Goodness-of-fit tests for extended Log-GARCH models

TL;DR

This paper develops and evaluates goodness-of-fit and specification tests for an extended, scale-stable Log-GARCH model, including LM and Portmanteau tests, with simulations and real data applications.

Contribution

It introduces new statistical tests for extended Log-GARCH models and compares them to EGARCH, enhancing model validation methods.

Findings

Lagrange-Multiplier test effectively distinguishes extended Log-GARCH from more general models.

Portmanteau tests successfully assess model fit for extended Log-GARCH.

Simulation results support the theoretical properties of the proposed tests.

Abstract

This paper studies goodness of fit tests and specification tests for an extension of the log-GARCH model which is stable by scaling. A Lagrange-Multiplier test is derived for testing the null assumption of extended log-GARCH against more general formulations including the Exponential GARCH (EGARCH). The null assumption of an EGARCH is also tested. Portmanteau goodness-of-fit tests are developed for the extended log-GARCH. Simulations illustrating the theoretical results and an application to real financial data are proposed.