I'm familiar with supervised learning algorithms like regression and neural networks which look at a bunch of input points and learn a function which outputs a value (the value varying depending on whether the algo is a classifier, logistic regression, or standard regression)..but I am facing a problem now where each observation I have is a couple of data points (TAQ data), and then after a fixed amount of these chronologically sorted events there is a spike and what appears to follow an exponential decay mean reversion. Every such instance described here is one of my observations and my goal is to predict/model this exponential decay mean reversion.
What type of algorithms would do something like this? time series models a-la ARCH/GARCH followed by a prediction look-ahead of N steps after training them or what else?
Thank you, any type of suggestions or advice/references are greatly appreciated.