The Kalman filter was an important tool in space exploration, and is often mentioned in connection with the Apollo XI guidance system. Let me make some remarks about where Kalman filtering ideas are used, in areas adjacent to operations research, such as economics.
I once asked Lord Eatwell, President of Queens', and a famous economist, "Is the Kalman filter much used in economics". He immediately replied, "Yes, all the time".
Eatwell is one of the compliers of the Palgrave Dictionary of Economics. It is a good place to go if ever you need to find a short article on any economics topic. I searched in Palgrave for the Kalman Filter, and read:
The Kalman filter
The Kalman filter deals with state-space representations where the transition and measurement equations are linear and where the shocks to the system are Gaussian. The procedure was developed by Kalman (1960) to transform (‘filter’) some original observables $y_t$ into Wold innovations at and estimates of the state $x_t$. With the innovations, we can build the likelihood function of the dynamic model. With the estimates of the states, we can forecast and smooth the stochastic process.
The use of unobserved components opens up a new range of possibilities for economic modelling. Furthermore, it provides insights and a unified approach to many other problems. The examples below give a flavour.
The local linear trend model generalizes (1) by the introduction of a stochastic slope, βt, which itself follows a random walk. Thus ...
Econometricians are often interested in building linear models in which some variables are explained by other variables (in some sort of regression model).
As the values of variables become known over time one wants to update estimates of other variables. The machinery for doing this is provided by the Kalman filter. Notice that the Kalman filter does not have anything to do with the Q assumptions of our LQG model. It is only the Linear Gaussian parts that are relevant.
You might like to try a Google search for "Kalman Filter and finance". Many things turn up. For example, here is a talk, Kalman Filtering in Mathematical Finance.
I once asked Lord Eatwell, President of Queens', and a famous economist, "Is the Kalman filter much used in economics". He immediately replied, "Yes, all the time".
Eatwell is one of the compliers of the Palgrave Dictionary of Economics. It is a good place to go if ever you need to find a short article on any economics topic. I searched in Palgrave for the Kalman Filter, and read:
The Kalman filter
The Kalman filter deals with state-space representations where the transition and measurement equations are linear and where the shocks to the system are Gaussian. The procedure was developed by Kalman (1960) to transform (‘filter’) some original observables $y_t$ into Wold innovations at and estimates of the state $x_t$. With the innovations, we can build the likelihood function of the dynamic model. With the estimates of the states, we can forecast and smooth the stochastic process.
The use of unobserved components opens up a new range of possibilities for economic modelling. Furthermore, it provides insights and a unified approach to many other problems. The examples below give a flavour.
The local linear trend model generalizes (1) by the introduction of a stochastic slope, βt, which itself follows a random walk. Thus ...
As the values of variables become known over time one wants to update estimates of other variables. The machinery for doing this is provided by the Kalman filter. Notice that the Kalman filter does not have anything to do with the Q assumptions of our LQG model. It is only the Linear Gaussian parts that are relevant.
You might like to try a Google search for "Kalman Filter and finance". Many things turn up. For example, here is a talk, Kalman Filtering in Mathematical Finance.
