A great deal of research can be seen as attempts to understand events that move the market suddenly, often in ways that are not embedded in the data. This can be seen in the popularity of a recent financial bestseller, which I shall not name, and must confess to not having read it as yet. It is on my to-do list.
Popular models that try to capture these sudden and different market conditions are listed next. They include regime-switching models based on hidden Markov processes, threshold auto-regressions, and the more complex and bewildering neural networks and other nonlinear processes. A simpler example, which is less about moving regimes, and more about abrupt moves, are what are called Levy processes, of which the most familiar is the Brownian motion with Poisson–Gaussian jumps. These processes can be estimated and applied to financial data.
The question of what data one should look at to find jumps is discussed next. Analyst's forecasts are an interesting example. Although a great deal of interest is focused on earnings forecasts, and their revisions, analysts also look at a company's future progress under different scenarios. These scenarios typically consist of events such as mergers, currency revaluations, significant shifts in the market or sector, and other events that could be thought of as jump processes. The emphasis here is not on a precise forecast of where the price might be in a year's time, but much more about an understanding of the structure of 'what if' events.
It is possible to analyse such forecasts and there are statistical procedures to strip out the jumps from the forecasted or actual returns. While these methods can be questioned because of their strong statistical assumptions, they nevertheless give a fascinating and quite different interpretation to the way we think about returns. In this 'jump world' interpretation of markets, the estimates that one sees puts most of the changes in prices down to jump events, and rather little down to the continuous process such as Brownian motion. Thus prices we see are really just aggregates of extreme events in both directions, often cancelling each other and being smoothed by an ongoing continuous process.
