I have got the following question relating to random walks. I would like to determine the moment when a random walk changes from being a simple random walk to start to drift at certain time. This sort of scenario could happen when temperatures start to rise or sea levels droppping. The idea is to detect that change as soon as possible. Clearly if the system is left to drift for a long time, it is fairly obvious it has changed from a given initial level (given by the simple random walk at the start), but I would like to know if it is possible to detect that change very quickly after it happens. What sort of analysis would be needed? Any suggestions greatly appreciated. Many thanks!!
Michael and whuber, I really appreciate your comments. My initial question was in fact related to Quality Control, as I am trying to model a CUSUM as a Random Walk: When the system is in-control, I see it as a simple random walk, when it starts to drift and eventually goes out-of-control, I see it as a drifting random walk. Thus my question as to how (and critically, how quickly) to detect this change from stationary to drifting within random walks. I can see it is not easy to detect the drift, specially when the drift is small due to the stochastic nature of the system. But I think the ARIMA idea will help me, I had not looked at this theory before and thank you for this advice. Mili.