Reconstructing deterministic economic dynamics from volatile time series data

Economists conventionally attribute observed volatility in economic time series data to exogenous random shocks that agitate otherwise stable real-world markets; and consequently, model volatility with a variety of linear-stochastic and probabilistic methods. However, some economists have recognized another possible explanation for volatility: Markets may be intrinsically unstable, and we might be able to model attending volatility parsimoniously with low-dimensional, nonlinear, deterministic dynamic models without resorting to stochastic inputs. Whether observed volatility is generated by inherently stable or unstable markets has serious policy implications. Will laissez-faire policies suffice to dampen volatility because markets are self-correcting, or are interventionist policies required? This chapter introduces nonlinear time series analysis (NLTS)—a collection of methods developed in mathematical physics to diagnose the source of real-world volatility from observed time series data. Depending on data quality, economists can potentially use NLTS to reconstruct phase-space market dynamics and extract equations of motion from a single price series.