A random walk with two absorbing barriers is certain to hit one or other of them in the end. If there is one absorbing barrier and one reflecting one, the random walk will always get to the absorbing barrier. 3.4 Modelling with Random Walks Many models are based on the simple random walk. Random walks may be used for minor elements of complex models. The process of fitting and testing a random walk model is the same in all cases.
Transformation First decide whether the raw process needs a transformation.
A plot should do. A typical transformation is the log-transform. Discretisation Next decide if you want to use a discrete state-space model. If so, the data will need to be adjusted to a grid, by rounding off every observation to the nearest multiple of the mesh size, d . Under a random walk model these should all be i.i.d.