Specification tests for nonlinear dynamic models

TL;DR

The paper introduces a new adequacy test and graphical evaluation tool for nonlinear dynamic models that effectively control for nonlinear behavior without relying on smoothing, applicable across various financial and economic models.

Contribution

It proposes a novel multivariate empirical process-based test that accounts for parameter uncertainty and does not require smoothing, improving model adequacy assessment.

Findings

Test controls nonlinear dynamics effectively

Maintains good size and power in finite samples

Successfully applied to stock index data models

Abstract

We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behavior in conditional distribution and does not rely on smoothing techniques which require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous and lagged probability integral transforms. We establish weak convergence of the process under parameter uncertainty and local alternatives. We justify a parametric bootstrap approximation that accounts for parameter estimation effects often ignored in practice. Monte Carlo experiments show that the test has good finite-sample size and power properties. Using the new test and graphical tools we check the adequacy of various popular heteroscedastic models for stock exchange index data.