Nonlinear Regression with Conditionally Stable Innovations: A new Definition of Financial Contagion

Abstract

We develop a new notion of nancial contagion, or the spread of negative character- istics from one market to another, by tting a conditionally stable model to residuals extracted from a nonlinear regression. More speci cally, 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 distribu- tion 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 (in our case, the U.S. stock market). Using a permutation test, we determine whether, given a value in the tail of the covariate market return distri- bution, the residuals are more likely to be left-skewed or heavy at the left tail than at the median of the covariate distribution.