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Approximation of π by financial historical data
Journal of the Korean Data & Information Science Society 2017;28:831-41
Published online July 31, 2017
© 2017 Korean Data & Information Science Society.

Dae-Heung Jang1 · TaeWoong Uhm2 · Seongbaek Yi3

123Department of Statistics, Pukyong National University
Correspondence to: Seongbaek Yi
Professor, Department of Statistics, 45 Yongsoro Namgu, Busan, Korea. E-mail: sbyi0108@gmail.com
Received June 27, 2017; Revised July 13, 2017; Accepted July 17, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The irrational number π is defined as the ratio of circumference of a circle to its radius and always becomes constant. This article does Monte Carlo approximation of its value using the famous Buffon’s needle experiment and shows that its convergence is not always proportional to the sample size. We also do Monte Carlo simulations to see the convergence of the computed π values from the random walk series with independent normal increment. Finally we apply the theoretical derivation to various financial time series data such as KOSPI, stock prices of Korean big firms, global stock indices and major foreign exchange rates. The historical data shows that log transformed data random walk process but most of their first lagged data don’t follow a normal distribution. More importantly the computed value from the ratio of the regression coefficient π tend to converge a constant, unfortunately not π. Using this result we could doubt on the efficient market hypothesis, and relate the degree of the hypothesis with the amount of deviation of the estimated π values.
Keywords : Buffon’s needle, π, random walk


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