Phase space reconstruction: methods in applied economics and econometrics

Michael Paul McCullough

doi:10.7273/000005733

Market responses to unpredictable events such as preference change, food contamination, or changes in technology and information are not always known. Phase space reconstruction, a tool designed to analyze nonlinear time series, is investigated for use as an econometric tool to detect nonlinear dynamics economic time series. It is applied to examine consumer responses to unpredictable events, changes in dynamic livestock cycles, and nonlinear structure in regression residuals. The empirical application of phase space reconstruction analyzing economic behavior demonstrates an intuitive, appealing, and straightforward demonstration as to the use of this diagnostic tool. The first essay investigates how to reconstruct dynamic consumer reactions from market events using phase space reconstruction. This approach can provide important and unique empirical insights into consumer reactions to product recall or contaminant events. We apply phase space reconstruction analysis to U.S. meat demand, demonstrating distinct differences between intertemporal shorter run impacts from food safety incidents (e.g., E. Coli and BSE) relative to longer run health effects (e.g., cholesterol). Moreover, we show that consumers have reacted to food safety events differently depending on the particular food contaminate associated with that event. In the second essay, phase space reconstruction is investigated as a diagnostic tool for determining the structure of detected nonlinear processes in regression residuals. Empirical evidence supporting this approach is provided using simulations from an Ikeda mapping and the S&P 500. Results in the form of phase portraits (e.g., scatter plots of reconstructed dynamical systems) provide qualitative information to discern structural components from apparent randomness and provide insights categorizing structural components into functional classes to enhance econometric/time series modeling efforts. The third essay applies the technique of phase space reconstruction to investigate U.S. livestock cycles. Results are presented for both pork and cattle cycles, providing empirical evidence that the cycles themselves have slowly diminished. By comparing the two livestock cycles important insights can be made. The phase space analysis suggests that the biological constraint has become a less significant factor in livestock cycles while technology and information are relatively more significant.

Phase space reconstruction: methods in applied economics and econometrics

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