Testing the Random Walk Hypothesis

Powerful Essays
Statistical Methods & Capital Markets
Testing Random Walk Hypothesis
Nicolas Mancini

* Table of Content

Abstract
Theoretical background
Methodology
Data & Results
Comparison
Conclusion
References

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I. Abstract

The aim of this paper is to test the random walk hypothesis by applying the runs test on time series of several selected stocks. The random walk theory is the theory that stock prices changes have the same distribution and are independent of each other, so the past movement or trend of a stock price or market cannot be used to predict its future movement. Shortly said it is the idea that stocks take a random and unpredictable path.
The motivation behind this work is to analyze whether the random walk hypothesis is valid in different periods of time. Therefore we will use recent data and more distant data in order to draw a conclusion. Furthermore it could be interesting to compare results for companies that are not specifically active the same industry.
The runs test will be carried out with the R software, a free software, though really powerful, for environmental and statistical computings and graphics. II. Theoretical background

Introduced for the first time by Burton Malkiel in his top-seller « A Random Walk Down Wall Street » in 1973, the model of random walk might be a reasonable approximation to the true dynamics of stock log prices. Random walk time series are time series {xt : t = 0,1,2,…} starting with x0, where any value over time can be calculated as follows : xt = xt-1 + at (for t >= 0) and where {at : t = 0,1,2,…} are sequences of independent and identically distributed random variables with zero mean. The independence of increments implies that the probability of the increment at is not influenced by past values. A mathematical formulation for this would be : P(at at-1, at-2,…) = P(at). The identical distribution of increments means that the



References: *Log returns in quantitative finance, (2009) David Harper. Retrieved from http://www.bionicturtle.com/how-to/article/why_we_use_log_returns_in_quantitative_finance_frmquant_xls *Random Walk Theory, (n.d) Investopedia. Retrieved from http://www.investopedia.com/terms/r/randomwalktheory.asp#axzz2GMaEvtac *Random Walk Theory, (n.d) InvestingAnswers. Retrieved from http://www.investinganswers.com/financial-dictionary/stock-market/random-walk-theory-907 *Runs test for detecting non-randomness, NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, date *Runs test, (n.d) Investopedia. Retrieved from http://www.investopedia.com/terms/r/runs_test.asp#axzz2GMaEvtac *Slides of Statistical Methods & Capital Markets, (2012) Mgr. Milan Basta, Ph.D. *Wald-Wolfowitz or Runs test for randomness, (1986) « Mathematical Statistics with Applications, 3rd Ed. » by Mendenhall, Scheaffer and Wackerly. Retrieved from http://support.sas.com/kb/33/092.html

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