Heterogeneous component multiplicative error models for forecasting trading volumes

Naimoli, Antonio and Storti, Giuseppe (2019): Heterogeneous component multiplicative error models for forecasting trading volumes.

Abstract

We propose a novel approach to modelling and forecasting high frequency trading volumes. The new model extends the Component Multiplicative Error Model of Brownlees et al. (2011) by introducing a more flexible specification of the long-run component. This uses an additive cascade of MIDAS polynomial filters, moving at different frequencies, in order to reproduce the changing long-run level and the persistent autocorrelation structure of high frequency trading volumes. After investigating its statistical properties, the merits of the proposed approach are illustrated by means of an application to six stocks traded on the XETRA market in the German Stock Exchange.

• Item Type: MPRA Paper
• Language: English
• Keywords: Intra-daily trading volume, dynamic component models, long-range dependence, forecasting.
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

References

Amado, C., A. Silvennoinen, and T. Terasvirta (2019). Models with Multiplicative Decomposition of Conditional Variances and Correlations, Volume 2. United Kingdom: Routledge.

Amado, C. and T. Teräsvirta (2013). Modelling volatility by variance decomposition. Journal of Econometrics 175(2), 142–153.

Andersen, T. G., T. Bollerslev, and J. Cai (2000). Intraday and interday volatility in the japanese stock market. Journal of International Financial Markets, Institutions and Money 10(2), 107–130.

Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2003). Modeling and forecasting realized volatility. Econometrica 71(2), 579–625.

Bauwens, L., M. Braione, and G. Storti (2016). Forecasting comparison of long term component dynamic models for realized covariance matrices.

Annals of Economics and Statistics (123/124), 103–134. Bauwens, L., M. Braione, and G. Storti (2017). A dynamic component model for forecasting high-dimensional realized covariance matrices. Econometrics and Statistics 1(C), 40–61.

Berkowitz, S. A., D. E. Logue, and E. A. Noser (1988). The total cost of transactions on the nyse. The Journal of Finance 43(1), 97–112.

Bougerol, P. and N. Picard (1992a). Stationarity of garch processes and of some nonnegative time series. Journal of Econometrics 52(1), 115 – 127.

Bougerol, P. and N. Picard (1992b). Strict stationarity of generalized autoregressive processes. The Annals of Probability 20(4), 1714–1730.

Brownlees, C. T., F. Cipollini, and G. M. Gallo (2011). Intra-daily volume modeling and prediction for algorithmic trading. Journal of Financial Econometrics 9(3), 489–518.

Brownlees, C. T. and G. M. Gallo (2006). Financial econometric analysis at ultra-high frequency: Data handling concerns. Computational Statistics & Data Analysis 51(4), 2232–2245.

Brownlees, C. T. and G. M. Gallo (2010). Comparison of volatility measures: a risk management perspective. Journal of Financial Econometrics 8(1), 29–56.

Brunetti, C. and P. M. Lildholdt (2007). Time series modeling of daily log-price ranges for chf/usd and usd/gbp. The Journal of Derivatives 15(2), 39–59.

Chou, R. Y. (2005). Forecasting financial volatilities with extreme values: the conditional autoregressive range (carr) model. Journal of Money, Credit and Banking, 561–582.

Cipollini, F., R. F. Engle, and G. M. Gallo (2006). Vector multiplicative error models: representation and inference. Technical report, National Bureau of Economic Research.

Cipollini, F., R. F. Engle, and G. M. Gallo (2013). Semiparametric vector mem. Journal of Applied Econometrics 28(7), 1067–1086.

Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 174–196.

Engle, R. (2002). New frontiers for arch models. Journal of Applied Econometrics 17(5), 425–446.

Engle, R. F., E. Ghysels, and B. Sohn (2013). Stock market volatility and macroeconomic fundamentals. Review of Economics and Statistics 95(3), 776–797.

Engle, R. F. and J. G. Rangel (2008). The spline-garch model for low-frequency volatility and its global macroeconomic causes. Review of Financial Studies 21(3), 1187–1222.

Engle, R. F. and J. R. Russell (1998). Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica, 1127–1162.

Engle, R. F. and M. E. Sokalska (2012). Forecasting intraday volatility in the us equity market. multiplicative component garch. Journal of Financial Econometrics 10(1), 54–83.

Francq, C. and J. Zakoian (2011). GARCH Models: Structure, Statistical Inference and Financial Applications. Wiley.

Gallant, A. R. (1981). On the bias in flexible functional forms and an essentially unbiased form: the fourier flexible form. Journal of Econometrics 15(2), 211–245.

Gallo, G. M. and E. Otranto (2015). Forecasting realized volatility with changing average levels. International Journal of Forecasting 31(3), 620–634.

Ghysels, E., P. Santa-Clara, and R. Valkanov (2006). Predicting volatility: getting the most out of return data sampled at different frequencies. Journal of Econometrics 131(1), 59–95.

Ghysels, E., A. Sinko, and R. Valkanov (2007). Midas regressions: Further results and new directions. Econometric Reviews 26(1), 53–90.

Glasserman, P. and D. D. Yao (1995). Stochastic vector difference equations with stationary coefficients. Journal of Applied Probability 32(4), 851–866.

Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50(4), 1029–1054.

Hansen, P. R., A. Lunde, and J. M. Nason (2011). The model confidence set. Econometrica 79(2), 453–497. Hautsch, N. (2003). Assessing the risk of liquidity suppliers on the basis of excess demand intensities. Journal of Financial Econometrics 1(2), 189–215.

Hautsch, N., P. Malec, and M. Schienle (2014). Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes.

Journal of Financial Econometrics 12(1), 89–121. Lanne, M. (2006). A mixture multiplicative error model for realized volatility. Journal of Financial Econometrics 4(4), 594–616.

Lee, S.-W. and B. E. Hansen (1994). Asymptotic theory for the garch (1, 1) quasi-maximum likelihood estimator. Econometric theory 10(01), 29–52.

Love, E. R. (1980). 64.4 some logarithm inequalities. The Mathematical Gazette 64(427), 55–57.

Madhavan, A. N. (2002). Vwap strategies. Trading 2002(1), 32–39.

Manganelli, S. (2005). Duration, volume and volatility impact of trades. Journal of Financial markets 8(4), 377–399.

Müller, U. A., M. M. Dacorogna, R. D. Davé, O. V. Pictet, R. B. Olsen, and J. R. Ward (1993). Fractals and intrinsic time: A challenge to econometricians. Unpublished manuscript, Olsen & Associates, Zürich.

Newey, W. K. and D. McFadden (1994). Chapter 36 large sample estimation and hypothesis testing. Volume 4 of Handbook of Econometrics, pp. 2111 – 2245. Elsevier.

Patton, A., D. N. Politis, and H. White (2009). Correction to "automatic block-length selection for the dependent bootstrap" by d. politis and h. white. Econometric Reviews 28(4), 372–375.

Rothenberg, T. J. (1971). Identification in parametric models. Econometrica 39(3), 577–591.

Russell, J. R. and R. F. Engle (2005). A discrete-state continuous-time model of financial transactions prices and times: The autoregressive conditional multinomial–autoregressive conditional duration model. Journal of Business & Economic Statistics 23(2), 166–180.

Wang, F. and E. Ghysels (2015). Econometric analysis of volatility component models. Econometric Theory 31(2), 362–393.