Do dynlm and dlm have same mathematical expressions?

Question

I am currently using dynamic linear regression (dynlm) for my analysis. However, I do also find another model called dynamic linear model (dlm).

I find that dlm has an official mathematical expression by West and Harrison (1989) and everywhere. However, I cannot find an official mathematical expression for dynlm elsewhere. Even the official R program document verbally explains that it is just an extended version of linear regression that allows additional feature but with no explicit mathematical expression.

Can I assume the official mathematical expression for dynlm and dlm identical? If not, may I know the official mathematical expression for dynlm in r programming?

Answer 1

From Furman university documentation:

The interface and internals of dynlm are very similar to lm, but currently dynlm offers two advantages over the direct use of lm: 1. extended formula processing, 2. preservation of time-series attributes.

For specifying the formula of the model to be fitted, there are additional functions available which facilitate the specification of dynamic models. An example would be d(y) ~ L(y, 2), where d(x, k) is diff(x, lag = k) and L(x, k) is lag(x, lag = -k), note the difference in sign. The default for k is in both cases 1.

The specification of dynamic relationships only makes sense if there is an underlying ordering of the observations. Currently, lm offers only limited support for such data, hence a major aim of dynlm is to preserve time-series properties of the data. Explicit support is currently available for "ts" and "zoo" series. Internally, the data is kept as a "zoo" series and coerced back to "ts" if the original dependent variable was of that class (and not internal NAs were created by the na.action).