The anomaly of randomness: - a random event is independent of anything that precedes or follows it; - however, if we fire off a number of random events, and record the outcomes over time, collectively they conform to at least two Univeral Laws (mathematically universal?) ... the Law Of Averages and Sample Error; - looked at from one perspective (over time) the independent events form a pattern i.e. they draw a straight line (a two dimensional pattern);
How can an independent event conform to a generalized Law? Somehow this seems congruent with my observations that the constituents of the S&P are random, from one perspective, and non-random from another (Yahoo EOD - 10 years, eSignal RT 6 months various timeframes). --- In [email protected], "brian_z111" <brian_z...@...> wrote: > > Mandelbrot is a math prof from NY ... his progressive ideas are opposed by > some in the scientific community. > > I read him for the first time when I stumbled over his Scientific American > article recently (decided immediately that I liked him). > > I had already decided that the RandomModel, as the NullHypothesis, was, or > would be, the source of a lot of trouble for financial modelers because I > tentatively thought that many are taking it (randomness) as absolute when it > is only a relative construct ... models based on it are approximations, which > is OK if the applications aren't critical (or highly leveraged, in which case > small +- errors are magnified). > > So, Mandelbrot is confirmation for me that the random model needs to be > rejected for some analysis (he had to reject it, what else could he do?) > > In hindsight there seems to have been a good deal of synchronous discussion > in the forum recently. > > --- In [email protected], "brian_z111" <brian_z111@> wrote: > > > > Very interesting topic. > > > > Mandelbrot is on my short list of fun reading.... obviously at some point I > > might have a look at the real code used by others to produce random data > > etc, including Mandelbrot's, and bring it into AB if it has not already > > been done (at the moment it is more of a trading hobby than a pursuit of > > applications) ... Howard is busy on his third book (advanced stuff) and > > other things so he might publish something interesting to stimulate us > > further on this subject ... perhaps some tools will appear (I am always > > confident that the AB community can surpass what is already out there, at > > least for non-academics). > > > > I also got fascinated by the idea of absolute randomness and started to > > question if it really exists or is it just a useful model? > > > > > > > > --- In [email protected], i cs <ics4mer@> wrote: > > > > > > Hi Brian, > > > > > > Interesting topic. > > > > > > Mandelbrot (seen one fractal, seen em all) has some excellent discussion > > > on synthetic data in his book "The (Mis)Behaviour of markets". He uses > > > a multifractal approach to producing simulated markets. The price > > > behaviour produced by his approach looks identical to real price data and > > > is not "psuedo random" in the ordinary sense. > > > > > > I think you'd like the book, it's very approachable, and all the maths > > > is hidden away in the back. > > > > > > Z > > > > > > > > > > > > > > > ________________________________ > > > From: brian_z111 <brian_z111@> > > > To: [email protected] > > > Sent: Thursday, 18 June, 2009 3:46:20 PM > > > Subject: [amibroker] Re: Benchmarking > > > > > > > > > > > > > > > > > > Fixup > > > > > > /*P_RandomPriceSeri es*/ > > > > > > //Use as a Scan to create PseudoRandomPriceSe ries > > > //Select Current symbol and All quotations in AA, select basetimeframe in > > > AA Settings > > > //It will also create the series if used as an indicator (add the > > > appropriate flag to ATC) > > > // but this is NOT recommended as it will recalculate them on every > > > refresh. > > > //Indicator mode is good for viewing recalculated curves (click in > > > whitespace) > > > //Do not have the indicator code uncommented while running the scan > > > //CommentOut the Scan code before using the indicator code. > > > > > > N = 100;//manually input desired Number - used in Scan AND Indicator mode > > > > > > ///SCAN///// ///////// ///////// ///////// ///////// ///////// ///////// > > > //////// > > > > > > Buy=Sell=0; > > > > > > for( i = 1; i < N; i++ ) > > > > > > { > > > > > > VarSet( "D"+i, 100 * exp( Cum(log(1 + (Random() - 0.5)/100)) ) ); > > > AddToComposite( VarGet( "D"+i ),"~Random" + i,"X",1|2|128) ; > > > //Plot( VarGet( "D"+i ), "D"+i, 1,1 ); > > > //PlotForeign( "~Random" + i,"Random" + 1,1,1); > > > } > > > > > > /* > > > ////PLOT//// ///////// ///////// ///////// ///////// ///////// //// > > > > > > //use the same period setting as for the Scan > > > > > > for( i = 1; i < N; i++ ) > > > > > > { > > > > > > PlotForeign( "~Random" + i,"Random" + i,1,1); > > > > > > } > > > > > > */ > > > > > > ////OPTIMIZE/ ///////// ///////// ///////// ///////// ///////// ///////// > > > //// > > > > > > //use the filter to run on Group253 OR add ~Random + i PseudoTickers to a > > > Watchlist and define by AA filter > > > > > > //fast = Optimize( "MA Fast", 1, 1, 10, 1 ); > > > //slow = Optimize("MA Slow", 4, 4, 20, 1 ); > > > > > > //PositionSize = -100/P; > > > //Buy = Cross(MA(C,fast) ,MA(C,slow) ); > > > //Sell = Cross(MA(C,slow) ,MA(C,fast) ); > > > > > > //Short = Sell; > > > //Cover = Buy; > > > > > > --- In amibro...@yahoogrou ps.com, "brian_z111" <brian_z111@ ...> wrote: > > > > > > > > Following recent discussions on benchmarking and using rule based > > > > systems to engineer returns to meet 'clients' profiles i.e.Samantha' s > > > > MA(C,10) example, I did some follow up R&D with the intent of expanding > > > > the examination a little further via a zboard post. > > > > > > > > I may, or may not, get around to that so in the meantime I decided I > > > > would share a couple of things while they are still topical. > > > > > > > > I made up some quick and dirty randomly generated eq curves so that I > > > > could optimise MA(C,10) on them (out of curiosity). > > > > > > > > Also, out of curiosity, I decided to see how the example signal/filter > > > > code that I made up, as the study piece for Yofas topic on > > > > benchmarking, would actually perform. > > > > > > > > Buy = Ref(ROC(MA(C, 1),1),-1) < 0 AND ROC(MA(C,1), 1) > 0 AND > > > > ROC(MA(C,10) ,1) > 0; > > > > Sell = Cross(MA(C,10) ,C);//no thought went into this exit and I > > > > haven't tried any optimization of the entry or the exit > > > > > > > > By chance I noticed that it outperformed on one or two of the > > > > constituents of the ^DJI (Yahoo data ... 2005 to 2009) and to the naked > > > > eye the constituents all seem to be correlated to a fair extent over > > > > that time range. > > > > > > > > Also, to the naked eye, it outperforms on randomly generated stock > > > > prices around 50% of the time and the outperformnce doesn't appear to > > > > be correlated to the underlying(I haven't attempted to find an > > > > explanation for this). > > > > > > > > Here is the code I used to make up some randomly generated 'stocks'. > > > > > > > > As we would expect it produces, say, 100 price series with a > > > > concatenated mean of around zero (W/L = 1 and PayoffRatio == 1) etc. > > > > When plotted at the same time ... individual price series are dispersed > > > > around the mean in a 'probability cone' ... in this case it is a > > > > relatively tight cone because the method doesn't introduce a lot of > > > > volatility to the series. > > > > > > > > /*P_RandomEquity* / > > > > > > > > //Use as a Scan to create PseudoRandom Equity curves > > > > //Current symbol, All quotations in AA, select basetimeframe in AA > > > > Settings > > > > //It will also create the curves if used as an indicator (add the > > > > appropriate flag to ATC) > > > > // but this is NOT recommended as it will recalculate them on every > > > > refresh. > > > > //Indicator mode is good for viewing recalculated curves (click in > > > > whitespace) > > > > //CommentOut the Scan code before using the indicator code. > > > > //Don't use a very large N or it will freeze up indicator scrolling etc > > > > > > > > n = 100;//manually input desired number - used in Scan AND Indicator > > > > mode > > > > > > > > ///SCAN///// ///////// ///////// ///////// ///////// ///////// > > > > ///////// //////// > > > > > > > > > > > > Buy=Sell=0; > > > > > > > > for( i = 1; i < n; i++ ) > > > > > > > > { > > > > > > > > VarSet( "D"+i, 100 * exp( Cum(log(1 + (Random() - 0.5)/100)) ) ); > > > > AddToComposite( VarGet( "D"+i ),"~Random" + i,"X",1|2|128) ; > > > > //Plot( VarGet( "D"+i ), "D"+i, 1,1 ); > > > > //PlotForeign( "~Random" + i,"Random" + 1,1,1); > > > > } > > > > > > > > /* > > > > ////PLOT//// ///////// ///////// ///////// ///////// ///////// //// > > > > > > > > //use the same number setting as for the Scan > > > > > > > > > > > > for( i = 1; i < n; i++ ) > > > > > > > > { > > > > > > > > PlotForeign( "~Random" + i,"Random" + i,1,1); > > > > > > > > } > > > > > > > > > > > > ////OPTIMIZE/ ///////// ///////// ///////// ///////// ///////// > > > > ///////// //// > > > > > > > > //use the filter to run on Group253 OR add ~Random + i PseudoTickers to > > > > a Watchlist and define by AA filter > > > > > > > > > > > > //fast = Optimize( "MA Fast", 1, 1, 10, 1 ); > > > > //slow = Optimize("MA Slow", 4, 4, 20, 1 ); > > > > > > > > //PositionSize = -100/P; > > > > //Buy = Cross(MA(C,fast) ,MA(C,slow) ); > > > > //Sell = Cross(MA(C,slow) ,MA(C,fast) ); > > > > > > > > //Short = Sell; > > > > //Cover = Buy; > > > > > > > > I also stumbled on this, which seems to have some relevance: > > > > > > > > http://www.scribd. com/doc/6737301/ Trading-eBookCan -Technical- > > > > Analysis- Still-Beat- Random-Systems > > > > > > > > > > > > It contains a link to a site that has a free download of some RNG > > > > produced datasets. > > > > > > > > There hasn't been much discussion on using synthetic data in the forum > > > > ... Patrick recommended it for testing? OR benchmarking? ... Fred is > > > > against using it ("If we knew enough about the characteristics of the > > > > data, in the first place, to be able to create synthetic data then we > > > > would know enough to design trading systems to exploit the data's > > > > profile anyway", OR something like that). > > > > > > > > I was titillated enough by my first excursion into benchmarking with > > > > synthetic data to bring me back for some more. > > > > > > > > > > > > > > > > > > > > > > Access Yahoo!7 Mail on your mobile. Anytime. Anywhere. > > > Show me how: http://au.mobile.yahoo.com/mail > > > > > >
