random walk and stationary process

Discussion relating to general questions on Market Risk Analysis
Forum rules
DISCLAIMER: We do not warrant or represent that this forum or its content is free of viruses, worms or other code that might be contaminating or destructive. We cannot guarantee that documents or files downloaded from the Site will be free from viruses and we do not accept any responsibility for any damage or loss caused by any virus. Accordingly, for your own protection, you must use virus-checking software when using the forum. You must not post or provide to us via the forum, any document or file which you believe may contain a virus. You must virus check any document or file which you intend to post or provide to us via the forum. You must ensure that any document or file you intend to post to the forum does not contravene any applicable laws or contravene any person's legal rights. We do not accept any responsibility for any damage or loss you may suffer.
Posts: 22
Joined: Thu Apr 07, 2011 10:28 am

random walk and stationary process

Postby david » Sun Apr 28, 2013 1:03 am

Dear Carol,

To assume GBM for stock price is equivalent to assume that log price is random walk and log returns is a stationary process in discrete time context. But log returns is a predictable process, as it is a mean-reverting process. But log price is non-predictable in the sense that the best prediction is the current value. So, suppose I am at time 0, i.e. the current time, i want to predict the log price at one time step later i.e. t+1, by random walk assumption, the best prediction is the current log price. But I can use the mean reverting model of the log return to predict the log return over this time step and once i have the predicted log return, i can derive the future log price since I know the log price at t=0. Isnt there an apparent contradiction here??

Look forward to your help,
Much appreciation.


Posts: 9
Joined: Thu Apr 11, 2013 7:06 am

Re: random walk and stationary process

Postby walterzelhofer » Wed May 01, 2013 7:41 am

Hey David,

Think of it this way: the path that the stock takes in log space is made up of random increments (log returns) that builds on itself over time; so no, there is no way to predict where the process will eventually end up...
At best if you're willing to accept the Gaussian distribution governing the distribution of log returns, you may be able to construct a confidence interval (it'll get wider and wider the farther out you look) for the stock price etc. I think what you're referring to is the following: if you know the mean of the return generating process, you're using that to forecast the stock price? It is true that that would give you the center of your confidence interval that I'm talking about, but other than that your forecasts won't be of much use... the interval widens very quickly. Furthermore, I'm very hesitant to believe that returns are independent and normally distributed...

Return to “General”

Who is online

Users browsing this forum: No registered users and 1 guest