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Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks

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  • Brännäs, Kurt

    (Department of Economics, Umeå University)

  • Quoreshi, Shahiduzzaman

    (Department of Economics, Umeå University)

Abstract

The integer-valued moving average model is advanced to model the number of transactions in intra-day data of stocks. The conditional mean and variance properties are discussed and model extensions to include, e.g., explanatory variables are offered. Least squares and generalized method of moment estimators are presented. In a small Monte Carlo study the least squares estimator comes out as the best choice. Empirically we find support for the use of long-lag moving average models in a Swedish stock series. News about prices are found to exert a symmetric and positive effect on the number of transactions.

Suggested Citation

  • Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    • Handle: RePEc:hhs:umnees:0637
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    References listed on IDEAS

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    Cited by:

    1. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    2. Boris Aleksandrov & Christian H. Weiß, 2020. "Parameter estimation and diagnostic tests for INMA(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 196-232, March.
    3. Annika Homburg & Christian H. Weiß & Gabriel Frahm & Layth C. Alwan & Rainer Göb, 2021. "Analysis and Forecasting of Risk in Count Processes," JRFM, MDPI, vol. 14(4), pages 1-25, April.
    4. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    5. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
    6. Brännäs, Kurt & Lönnbark, Carl, 2006. "Effects of Explanatory Variables in Count Data Moving Average Models," Umeå Economic Studies 679, Umeå University, Department of Economics.
    7. Mohammadipour, Maryam & Boylan, John E., 2012. "Forecast horizon aggregation in integer autoregressive moving average (INARMA) models," Omega, Elsevier, vol. 40(6), pages 703-712.
    8. A.M.M. Shahiduzzaman Quoreshi, 2017. "A bivariate integer-valued long-memory model for high-frequency financial count data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1080-1089, February.
    9. A. M. M. Shahiduzzaman Quoreshi & Reaz Uddin & Naushad Mamode Khan, 2019. "Quasi-Maximum Likelihood Estimation for Long Memory Stock Transaction Data—Under Conditional Heteroskedasticity Framework," JRFM, MDPI, vol. 12(2), pages 1-13, April.
    10. Harry Joe, 2019. "Likelihood Inference for Generalized Integer Autoregressive Time Series Models," Econometrics, MDPI, vol. 7(4), pages 1-13, October.
    11. Quoreshi, Shahiduzzaman, 2006. "Time Series Modelling Of High Frequency Stock Transaction Data," Umeå Economic Studies 675, Umeå University, Department of Economics.
    12. Quoreshi, Shahiduzzaman, 2006. "LongMemory, Count Data, Time Series Modelling for Financial Application," Umeå Economic Studies 673, Umeå University, Department of Economics.
    13. Quoreshi, A.M.M. Shahiduzzaman, 2008. "A vector integer-valued moving average model for high frequency financial count data," Economics Letters, Elsevier, vol. 101(3), pages 258-261, December.
    14. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    15. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    16. Khan Naushad Mamode & Sunecher Yuvraj & Jowaheer Vandna, 2017. "Analyzing the Full BINMA Time Series Process Using a Robust GQL Approach," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-12, July.
    17. Christian H. Weiß & Martin H.-J. M. Feld & Naushad Mamode Khan & Yuvraj Sunecher, 2019. "INARMA Modeling of Count Time Series," Stats, MDPI, vol. 2(2), pages 1-37, June.

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    More about this item

    Keywords

    Count data; Intra-day; High frequency; Time series; Estimation; Finance.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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