem is that most of the interesting methods are treated from mainstream economists as 'heterodox economics', so they cannot find a place in a first class journal. If we accept that risk then, be my guest:
1)ordinary and partial differential equations for continous time
2)equations of differences for discrete time
3)spectrum analysis of every kind in order to recover the existed harmonics
4)power laws in economics and 'fat tailed distributions'
5)matrix formating of a problem (aka Leontieff)
Of course we are not waiting all the above techniques to be understood and be accepted, but who knows...
The are many methods for the analysis of economic dynamics. The most common methods include matrix formating and the optimal control.
Agent based modelling(ABM) can be used to model complex dynamic systems like economic systems and if the modelling is done properly you can get some insight about the dynamics of a system.
As an engineer in the field of automation and control, I can suggest You many approaches, as some were already given. But, MIT paper by Sergey Paltsev "Moving from Static to Dynamic General Equilibrium Economic Models..." is fine reading for an issue.Also, stability issues are relevant!
http://test2-globalchange.mit.edu/files/document/MITJPSPGC_TechNote4.pdf
A complete study of economic dynamics is given in the following book:
R. Shone, Economic Dynamics. Phase Diagrams and Their Economic Application, second edition, Cambridge, 2002, 724 pages:
http://www.econ.uniurb.it/materiale/5773_Shone%20%20Economic%20Dynamics.pdf
One of the outstanding features is its provision of Mathemematica and Maple examples. It also includes a complete introduction to dynamic modelling (including Chaos theory) in Part 1 and chapters in applied economic dynamics (including a chapter on population models).
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