## Signal Extraction & State Space Models

Today, most applications of the technology used at OttoQuant are physical. For example, when a GPS plots your position on a map, it is using similar filtering and smoothing algorithms to those we employ for forecasting and nowcasting. This happens in two steps, illustrated to the right. First, we make a forecast for the next period. Then, as data becomes available, we update this prediction (or nowcast), so that it always incorporates the latest data. The name “state space” comes from the fact that the true state of the model, position in the example to the right, is unobserved. Instead, we use a variety of incoming signals to estimate it.

The big difference between financial, economic, and business applications of these state space models and physical models is how we find parameters. In the latter case, physics provides the answer. Acceleration, for example, is the first derivative of velocity. In the former case, we must estimate parameters. Which brings us to Bayesian statistical methods.

## Bayesian Modeling

Statistical models can generally be described as Bayesian or frequentest. At OttoQuant, we use both methods, and one is not necessarily better than the other, depending on the application. You can, in fact, replicate our frequents (maximum likelihood) models using our open source code. A key difference between the two methods is the use of prior beliefs. In a Bayesian framework, parameters are themselves random variables, and we begin with some belief about their distribution, called a prior. Using priors allows us, for example, to increase or decrease the impact of a certain variable on our model by imposing the belief that a variable is important or unimportant. That is exactly what you do when you adjust the gain for input variables to Bayesian factor models in the OttoQuant interface; you are in fact changing the (inverse-gamma) prior distribution of shocks to the variable. But, of course, you don’t need to know that to use OttoQuant.

## Resources

If you’d like to get your hands dirty, have a look at some of the notes we’ve put together on the subject. These are oriented towards graduate level studies, and assume some familiarity with statistics, calculus, and linear algebra.

An introduction to univariate filters as well as Kalman filtering and smoothing.

An introduction to Bayesain econometrics

An introduction to dynamic factor models