Notebook ON Stock Price Randomness

Prove that Stock Price is random.

H0 = hypothesis that the sequence of stock price is random

Ha = alternate hypothesis that the sequence of stock price is NOT random

The Amazon stock price information as below

Start date from 28 March 2013

End date to 28 March 2018

We are going to use (NON-PARAMETRIC) ONE-SAMPLE RUN TEST statistical procedure to determine its randomness.

https://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm

The MEAN formula is below

The Standard Deviation formula is below

Procedures

1. Calculate the BELOW or ABOVE labels. Example

• =IF(F2>F3,“above”,“below”)

2. Calculate the RUNS (refer to first few rows of the spreadsheet)

• Set the first row of the spreadsheet to 1
• set the 2nd row to be of his formula =IF(I3=I2,J2,J2+1)

3. Get the pivot table of ABOVE and Below

4. Calcluate the MEAN

• =(2 x577 x 683) / (577+683) + 1 = 626.5412698

5. Calculate the Standard Deviation. For this example, i break the formulas into numerator and denoimator

• numerator =(2 x 577 x 683) x (2 x 577 x 683 - 577-683) = 6.20648E+11
• denominator = =1260^2 x (1260-1) = 1998788400
• Divide the numerator / denominator = 310.5119133
• Square root the final answer = SQRT(310.5119133) = 17.62134823

6. Calculate the 95% confidence interval

• Upper Limit = Mean + 1.96 x Standard Deviation = 661.0791124

• Lower Limt = Mean - 1.96 x Standard Deviation = 626.5412698

7. Number of RUNS = 629 (see last excel on the number of RUNS)

Since RUNS (629) is within the 95% confidence interval (between 626.5412698 and 661.0791124), we therefore do not reject the Null Hypothesis which is THERE ARE PRICE RANDOMNESS.

Since there are price randomness, there is no way to predict stock price.