Kalman Filter
The Kalman filter is the recursive Bayesian update for a linear-Gaussian state-space model: predict the hidden state, then correct with the new observation.
Definition
State x_t = F x_{t−1} + w, observation y_t = H x_t + v, with Gaussian noise. The filter produces a mean and covariance at each t. Smoothers use future data; extended/unscented variants relax linearity.
Why it matters
Nowcasts, term-structure factors, and many ‘unobserved gap’ series are Kalman objects. If the state is wrong, the pretty line is fiction.
Case
GDP nowcasts and Diebold–Li yield-curve factors are often filtered this way. A filter on a misspecified inflation trend will look ‘precise’ and be late.
How to read it
Inspect residuals and whether Q, R were estimated or imposed. A filter that never has large residuals is over-smoothed.
Key papers
Landmark references with real publisher or arXiv links — not token-overlap noise.
- A New Approach to Linear Filtering and Prediction ProblemsKalman · 1960 · ASME J. Basic EngineeringThe Kalman filter.