Kalman will take as an input whatever time-series you give it and will provide as an output a smoothed out version of that time series, with smoothing being optimal in a statistical sense. It can even extrapolate those time-series forward, though I always have less faith in extrapolation than interpolation. It can also provide an estimate of the variance of the prediction, which may be useful for setting entry/exit values for some strategies.
Use of Kalman for smoothing out price or indicator time series is straight forward and obvious, - just a much more powerful version of EMA. I am less clear how to use it at the Strategy level for entry/exit optimization? Are you proposing taking historical entry and exit time series and apply Kalman to smooth out the fluctuations due to noise and then forecast the optimum value one step forward? ________________________________ From: John-Crichton McCutcheon <[email protected]> To: [email protected] Sent: Fri, October 22, 2010 9:55:14 AM Subject: Re: [JBookTrader] Re: Status of Kalman filter? This is more directed at Eugene's previous message. But I'm replying to Michaels email for context. Not to say that applying the Kalman filter for the purpose of getting smoother ( or truer) values for a time series is not a good idea, because it is, but I thought it to be even more than that. Currently, we use the optimizer in JBT to find the 'averaging coefficients' which are most profitable and ( least risky, most consistent, etc. ) then we hard code those coefficients into the Strategy. So those coefficients are optimized based upon their influence on profitability not smoothness. Can we apply Kalman to adapt the 'averaging coefficients' in JBT towards values that are more profitable rather than necessarily for smoothing? Perhaps we can do both: 1) Use Kalman at the Indicator level to smooth out indicators. 2) Use Kalman at the Strategy level to adapt entry - exit parameters to current conditions. ? On 10/21/2010 8:14 PM, Alexana wrote: > Guys, here is some background on Kalman filter: > > There are many flavors of Kalman filter. I think a plain vanilla > implementation of scalar Kalman will be a big imporovement over > Exponential Moving Average (EMA). Kalman filter has a lot of > similarities with EMA and can be used in a similar way but it has one > important advantage, - it adapts to changing conditions. In EMA the > averaging coefficient is constant and, therefore, contribution of the > new information to the average is constant. > > ,In Kalman filter the averaging coefficient it is variable and > adaptive. Kalman, at each prediction step, evaluates the value of new > received information and reduces the averaging coefficient, (or its > equivalent) to give more weight to such information if it is valuable. > Alternatively, it increases the averaging coefficient and reduces the > contribution of the new information if the new information is mostly > noise. > > Because it is such a useful tool, Kalman filter has been used > extensively anywhere where signal has to be extracted from noise. > Every FM radio uses some version of it hard coded into the circuitry. > Vector kalman filters can deal with multiple time-series > simultaneously. Scalar kalman filters deal with only one time series, > like the EMA. > > To give a better intutitive feel, here is a simple modifcation of EMA, > which, while not Kalman, has some of the kalman-like adaptability: > > > Here EMA is the moving average, P(t) is the new data point and K is > the averaging constant: EMA(t) = EMA(t-1) + K*[P(t) - EMA(t-1)] > If we define average error of the prediction > as: > E = Average( [P(t) - EMA(t-1)]^2 ) > and volatility of the predictor > as: > EP = Average ( [EMA(t) - EMA(t-1)]^2 ) > Then adaptive K can be re-computed for each step t > as: K = E / > (EP + E) > E and EP are also re-computed at each step. > > Following Kalman terminology, values of EMA(t), E, EP and K together > define the "state" of the filter at step t. However, a true Kalman > filter would forecast those in a much more sophisticated way. > > > > > > > > > > > > > On Oct 21, 4:38 pm, John-Crichton McCutcheon > <[email protected]> wrote: >> I'm still trying to understand exactly how it works and I'm trying to >> dust up a bit >> on probability/stat,linear algebra, etc. >> >> From a high level, I know It works by making predictions ( state of >> system) and comparing predicted result to actual result and >> then learning from that. So its a self-optimizing system. So what are >> we to predict ? The book ? Makes no sense. >> Price ? If that worked, we'd all be rich. I'm not sure how the "state >> of the system" maps to JBT. It could be a vector of values that tells >> us how much >> money we would have gained by buying or selling , what the book >> indicator is , and what the hold time is for the position. But I'm not >> confident yet. >> >> On 10/21/2010 5:13 PM, new_trader wrote: >> >> >> >>>> I'm not convinced its a big task because we can treat is as a black box >>>> and use some of the 3rd party implementations. I think it boils down to >>>> figuring out how to apply it to JBT. For example, what is to be >>>> estimated by >>>> the filter ? Perhaps the price reactivity to book indicators ? If so, >>>> the we >>>> need an indicator for "price reactivity to book indicator." >>> sounds interesting - can you elaborate a bit more on this? >>> which ready-to-go implementation(s) would you favor/recommend? >>> what data from JBT - either native balance or price or preprocessed >>> and/or smoothed by some indicators - would we feed into such an >>> implementation?- Hide quoted text - >> - Show quoted text - -- You received this message because you are subscribed to the Google Groups "JBookTrader" group. To post to this group, send email to [email protected]. 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