Specification Test based on Convolution-type Distribution Function Estimates for Non-linear Auto-regressive Processes

TL;DR

This paper introduces a new convolution-type distribution function estimate for non-linear autoregressive processes and develops a specification test that outperforms benchmarks in simulations.

Contribution

It proposes a novel convolution-type distribution function estimate and a corresponding test for model specification, with proven asymptotic properties and superior finite-sample performance.

Findings

The new estimate has desirable asymptotic properties.

The proposed test performs well in finite samples.

Simulation results favor the new test over benchmarks.

Abstract

The paper proposes a specification test based on two estimates of distribution function. One is the traditional kernel distribution function estimate and the other is a newly proposed convolution-type distribution function estimate. Asymptotic properties of the new estimate are studied when the innovation density is known and when it is unknown. The MISE-type statistic based on these estimates is suggested to test parametric specifications of the mean and volatility functions. The relating asymptotic results are obtained and the finite-sample properties are studied based on the bootstrap methodology. A simulation study shows that the proposed test competes favorably to benchmark tests in terms of the empirical level and power.