Kalman Filtering

The Kalman filter is a recursive algorithm for linear Gaussian state space models that estimates an unobserved state, such as a time-varying level or trend, by combining model predictions with each new noisy observation.

칼만 필터는 선형 가우시안 상태공간모형에서 모형의 예측과 새로 들어오는 잡음 섞인 관측값을 결합하여 시변 수준이나 추세 같은 관찰되지 않은 상태를 순차적으로 추정하는 알고리즘입니다.

How do I estimate an underlying trend or hidden state from a noisy time series?

잡음이 많은 시계열에서 숨어 있는 추세나 상태를 어떻게 추정하나요?

The Kalman filter estimates unobserved components of a time series, such as a changing level, trend, or regression coefficient, by updating its estimate each time a new observation arrives. It fits linear state space models with Gaussian noise and also handles missing observations, smoothing, and forecasting within one framework.

When to use Kalman Filtering

• A noisy time series whose underlying level or trend changes over time
• Series with missing observations that need filtering or interpolation
• Time-varying parameter regression or structural time-series models

When to use something else

• Strongly nonlinear dynamics: use the extended or unscented Kalman filter, or a particle filter
• Routine level, trend, and seasonal forecasting: use exponential smoothing (Holt-Winters)

Assumptions and requirements

• Linear state and observation equations
• Gaussian, uncorrelated state and observation errors
• Noise variances specified or estimated by maximum likelihood
• Reasonable initial state values or diffuse initialization

What the analysis reports

• Filtered and smoothed state estimates with variances
• One-step-ahead predictions and prediction errors
• Estimated observation and state noise variances
• Log-likelihood and information criteria
• Forecasts with prediction intervals

How to report it

A local level model estimated with the Kalman filter yielded an observation variance of [value] and a state variance of [value], and the smoothed level of [outcome] [description of pattern].

Related methods

• State Space Models
• Exponential Smoothing (Holt-Winters)
• ARIMA

Run Kalman Filtering on Quorant