**Keywords:**Kalman filter | mean-reverting conditional probabilities | pairs trading | spread | state space models | statistical arbitrage.

Among many strategies for financial trading, pairs trading has been playing an important role

in practical and academic frameworks. Loosely speaking, it consists of a statistical arbitrage

tool for identifying and exploiting ineficiencies of two long-term related financial assets. When

a signficant deviation from this equilibrium is observed, a profit might result. In this work,

we propose a pairs trading strategy entirely based on linear state space models designed for

modeling the spread formed with a pair of assets. Once an adequate state space model for

the spread is estimated, we calculate conditional probabilities that the spread will return to its

long-term mean. The strategy is activated upon large values of these conditional probabilities:

if the latter become large, the spread is bought or sold accordingly. Three applications with

real data from the US and Brazilian markets are offered and indicate that a very basic portfolio

consisting on a sole spread already outperforms some of the main market benchmarks.