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The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data

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  • N. Taylor
  • Y. Xu

Abstract

We develop a general form logarithmic vector multiplicative error model (log-vMEM). The log-vMEM improves on existing models in two ways. First, it is a more general form model as it allows the error terms to be cross-dependent and relaxes weak exogeneity restrictions. Second, the log-vMEM specification guarantees that the conditional means are non-negative without any restrictions imposed on the parameters. We further propose a multivariate lognormal distribution and a joint maximum likelihood estimation strategy. The model is applied to high frequency data associated with a number of NYSE-listed stocks. The results reveal empirical support for full interdependence of trading duration, volume and volatility, with the log-vMEM providing a better fit to the data than a competing model. Moreover, we find that unexpected duration and volume dominate observed duration and volume in terms of information content, and that volatility and volatility shocks affect duration in different directions. These results are interpreted with reference to extant microstructure theory.

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  • N. Taylor & Y. Xu, 2017. "The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1021-1035, July.
  • Handle: RePEc:taf:quantf:v:17:y:2017:i:7:p:1021-1035
    DOI: 10.1080/14697688.2016.1260756
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    3. Cipollini, Fabrizio & Gallo, Giampiero M. & Otranto, Edoardo, 2021. "Realized volatility forecasting: Robustness to measurement errors," International Journal of Forecasting, Elsevier, vol. 37(1), pages 44-57.
    4. Xuehai Zhang, 2019. "A Box-Cox semiparametric multiplicative error model," Working Papers CIE 125, Paderborn University, CIE Center for International Economics.
    5. Carol Alexander & Daniel F. Heck & Andreas Kaeck, 2022. "The Role of Binance in Bitcoin Volatility Transmission," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(1), pages 1-32, January.
    6. Fabrizio Cipollini & Giampiero M Gallo & Alessandro Palandri, 2020. "Realized Variance Modeling: Decoupling Forecasting from Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 532-555.
    7. E. Otranto, 2024. "A Vector Multiplicative Error Model with Spillover Effects and Co-movements," Working Paper CRENoS 202404, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    8. Xuehai Zhang, 2019. "A Box-Cox semiparametric multiplicative error model," Working Papers CIE 122, Paderborn University, CIE Center for International Economics.

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    JEL classification:

    • 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
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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