Thank Eugene. That will be a good tool to have.
>From your graph, as expected Kalman responds faster than the EMA to sharp
changes in price. That is to be expected because the averaging constant adapts
to increased volatility. It also appears to overshoot in a few places. That
could be because you have set up the transition matrix to forecast the price by
local linear regression of the price trend, which causes the filter to
overshoot
at discontinities in price trend (i.e. where first derivative of the
time-series
is not defined).
The transition matrix is where the forecasting resides. Also, the filter can
simultaneously forecast multiple time-series, which may affect each other. This
relationship also is encoded in transition matrix.
1. The simplest kalman filter is scalar filter without linear regression
forecasts. This filter provides adaptive average of a single time series and is
most similar to EMA. To set it up in the code, the constructor parameters
should
be set at (1,1):
kalman = new JKalman(1, 1);
The transition matrix should be set up as:
transition_matrix = Matrix.identity(dp, dp);
This should be equivalent to setting the transition matrix tr = 1 ( a scalar,
not a matrix - hence scalar kalman filter).
2. If you think that you want a linear regression forecasts after all, then
the constructor should be: kalman = new JKalman(1, 1);
The transition matrix should be tr = {{1,1},{0,1}}. That non-zero off-diagonal
element in the matrix increments each next step by dx, and creates the
localized
linear regression behavior.
3. If you want to forecast two time series (price and volume, lets say) with
linear regression for each, for example x and y, then the constructor is:
kalman
= new JKalman(4, 2); and tr = { {1, 0, 1, 0}, {0, 1, 0, 1}, {0, 0, 1, 0}, {0,
0,
0, 1} }; By changing off-diagonal elements from 0 to 1 in matrix tr, you could
model linear interaction between those time series.
Another useful information that can be extracted from this software is:
error_cov_post. This is ex post forecasted covariance of the error matrix.
Diagonal elements could be usefull for entry / exit points. Off-diagonal
elements may give some insights into cross- indicator noise sensitivity.
________________________________
From: Eugene Kononov <[email protected]>
To: [email protected]
Sent: Fri, October 22, 2010 9:16:30 PM
Subject: Re: [JBookTrader] Re: Status of Kalman filter?
And here is a comparison.
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