Resonance in Economic Time Series and Market Moves

Summary

The document asks whether resonant interactions in economic time series could help explain selloffs or squeezes, and whether resonance might be detected across stock prices. It distinguishes resonance from ordinary correlation, which the question describes as a measure of linear association rather than a mechanism.

The response argues that observing resonance requires system dynamics described by a second-order differential equation. It contrasts this requirement with geometric Brownian motion and the Ornstein–Uhlenbeck process, both presented as first-order stochastic models. The exchange excerpt does not develop a detection method or analyze market data, and its brief argument does not establish whether other economic models could exhibit resonant behavior.

Key ideas

• The document asks whether resonant interactions could help explain market selloffs and squeezes.
• It distinguishes the proposed resonance mechanism from correlation between time series.
• The response says resonance requires dynamics described by a second-order differential equation.
• It notes that geometric Brownian motion and the Ornstein–Uhlenbeck process are not such equations.

Tags

# Is there such a thing as resonance in economic underliers?


# Is there such a thing as resonance in economic underliers?












In physics the occurence of resonance is explained and widely understood in its linear form and subject to research in nonlinear resonance.

Example for instance are resonant frequencies of objects.

Now it is not so much of a stretch of imagination to look for resonance in economic times series.

Correlation is only a linear measure of linking time series and it doesnt explain the mechanism for resonance.

Can we explain selloffs and squeezes by resonant interactions of a complex system and is it possible to detect resonance in stock price time series of multiple stocks?

## Answer by ZRH (score 1)

https://quant.stackexchange.com/a/44836

I would argue as follows: In order to observe any type of resonant behaviour, the dynamics of the system you are looking at needs to be described by a second order differential equation. The equations of motions that come to mind in economics are clearly not:

GBM: $dS=\mu S dt+\sigma S dZ$

OU: $dX=\theta(\mu - X)dt+\sigma dW$

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