Hi, So... hummm ... maybe :
3- I implemented in the function Hamming Widowing for Burg on the reflection coefficients (from the paper source i send in past mail). I have to test it now. But theorically Burg method don't need windowing so we will see the diff. Noise variance won't be minimised. It is minimised in case of no-windowing. With windowing, we are no more sure to have best fit : http://sepwww.stanford.edu/public/docs/sep65/gilles1/paper_html/node14.html 2- Maybe we can test down sampling the data and interpolate them, like Fred tell to do for his TrigFit. But there is maybe some slightly problem like for exemple : taking in account an notusefull quote (last quote from a consolidating periods for exemple) an dissmis just next quote wich is an importante quote (big price improvements with high volume for exemple). So maybe we have to do non-linear downsampling by just keep dominant in importance (volume, new price...) data. After make a spline interpolation on those data. This can be a good procedure because it is iterative and so don't lose any information if many different sample periods are take. Fred how do you handle this phase in TrigFit (downsampling + interp) ? How does it compare versus classic moving average ? The way i choose for now is to take directly a moving average with high order low pass filter(that is why i choose T3). Noise variance can be a measurment between different method. but I think fit with less sample will be better (because less sample to fit), but prediction will be less good because maybe lose some importante information. To much artifact will be added (spectrogramme will be very different if downsampling is made). 1- The last parameters .... the only one héhé. Like moving average or many indicators... periods on wich we make work the indicator. Euh... heuu... hé : ) Maybe if we take back to the roots of AR modeling... It is said : signal must be stationnary. So we have to choose a period not to long so the signal is stationnary and not to short to find some frequency ! Some idea : minimum = 4 (bacause difficult to draw one period of a sinus with less than 4 points... ?) long = some criterion to test stationnarity... (but those criterion will need a period look back too hé !! : )) ) Cheers, Mich ----- Original Message ----- From: Paul Ho To: [email protected] Sent: Friday, November 17, 2006 3:26 PM Subject: RE: [amibroker] Re: Polynomial Trendlines Thank mich for the info So we have a mechanism to optimize the order of the AR estimator. There remains a couple of interesting areas that would affect the performance of this linear predictor 1. The No of Samples 2. The sample period 3. Windows for I and 2. would Noise Variance still be the measure to minimise? Any thoughts? Paul. From: [email protected] [mailto:[EMAIL PROTECTED] On Behalf Of Tom Tom Sent: Thursday, 16 November 2006 12:28 PM To: [email protected] Subject: Re: [amibroker] Re: Polynomial Trendlines rmserror is the white (theoricaly if AR fitting is good) noise variance estimator. this is compute recursively as you state it with : NoiseVariance[i] = NoiseVariance[i-1] * (1 - K[i]^2) where i is the number of the actual iteration, K reflexion ceof. For i = 0 (before begining iteration from i=1 to P, P the final order desired for the AR), NoiseVariance[0] = Autocorrelation_data[0]; This result comes from Durbin-Levison algorythm wich is used for Burg and Yule-Walker metod. Durbin levison algo gives by recursion : reflexion coef and noise variance. >From this noise variance you can compute Order AR selection for each order during the recursion (FPE, etc...). Your formula seems not good because the reflexion coefs K are not multiplied by anything !? Numerical recipes to take an exemple ( http://www.nrbook.com/a/bookfpdf/f13-6.pdf ) : /* Compute Autocorrelation[0] from data and put it as XMS[0] */ p=0 do 11 j=1,n p=p+data(j)**2 enddo 11 xms=p/n /* during recursion, update is done with */ xms=xms*(1.-d(k)**2) /* where d(k) is last coef. reflex. in the k-th iteration */ Hope it helps. Cheers, Mich. ----- Original Message ----- From: Paul Ho To: [email protected] Sent: Wednesday, November 15, 2006 11:55 PM Subject: RE: [amibroker] Re: Polynomial Trendlines Yes Mich, I noticed that as well, In addition, Currently, memcof seems to calculate the rmserror as sum(data^2) - sum(1 - reflection Coeff^2). Is this valid? if not what do you use to calculate it recursively. Cheers Paul. From: [email protected] [mailto:[EMAIL PROTECTED] On Behalf Of Tom Tom Sent: Thursday, 16 November 2006 7:56 AM To: [email protected] Subject: Re: [amibroker] Re: Polynomial Trendlines Hi ! Thanks Paul ! It is around the same for MEM yes. I find a way to compute it during the recursive process (as you tell it). I have made comparaison between MEM in Numerical Recipes and formula i make from original mathematical recursive formula from Burg. In NR, they make the recurrent loop to compute the Num and Den (use to calculate the coefficient of reflexion k), loop from 1 to M-i (M is number of quotes data, i is incrementing from 1 to ORDER_AR). So for high order AR, most recent data are not taken in consideration !? Same for updating the forward and backward error from the lattice filter, they just considere from 1 to M-i. Original burg formula goes loop from i to M-1, so last data are always here even for high order. -> memcof on Numerical Recipes doesn't respect original algorithm. I don't know why they do this on NR mem algo !? i don't find any source stating than taking [1:M-i] (memcof NR) is better than [i:M-1] (original burg). Mich. __________________________________________________________ Découvrez Windows Live Messenger : le futur de MSN Messenger ! www.windowslivemessenger.fr _________________________________________________________________ Découvrez Windows Live Messenger : le futur de MSN Messenger ! www.windowslivemessenger.fr
