I am currently exploring advanced mathematical techniques within the field of econometrics and am particularly interested in understanding how third-order differential equations, commonly referred to as "jerk equations," may be applied in time series forecasting.
Has anyone come across any scientific papers or research where jerk equations have been applied or considered for econometric time series forecasting? Any insight into the methodologies employed, advantages, disadvantages, or applications in various economic contexts would be greatly appreciated. If available, please provide the references or links to the relevant literature.
Thank you in advance for your assistance!
I found a paper titled “Approximate Analytical Solutions to Jerk Equations” by Nicolae Herişanu & Vasile Marinca which discusses the application of nonlinear third-order differential equations, known as nonlinear jerk equations, involving the third temporal derivative of displacement in analyzing some structures exhibiting rotating and translating motions such are robots or machine tools1. The paper proposes a new analytical technique called the Optimal Auxiliary Functions Method (OAFM) to analyze some particular cases of jerk functions involving cubic nonlinearity.
Here is a link for these papers
https://research-repository.griffith.edu.au/bitstream/handle/10072/5746/25364.pdf?sequence=2
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