Does anybody have a good example for Time Series Forecasting/smoothing using Kalman Filter in R?
Solved – R code for time series forecasting using Kalman filter
kalman filterrtime series
Related Solutions
Yes. In fact, this is how the Kalman Filter (KF) is also set up, at least implicitly. The assumptions in place when choosing the KF model, are that the movements and measurements compose a linear dynamical system. The transition matrix, $F_{t-1}$, (in the equation: $\hat{x}_{t|t-1} = F_tx_{t-1} + ...$, where $\hat{x}$ is the predicted state estimate) is in fact indexed by time, so irregular observations shouldn't be an issue.
For a more mathematically rigorous explanation of the KF, Max Welling has a really good tutorial that I highly recommend.
The primary idea behind a Kalman Filter is the optimal or nearly-optimal integration of an analytic model (and its errors) with real world measurements (and the associated measurement errors) to get a best estimate of both the most likely state and the uncertainty in this estimate.
I like to think of the following cartoon as a good way to describe this:
If you can provide the state update relationship then it is pretty straightforward to implement the Kalman filter. The "particle" or "unscented" are about handling the state estimate uncertainty. Given an initial state estimate $ \hat x_{n}(+)$ at time $ t(n)$ what is the function that produces the prediction $ \hat x_{n+1}(-)$ for time $ t(n+1)$? (using notation from pg number 190 on discrete-extended Kalman filters). What is "f"?
Would you think that assuming the value of the stock is constant over time is sufficient? Linear? Personally I like a system of four coupled 4th order ODE's. They have given me some good numeric results.
Best Answer
Have you looked at Time Series Task View at CRAN?
It lists several entries for packages covering Kalman filtering:
and more as this is a pretty common techique for time series estimation.