Computational Experiments Successfully Predict the Emergence of Autocorrelations in Ultra-High-Frequency Stock Returns
- 341 Downloads
Social and economic systems are complex adaptive systems, in which heterogenous agents interact and evolve in a self-organized manner, and macroscopic laws emerge from microscopic properties. To understand the behaviors of complex systems, computational experiments based on physical and mathematical models provide a useful tools. Here, we perform computational experiments using a phenomenological order-driven model called the modified Mike–Farmer (MMF) to predict the impacts of order flows on the autocorrelations in ultra-high-frequency returns, quantified by Hurst index \(H_r\). Three possible determinants embedded in the MMF model are investigated, including the Hurst index \(H_s\) of order directions, the Hurst index \(H_x\) and the power-law tail index \(\alpha _x\) of the relative prices of placed orders. The computational experiments predict that \(H_r\) is negatively correlated with \(\alpha _x\) and \(H_x\) and positively correlated with \(H_s\). In addition, the values of \(\alpha _x\) and \(H_x\) have negligible impacts on \(H_r\), whereas \(H_s\) exhibits a dominating impact on \(H_r\). The predictions of the MMF model on the dependence of \(H_r\) upon \(H_s\) and \(H_x\) are verified by the empirical results obtained from the order flow data of 43 Chinese stocks.
KeywordsComputational experiment Order-driven model Market efficiency Order direction Long memory
Zhi-Qiang Jiang, Gao-Feng Gu and Wei-Xing Zhou received support from the National Natural Science Foundation of China (71501072) and the Fundamental Research Funds for the Central Universities. Xiong Xiong and Wei Zhang received support from the National Natural Science Foundation of China (71532009,71131007) and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1028). Wei Chen received support from the National Natural Science Foundation of China (71571121).
- Bachelier, L. (1900). Théorie de la Spéculation. Ph.D. thesis, University of Paris, Paris.Google Scholar
- Carbone, A. (2009). Detrending moving average algorithm: A brief review. Science and Technology for Humanity (TIC-STH) IEEE pp 691–696. doi: 10.1109/TIC-STH.2009.5444412
- Carbone, A., Castelli, G., & Stanley, H. E. (2004a). Analysis of clusters formed by the moving average of a long-range correlated time series. Physical Review E, 69, 026105. doi: 10.1103/PhysRevE.69.026105.
- Clark-Joseph, A. D. (2013) Exploratory trading, job market paperGoogle Scholar
- Cootner, P. H. (1964). The random character of stock market prices. Cambridge: MIT Press.Google Scholar
- Fishe, R. P. H., Haynes, R., & Onur, E. (2015). Anticipatory traders and trading speed, http://ssrn.com/abstract=2606949
- Hayes, R., Paddrik, M., Todd, A., Yang, S., Beling, P., & Scherer, W. (2012). Agent based model of the e-mini future: Application for policy making. In C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, & A. M. Uhrmacher (Eds.), Proceedings of the 2012 Winter Simulation Conference. pp. (1–12) Berlin: IEEE. doi: 10.1109/WSC.2012.6465037
- Mandelbrot, B. B. (1971). Analysis of long-run dependence in economics: The R/S technique. Econometrica, 39(Suppl), 68–69.Google Scholar
- Meng, H., Ren, F., Gu, G. F., Xiong, X., Zhang, Y. J., Zhou, W. X., et al. (2012). Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations. EPL (Europhysics Letters), 98(5), 38003. doi: 10.1209/0295-5075/98/38003.CrossRefGoogle Scholar
- Xu, L. M., Ivanov, P. C., Hu, K., Chen, Z., Carbone, A., & Stanley, H. E. (2005). Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques. Physical Review E, 71, 051101. doi: 10.1103/PhysRevE.71.051101.CrossRefGoogle Scholar