Dynamic Models

At one point or another, everyone has to face modeling dynamic datasets, by which we mean series of observations that are obviously dependent (like both series in the picture above!). As in the previous chapters, the difficulty in modeling such datasets is to balance the complexity of the representation of the dependence structure against the estimation of the corresponding model—and thus the modeling most often involves model choice or model comparison. We cover here the Bayesian processing of some of the most standard time series models, namely the autoregressive and moving average models, as well as models that are also related to the previous chapter in that the dependence is modeled via a missing variable structure. These models belong to the category of hidden Markov models and include for instance the stochastic volatility models used in finance. Extended dependence structures met in spatial settings will be briefly considered in Chapter 8. The reader should be aware that, due to special constraints related to the long-term stability of the series, this chapter contains more advanced material.