Investigating Randomness By Walsh-Hadamard Transform in Financial Series

Subject Areas : Economic and Financial Time Series

Seyed Jalal  Tabatabaei ¹ (Department of Financial Management, Payamenoor University,Tehran.iran)

Received: 2023-09-23 Accepted : 2024-03-05 Published : 2024-05-26

Keywords: Walsh Transform , Randomness, Financial Series ,

Abstract :

The objective of the ongoing research is to introduce the initial, substantial, and practical implementation of the Walsh-Hadamard Transform in the realm of quantitative finance. It is worth noting that this particular tool, which has limited utility in the domain of digital signal processing, has demonstrated its effectiveness in evaluating the statistical significance of any binary sequence. Therefore, employing this approach in financial series would be exceptionally noteworthy. By employing five primary tests to assess the randomness of the series, including those pertaining to the Tehran Stock Exchange, as well as copper and gold, the outcomes reveal the presence of randomness in the transformed series in all aspects. Naturally, this random-ness could be examined to identify any underlying trends.

References:

[1] Antoniadis, J., Arumugam, P., Arumugam, S., Babak, S., Bagchi, M., Nielsen, A., The second data re-lease from the European Pulsar Timing Array II, Customised pulsar noise models for spatially correlated gravitational waves. arXiv preprint arXiv:230616225. 2023.
[2] Broadbent, H.A., Maksik, Y.A., Analysis of periodic data using Walsh functions ,Behavior Research Methods, Instruments, Computers,1992; 24(2):238-47.
[3] Fama, E.F., The behavior of stock-market prices, The journal of Business, 1965; 38(1):34-105.
[4] Fox, M.D., Halko, M.A., Eldaief, M.C., Pascual-Leone, A., Measuring and manipulating brain connec-tivity with resting state functional connectivity magnetic resonance imaging (fcMRI) and transcranial magnetic stimulation (TMS), Neuroimage. 2012; 62(4):2232-43.
[5] Golubov, B., Efimov, A., Skvortsov, V., Walsh series and transforms: theory and applications: Spring-er Science and Business Media; 2012.
[6] Johnson, J., Puschel, M., editors. In search of the optimal Walsh-Hadamard transform. 2000 IEEE In-ternational Conference on Acoustics, Speech, and Signal Processing Proceedings (Cat No 00CH37100); 2000: IEEE.
[7] Kendall, M.G., Hill, A.B., The analysis of economic time-series-part i: Prices, Journal of the Royal Statistical Society Series A (General), 1953; 116(1):11-34.
[8] Kim, S-J., Umeno, K., Hasegawa, A., Corrections of the NIST statistical test suite for randomness, arXiv preprint nlin/0401040. 2004.
[9] Mardan, S.S., Hamood, M.T., New fast Walsh–Hadamard–Hartley transform algorithm, International Journal of Electrical and Computer Engineering, 2023;13(2):1533.
[10] Marsani, MF., Shabri, A., Random Walk Behaviour of Malaysia Share Return in Different Economic Circumstance, MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 2019.
[11] Mazumder, P., Chandra, S., Rana, S., Mukhopadhyay, M., Naskar, MK., Parallel Hardware Implemen-tation of Walsh Hadamard Transform, Journal of Scientific and Industrial Research, 2022; 81(07):748-53.
[12] Oczeretko, E., Borowska, M., Brzozowska, E., Pawlinski, B., Borusiewicz, A., Gajewski, Z., editors. Walsh-Hadamard spectral analysis of signals representing bioelectrical activity of the reproductive tract in pigs, IEEE 15th International Conference on Bioinformatics and Bioengineering (BIBE), 2015; IEEE.
[13] Oprina, A-G., Popescu, A., Simion, E., Simion, G., Walsh− Hadamard randomness testand new meth-ods of test results integration, Bulletin of the Transilvania University of Brasov Series III: Mathematics and Computer Science, 2009:93-106.
[14] Pan, H., Badawi, D., Cetin, A.E., editors. Fast walsh-hadamard transform and smooth-thresholding based binary layers in deep neural networks, Proceedings of the IEEE/CVF Conference on Computer Vi-sion and Pattern Recognition; 2021.
[15] Pratt, J.W., Gibbons, J.D., Concepts of nonparametric theory: Springer Science & Business Media; 2012.
[16] Walsh, J.L., A closed set of normal orthogonal functions, American Journal of Mathematics, 1923; 45(1):5-24.