We propose the usage of an innovative method for selecting transients and variables. These sources are detected at different wavelengths across the electromagnetic spectrum spanning from radio waves to gamma-rays. We focus on radio signals and use State Space Models, which are also referred to as Dynamic Linear Models. State Space Models (and more generally parametric autoregressive models) have been the mainstay of economic modelling for some years, but rarely they have been used in Astrophysics. The statistics currently used to identify radio variables and transients are not sophisticated enough to distinguish different types of variability. These methods simply report the overall modulation and significance of the variability, and the ordering of the data in time is insignificant. State Space Models are much more advanced and can encode not only the amount and significance of the variability but also properties, such as slope, rise or decline for a given time t. In this work, we evaluate the effectiveness of State Space Models for transient and variable detection including classification in time-series astronomy. We also propose a method for detecting a transient source hosted in a variable active galaxy, whereby the time-series of a static host galaxy and the dynamic nature of the transient in the galaxy are intertwined. Furthermore, we examine the hypothetical scenario where the target transient we want to detect is the gravitational wave source GW170817 (or similar).