So my question is as follows. State the conditions a data have to satisfy in order to be represented by a Geometric Brownian motion. Does your data satisfy this condition? Produce appropriate evidence to support your answer.
I have written the following as the answer.
• Since relative change in S is normally distributed, S will be log-normally distributed with parameters μ and σ.
• Over a time t, he random component of a Geometric Brownian motion is normally distributed with mean 0 and variance t.
• The increments St1 – St2, St2 – St3, St3 – St4, etc… are jointly independent random variables.
• Distribution of St1 – St2 = Distribution of St1+1 – St2+1 = Distribution of Stn+k – St2+k . That is distribution depends only on the interval of time between the processes.
Is anything missing? How do I test it using a data that I have?