Combined Lagrange Multiplier Test for ARCH in Vector Autoregressive Models

Niklas Ahlgren, Paul Catani

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientific


In this paper we propose a combined Lagrange multiplier (LM) test for autoregressive conditional heteroskedastic (ARCH) errors in vector autoregressive (VAR) models by following a suggestion in Dufour et al. (2010) of replacing an exact Monte Carlo (MC) test by a bootstrap MC test when the model includes lags. The test circumvents the problem of high dimensionality in multivariate tests for ARCH in VAR models. It is computationally simple since it only requires computing univariate statistics. The bootstrap MC test is shown to be asymptotically exact. Monte Carlo simulations show that the test has good finite-sample properties. It is found that the test is robust against a non-normal error distribution, while other multivariate LM tests for ARCH suffer from size distortion. We present two financial applications of multivariate LM tests for ARCH to credit default swap (CDS) prices and Euribor interest rates. The results indicate that the errors are skewed and heavy-tailed, and that there are significant ARCH effects.
Original languageEnglish
Title of host publicationProceedings of EEA-ESEM Geneva 2016
Number of pages34
Place of PublicationGeneva
Publication date22.08.2016
Publication statusPublished - 22.08.2016
MoE publication typeB3 Article in conference proceedings
Event69th European Meeting of the Econometric Society (ESEM) - Geneva, Geneva, Switzerland
Duration: 22.08.201626.08.2016
Conference number: 69


  • 511 Economics
  • ARCH
  • Bootstrap
  • Lagrange multiplier test
  • Monte Carlo test
  • VAR model


Dive into the research topics of 'Combined Lagrange Multiplier Test for ARCH in Vector Autoregressive Models'. Together they form a unique fingerprint.

Cite this