DYNAMICLINEAR Procedure
Overview of Dynamic Linear Models
Dynamic linear models (DLMs) emerged in the early 1960s and are intricately linked with state space models (SSMs). Petris, Petrone, and Campagnoli (2009) stated that DLMs held an advantage over the then-popular ARMA models by providing more flexibility in handling nonstationary data, modeling structural changes, and offering increased interoperability.
At the core of DLMs is the idea of considering the outputs of a dynamic system as functions of unobservable or latent state processes that are influenced by random disturbances. By conditioning on these latent variables, DLMs can effectively capture the dependencies within data. A standout feature of DLMs is their Bayesian structure, which facilitates recursive computation. This capability ensures that conditional distributions can be seamlessly updated to incorporate fresh data. Significantly, this can be achieved without the need to retain past data, making DLMs especially well suited for sequential data analysis, online learning, and handling voluminous data sets.
General one-dimension DLMs have the following format:
where
is the observation at time t. 
is the known 
constant or regressor matrix at time t. 
is the state variable. 
is the observation noise, where 
. 
is the state evolution noise, or innovation, where 
. - and are mutually independent.
is the known 
state evolution matrix at time t. 
, where 
is independent of 
and 
for all t.