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Univariate Multiplicative Error Models

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Econometrics of Financial High-Frequency Data

Abstract

The terminology multiplicative error model (MEM) has been introduced by Engle (2002b) for a general class of time series models for positive-valued random variables which are decomposed into the product of their conditional mean and a positive-valued error term. Such models might be alternatively classified as autoregressive conditional mean models where the conditional mean of a distribution is assumed to follow a stochastic process. The idea of a MEM is well known in financial econometrics and originates from the structure of the autoregressive conditional heteroscedasticity (ARCH) model introduced by Engle (1982) or the stochastic volatility (SV) model proposed by Taylor (1982) where the conditional variance is dynamically parameterized and multiplicatively interacts with an innovation term. In high-frequency econometrics, a MEM has been firstly introduced by Engle and Russell (1997, 1998) to model the dynamic behavior of the time between trades and was referred to as autoregressive conditional duration (ACD) model.

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Notes

  1. 1.

    For more details, see Sect. 5.3.1, where the asymptotic properties of the GARCH QML estimator are carried over to ACD models.

  2. 2.

    In the case \(P = Q = 1\), we set α : = α1 and β : = β1.

  3. 3.

    See also the descriptive statistics in Chap. 3.

  4. 4.

    UWLLN: Uniform Weak Law of Large Numbers.

  5. 5.

    For an overview of mixture distributions, see, e.g., Lancaster (1997).

  6. 6.

    In some studies, this model is also called “Nelson type” ACD model since it resembles the EGARCH specification proposed by Nelson (1991).

  7. 7.

    For more details, see e.g., Bauwens et al. (2004) or Dufour and Engle (2000), who apply this concept to the comparison of alternative financial duration models.

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  1. Institute for Statistics and Econometrics School of Business and Economics, Humboldt-Universität zu Berlin, Spandauer Str. 1, 10178, Berlin, Germany

    Professor Dr. Nikolaus Hautsch

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Hautsch, N. (2012). Univariate Multiplicative Error Models. In: Econometrics of Financial High-Frequency Data. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21925-2_5

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