Bayesian Risk Management

Chapter 4Introduction to Sequential Modeling

In the first part of the book, we developed an analysis of how classical statistical methods overlook important dimensions of uncertainty in statistical inference, which lead to errors in estimation and model specification. We undertook that analysis in a static setting in order to make the sources of uncertainty plain with a minimum of complication. Now we begin the work of extending the Bayesian analysis developed previously to a time series setting, allowing us to focus on what is arguably the most important source of model risk: the risk that an adequate description of market phenomena today will not be adequate in the future.

Over the next chapters we develop an approach to time series modeling that is entirely sequential in its orientation, allowing models to adapt themselves continuously to changing market conditions. Developing models that revise and update themselves with each subsequent observation is a necessary response once the assumption of a time-invariant data-generating process is abandoned. We have already argued that it is untenable to assume time-invariant processes for financial data, as well as an abdication of the requisite vigilance for ruptures in market dynamics. Sequential models adapt in response to new information. The more surprising the new information, the more significantly the model adapts. Parameter estimates and their uncertainties will change, models will be assigned more or less posterior probability, ...