Autocontours: Dynamic Specification Testing

Abstract

We propose a new battery of dynamic specification tests for the joint hypothesis of iid-ness and density function based on the fundamental properties of independent random variables with identical distributions. We introduce a device — the autocontour — whose shape is very sensitive to departures from the null in either direction, thus providing superior power. The tests are parametric with asymptotic t and chi-squared limiting distributions and standard convergence rates. They do not require a transformation of the original data or a Kolmogorov style assessment of goodness-of-fit, explicitly account for parameter uncertainty, and have superior finite sample properties. An application to autoregressive conditional duration (ACD) models for trade durations shows that the difficulty with the assumed densities lies on the probability assigned to very small durations. Supplemental materials for this article are available online.

Keywords: Autoregressive conditional duration model, Bootstrap, Parameter uncertainty, Probability contour plot