Pairs Trading: Quantitative Methods and Analysis

CHAPTER 4

Kalman Filtering

INTRODUCTION

Control theory is a branch of engineering that deals with the control of engineering systems. The engineering systems could be from diverse domains, and the applications include controlling the power output of an automotive engine, stabilizing the rate of rotation of an electric motor, and controlling the “rate of reaction” (or the speed of a chemical process). The control of these systems is exercised by the manipulation of so-called control variables. For example, in the case of controlling the power output of an automotive engine, the control variable could be the amount of fuel injected into the engine. This would control the thrust of the piston and therefore the power output from the engine. Similarly, in the other two examples, the control variables could be the amount of current flowing through the motor coils or the ambient temperature of a chemical process. Thus, the control variables provide a harness that helps us to control the system effectively.

Prior to the proposal of Kalman filtering, the typical approach for system control involved the specification of a fully comprehensive mathematical model describing the system dynamics. The model is usually formulated in the form of a differential equation. This helps to determine in a quantitative manner the effects of the control variables on system dynamics. Control is then effected by manipulating the variables as prescribed by the model.

Along with the preceding approach also ...