Aug 18, 2016 · Kalman filter step (_kalman_filter_step method in KalmanFilter class). During this phase we use Kalman filter for every value of current and previous regimes and thus get a battery of P x P filtered states and their covariances, conditional on every previous and current regime combination.
The class Kalman from the QuantEcon.py package implements the Kalman filter. Instance data consists of: the moments $ (\hat x_t, \Sigma_t) $ of the current prior. An instance of the LinearStateSpace class from QuantEcon.py. The latter represents a linear state space model of the form
If interested, I am using Durbin and Koopman's "Time Series Analysis by State Space Methods" and Andrew Harvey's "Forecasting, Structural Time Series Models, and the Kalman Filter" as my main references for this. The former is nice and concise but has a lot of details, suggestions, and use cases.
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We provide introductions to general forecasting methods, time series models in state space form, the Kalman filter and related methods for signal extraction and forecasting. The methods are illustrated for a range of financial time series including asset returns, risk measures, interest rates and the yield curve, house prices, inflation, etc.
But in practice, most pre-packaged time series model programs do not have this facility. (Do add a comment if anyone knows of such a package in Matlab, R, or Python!) Instead of modifying the guts of a likelihood-maximization routine of a time series fitting package, we will examine a short cut in the next proposal.
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