Practical Time Series Analysis

Chapter 7. State Space Models for Time Series

State space models are similar to the statistical models we looked at in the previous chapter but with a more “real-world” motivation. They address concerns that emerge in real-world engineering problems, such as how to factor in measurement error when making estimates and how to inject prior knowledge or belief into estimates.

State space models posit a world in which the true state cannot be measured directly but only inferred from what can be measured. State space models also rely on specifying the dynamics of a system, such as how the true state of the world evolves over time, both due to internal dynamics and the external forces that are applied to a system.

While you may not have seen state space models before in a mathematical context, you have likely used them in your day-to-day life. For example, imagine you see a driver weaving in traffic. You try to determine where the driver is going and how you can best defend yourself. If the driver might be intoxicated, you would consider calling the police, whereas if the driver was temporarily distracted for a reason that won’t repeat itself, you’d probably mind your own business. In the next few seconds or minutes you would update your own state space model of that driver before deciding what to do.

A classic example of where you would use a state space model is a rocket ship launched into space. We know Newton’s laws, so we can write the rules for the dynamics of the system and what ...