# Kalman Filter vs. Regression

I'm an economics undergraduate with a fundamental understanding of regression and some experience with machine learning models (e.g. regression trees, boosting). To my knowledge, Kalman Filter is superior in that 1. it can converge to a reliable estimate quickly without the entire population data, and 2. as it updating based on the errors of both the prior estimate and the measurement, it is computationally faster than say rerunning an entire regression.

My application is intended for the finance industry (e.g. asset prices & returns data). My question is: is Kalman Filter more accurate? I think that as a state-space model, it is able to adapt to time series with irregular intervals. As an online model, it should also be far more performant than say a traditional regression model. I think that it is also more accurate than a traditional ARMA model, but I'm not sure how?

Also, I think I have some fundamental misconceptions about the Kalman Filter. From my understanding, it is an algorithm and not a model—what does that mean? K-means is an algorithm that separates data into homogeneous clusters; heterogeneously apart. This answer refers to Kalman Filter as a linear estimator—does that mean that KF is just a way of estimating things, and isn't actually a different way of modelling things?

1. The transition distribution of the state: $$p(X_t|X_{t-1}, \theta)$$.
2. The observation distribution, conditional on the state: $$p(Y_t|X_t, \theta)$$
In the special case where the state space model is linear and Gaussian, the Kalman filter is then a way of deriving the associated sequence of filtering distributions $$p(X_t|Y_1, ..., Y_t, \theta)$$, for each $$t$$, recursively. It also produces the likelihood, as a function of the parameters $$\theta$$, allowing for maximum likelihood estimation of those parameters. So, the state space model is the model, and the Kalman filter is an algorithm which allows for estimation of that model, yes.