2262 WordsApr 15, 201310 Pages

Statistical Methods & Capital Markets
Testing Random Walk Hypothesis
Nicolas Mancini
* Table of Content
Abstract
Theoretical background
Methodology
Data & Results
Comparison
Conclusion
References
-------------------------------------------------
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*…show more content…*

More commonly and in a standardized output, we would rather use the p value in order to draw a conclusion about the hypothesis but as we don’t have one, we are forced to compare the absolute Z value to the quantile. In other words, an absolute value greater than 1.96, called the critical value, indicates non-randomness and disproves the random walk theory. The mathematical form of this statement is:
Z ≥Z1-α2=0.975
As the reader has got now all the information available about theory and methodology, it’s time to move on to the concrete part. Indeed, next header explains the extraction of data.
IV. Data
The data of the historical prices of the chosen stocks will be taken from the official source Yahoo! Finance. The R software uses this source by default and therefore the end user can simply assess this data by installing the package « quantmod » and using the library command.
In this paper three stocks have been chosen, Apple Inc. (NASDAQ: AAPL), IBM (NYSE: IBM) and

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