Nonlinear Regression With Conditionally Stable Innovations: A New Definition Of Financial Contagion

• Activity Number: 584
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Eric Grant Stradley*+ and Jeff Hamrick
• Companies: Rhodes College and Rhodes College
• Keywords: contagion ; crisis ; heavy tails ; stable distribution ; nonlinear regression ; skewness

Abstract

We develop a new notion of financial contagion, or the spread of negative characteristics from one market to another, by fitting a conditionally stable model to residuals extracted from a nonlinear regression. More specifically, we estimate the return on a dependent market given the return on an independent market using a spline-based local mean function. Then, instead of assuming that the residuals have a Gaussian distribution, we assume that the residuals are independent stable random variables when conditioned on the covariate market return. In general, the stable distribution depends on four parameters, two of which control skewness and tail heaviness. With our approach, these parameters become functions that are nonparametrically estimated. For various dependent markets, we study the change in the skewness and heaviness functions from the median to the tail of an associated covariate market return distribution. After bootstrapping the results of our function estimation, we test whether, given a value in the tail of the covariate market return distribution, the residuals are more likely to be left-skewed or heavy at the left tail than at the median of the distribution.