A Specification Test Based on Convolution-Type Distribution Function Estimates for Non-Linear Autoregressive Processes

Abstract

This chapter proposes a test for a parametric specification of the autoregressive function of a given stationary autoregressive time series. This test is based on the integrated square difference between the empirical distribution function estimate and a convolution-type distribution function estimate of the stationary distribution function obtained from the autoregressive residuals. Some asymptotic properties of the proposed convolution-type distribution function estimate are studied when the model’s innovation density is unknown. These properties are in turn used to derive the asymptotic null distribution of the proposed test statistic. We also discuss some finite sample properties of the test statistic based on the block bootstrap methodology. A simulation study shows that the proposed test competes favorably with some existing tests in terms of the empirical level and power.

Citation

Kim, K.H., Koul, H.L. and Kim, J. (2023), "A Specification Test Based on Convolution-Type Distribution Function Estimates for Non-Linear Autoregressive Processes", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Theory (Advances in Econometrics, Vol. 45A), Emerald Publishing Limited, Leeds, pp. 187-206. https://doi.org/10.1108/S0731-90532023000045A006