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Adequacy of Lagrange Multiplier Test


  • Lee , Mei-Yu

    (Department of Applied Finance, Yuanpei University, HsinChu, Taiwan)


This paper examines the distribution of the Lagrange multiplier test, LM test, and focuses on what factors affect the distribution of the LM test estimator. It is worth noting that due to Chi-square distribution properties, the degree of freedom depends not only on the lagged-number of autocorrelation, but also on the number of independent variables whatever the sample sizes, that is, degree of freedom is the lagged-number of autocorrelation plus the number of independent variables. The result also indicates that the LM test estimator is not necessary to become Chi-square distribution because the different effect of the sample size and the number of independent variables, nevertheless, the law of large number, sample size is larger than 1000, leads the LM test estimator toward to Chi-square distribution.

Suggested Citation

  • Lee , Mei-Yu, 2014. "Adequacy of Lagrange Multiplier Test," European Economic Letters, European Economics Letters Group, vol. 3(2), pages 32-35.
  • Handle: RePEc:ris:eueclt:0025

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    More about this item


    Lagrange multiplier test; degree of freedom; serial correlation; autocorrelation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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