User:NicolaK

Practical Methods for Analysis of Early - Warnings for Regime Shifts

October 10 - 12, 2011

Complex systems ranging from ecosystems to financial markets and the climate may have tipping points where a sudden shift to a contrasting regime can occur. As such critical transitions can have dire consequences, being able to predict them is very important. Unfortunately, detecting critical points is extremely difficult as good predictive models are mostly lacking. However, recent work suggests that we may find empirical indicators to assess whether a system is approaching a tipping point. Such generic early-warning indicators appear to work for all kinds of critical transitions and, in principle, can be identifiable in a wide range of complex systems like ecosystems, financial markets, or the climate.

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Economic models in current use do not pretend to be theories of everything economic; any such pretensions would immediately be thwarted by computational infeasibility and the paucity of theories for most types of economic behavior. Therefore conclusions drawn from models will be approximate representations of economic facts. However, properly constructed models can remove extraneous information and isolate useful approximations of key relationships. In this way more can be understood about the relationships in question than by trying to understand the entire economic process.

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Practical Methods for Analysis of Early - Warnings for Regime Shifts

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Early warning signals (EWS) of regime shifts are challenging in cases where the true natural data generating process is uncertain. Nonparametric drift-diffusion-jump models address this problem by fitting a general model that can approximate a wide range of data generating processes. Drift measures the local rate of change. Diffusion measures relatively small shocks that occur at each time step. Jumps are large intermittent shocks. Total variance combines the contributions of diffusion and jumps. Nonparametric methods are well-suited to emerging technology for automated, high-frequency sensors. Total variance is the most precisely measured indicator. Jump intensity appears to be a useful EWS. Estimates of the drift are highly uncertain unless long time series with many regime shifts are available. EWS computed from drift estimates (such as autocorrelation coefficients or return rates) have low precision and should be used with caution. Nonetheless, in the current state of knowledge it is premature to disregard any potential EWS.

Multivariate jumps are superimposed on the binomial model of Cox, Ross, and Rubinstein (1979) to obtain a model with a limiting jump diffusion process. This model incorporates the early exercise feature of American options as well as arbitrary jump distributions. It yields an efficient computational procedure that can be implemented in practice.

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http://www.esajournals.org/doi/abs/10.1890/11-0716.1?journalCode=ecol http://www.jstor.org/pss/2329069 http://en.wikipedia.org/wiki/Poisson_process http://www.buypowerwheels.com http://en.wikipedia.org/wiki/Luminous_intensity