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Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model


  • Nakatani, Tomoaki

    () (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    () (School of Management and Economics)


In this paper we propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation GARCH model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that model in which volatility is modelled as a linear combination not only of its own lagged squared innovations and volatility but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatility transmissions among variables in the model. Monte Carlo experiments show that the proposed test has satisfactory finite sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables.

Suggested Citation

  • Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model," SSE/EFI Working Paper Series in Economics and Finance 649, Stockholm School of Economics, revised 04 May 2008.
  • Handle: RePEc:hhs:hastef:0649

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    More about this item


    Multivariate GARCH; Volatility interactions; Lagrange multiplier test; Monte Carlo simulation; Conditional correlations;

    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G19 - Financial Economics - - General Financial Markets - - - Other

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