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Testing for Nonlinearity in Conditional Covariances

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  • Sanhaji Bilel

    (Université Paris8, LED, 2, rue de la Liberté, 93526Saint-Denis, France)

Abstract

We propose two Lagrange multiplier tests for nonlinearity in conditional covariances in multivariate GARCH models. The null hypothesis is the scalar BEKK model in which covolatilities of time series are driven by a linear function of their own lags and lagged squared innovations. The alternative hypothesis is an extension of the model in which covolatilities are modeled by a nonlinear function of the lagged squared innovations, represented by an exponential or a logistic transition function. Moreover, on the same basis we develop two other tests that are robust to leverage effects. We investigate the size and power of these tests through Monte Carlo experiments, and we provide empirical illustrations in many of which cases these tests encourage the use of nonlinearity in conditional covariances.

Suggested Citation

  • Sanhaji Bilel, 2017. "Testing for Nonlinearity in Conditional Covariances," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-22, July.
    • Handle: RePEc:bpj:jtsmet:v:9:y:2017:i:2:p:22:n:3
    DOI: 10.1515/jtse-2016-0010
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    Keywords

    Lagrange multiplier test; nonlinearity; smooth transition; scalar BEKK; multivariate GARCH;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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