SSreg

SSreg, short for state-space regression, is a term used in statistics and signal processing to denote a class of regression models that incorporate latent state dynamics through a state-space form. In some contexts, SSreg also refers to software packages or libraries that implement these models. The core idea is to combine a regression structure with a dynamic system that evolves over time, allowing coefficients to change and latent processes to influence observations.

A typical SSreg specification uses an observation equation that links the observed series y_t to a latent state alpha_t and possibly observed regressors x_t, such as y_t = Z_t alpha_t + D_t x_t + epsilon_t. The latent state evolves according to a state equation alpha_{t+1} = T_t alpha_t + R_t eta_t. Estimation relies on Kalman filtering and smoothing, with parameters learned by maximum likelihood, quasi-maximum likelihood, or Bayesian methods. The framework accommodates irregular sampling, missing data, measurement error, and time-varying relationships, making it suitable for time series with evolving dynamics.

Applications span econometrics, engineering, environmental science, and beyond, including dynamic regression, signal decomposition, and forecasting. Software implementations typically provide model specification through matrices or a formula interface, support for exogenous regressors, options for initialization, and facilities for diagnostic checks and out-of-sample forecasts. While several independent projects use the SSreg terminology, the underlying approach remains consistent: represent regression as a state-space model and estimate it with state-space methods.