Hi Mike,
Thank you so much for your reply. I really appreciate your step-by-step
advices. This is really amazing to see the work you've done with Aronson's
ideas!
I tried to follow your step-by-step guide but unfortunately it seems there
may be a mistake in the following code:
SetTradeDelays(1, 1, 1, 1); // All trades on next Open afterEOD Signal
SetBacktestMode(backtestRegular); // One symbol, no redundant signals
SetOption("InitialEquity", 100000);
SetOption("AccountMargin", 100);
For some reason I get an error Line 2, Col.: 16 Error 30. Syntax error.
Did I do something wrong? Is it possible to do the same thing in another
way?
Anyway I now fully understand what we're trying to do here. After I got the
ALR for each day, all that will be needed will be to subtract it from day1
to day 2 log. Then we will need to set rules with +1 and -1 value... Well,
I am not 100% sure I fully understand, but it's getting close. If I can
only get past this error...
Thanks a lot!
Louis
2008/3/2, Mike <[EMAIL PROTECTED]>:
>
> I've provided an example of how to use it below. I'm still working on
> this myself, so take all of this with a measure of caution. I have
> not yet gone through all results to verify that there aren't any
> bugs...
>
> If I understand Aronson correctly, after you have have detrended the
> market for the desired period, you then apply your trading strategy
> to generate new log daily returns by multiplying your system state
> (+1 for long, -1 for short) by the detrended log daily returns. You
> then take the mean log daily return generated by your strategy and
> compare it to the mean log daily return of the detrended daily
> returns (i.e. zero).
>
> The purpose is to remove the "conjoint effect of position bias and
> trend" from your strategy results.
>
> If the two means are found to be different (i.e. your strategy
> generates non zero mean) with statistical significance (e.g. using
> student's t-test), then you may conclude* that the returns generated
> by the strategy are not purely by chance.
>
> I use a "*" there because Aronson continues to say that a simple t-
> test is NOT sufficient if you have used data mining to produce your
> strategy. In that case, your results will still include a data mining
> bias that must be removed by applying the Bootstrap method with
> White's reality check, or else the Monte Carlo analysis.
>
> Now for what you're really looking for, a concrete example :)
>
> Still in Chapter 1 of the book, Aronson refers to an example of
> taking signals based on the Dow Jones Transportation Average (DTX--X
> by my data provider), and applying those signals to trade the SP-500.
> The strategy has a long bias and is defined as follows:
>
> Draw a moving average of DTX--X
> Draw an upper band 3% above the moving average
> Draw a lower band 3% below the moving average
> Short the SP-500 when the DTX--X crosses below the lower band.
> Long the SP-500 at all other times.
>
> I believe that I have captured these rules and added backtesting
> support in the script below. After running the backtest, a new symbol
> will be added to your system holding the returns in the Close field
> (e.g. ~SP-500Returns).
>
> Aronson does not say what the moving average should be. It is
> actually a bit of a challenge to find a period where the above is
> profitable! However, after optimizing for the moving average, I found
> that the period 4/27/1998 - 12/31/2000 will show you fully invested
> for the entire range with a 13.69% CAR.
>
> Applying my Detrend.afl script (posted in my last note) against the
> SP-500 over those dates will give a mean log daily return of 2.40265E-
> 10 (i.e. zero).
>
> You can compute the mean log daily return by opening the Quote Editor
> (e.g. select ~SP-500 in symbols tree, then use Symbol | Quote
> Editor... menu item) and copying all the data into Excel, then
> summing all the Close values for the given date range and dividing by
> the number of quotes in that range (678 in this example).
>
> Running the script below against the SP-500 for the same dates will
> will give a mean log daily return of 0.000428057
>
> Again, copy ~SP-500Returns from Quote Editor into Excel and compute
> the mean from the Close data.
>
> Peforming a Student's T-Test over the two sets of log daily returns,
> assuming a shared variance and hypothesizing a shared mean of zero,
> returns a one tailed p-value of 0.272346792. This is well above 0.05
> (the p-value required to reject the hypothesis with 95% confidence)
> and so we cannot reject the hypothesis.
>
> In other words, despite a 13.69% CAR over the period tested, the
> strategy is no better than chance alone and thus should not be traded.
>
> If the p-value had been .05 or less, we still could not conclude
> (according to Aronson) that the strategy was any good because I used
> Optimization (MA period ranging from 5 to 200 increments of 5) to
> find the best rule (data mining bias) and because I used the 3% band
> width suggested in the book (snooping bias - have no idea how much
> optimization was applied to reach that number). Applying Monte Carlo
> analysis would remove the data mining bias (my next effort). There's
> no getting around the snooping bias.
>
> 1. Copy paste the script below to a file on your machine (say
> c:\Program Files\AmiBroker\Formulas\Custom\Results.afl). Make sure
> that you correct any formatting that gets messed up from this post,
> such that AmiBroker likes everything. Use the Tools | Verify Syntax
> menu from the code editor.
>
> 2. Open a chart on the symbol that you want to detrend. For example;
> Aronson used the SP-500 for all his tests.
>
> 3. Open the Automatic Analysis Window
>
> 4. Click the "Pick" button and select the script that you just saved
> (i.e. Results.afl).
>
> 5. Select "current symbol" for the Apply To.
>
> 6. Select "from" for the Range, and enter a from date and a to date
> (e.g. from 4/27/1998 to 12/31/2000).
>
> 7. Click on Backtest
>
> A new symbol will be added to your system having the same name as the
> original, but prefixed with a "~" and appended with "Return", for
> example "~SP-500Return". This symbol will appear in Market 253 and
> contain detrended performance results for the range selected and
> zeros for all other dates.
>
> For each bar in the detrended symbol, the information will be
> arranged as follows:
>
> Close: The detrended log daily return of the strategy (i.e. Pos0 x log
> (Open2/Open1) - ALR).
>
> Note: As per Aronson, Pos0 refers to the strategy signal (+1 for
> long, -1 for short), Open2 refers to the Open two days from now,
> Open1 refers to the Open one day from now, ALR refers to the average
> log daily return of the market (not your strategy results) over the
> period being detrended.
>
> As always, comments, corrections and enhancements are welcomed.
>
> Again, I'm a software developer, not a statistics guy, and this is my
> interpretation of the book. Do your own research before accepting
> taking this as acurate.
>
> If anyone else has done any work in this area, I would very much like
> to hear if their approach agrees with my interpretation.
>
> Thanks,
>
> Mike
>
> SetTradeDelays(1, 1, 1, 1); // All trades on next Open after
> EOD signal
> SetBacktestMode(backtestRegular); // One symbol, no redundant signals
> SetOption("InitialEquity", 100000);
> SetOption("AccountMargin", 100);
>
> Plot(Close, "Close", colorBlue, styleLine);
>
> SetForeign("DTX--X");
> center = MA(Close, Optimize("MA", 40, 5, 200, 5));
> upper = 1.03 * center;
> lower = .97 * center;
>
> Buy = Cross(Close, lower);
> Sell = Cross(lower, Close);
> Short = Sell;
> Cover = Buy;
>
> Plot(Close, "DTX--X Close", colorYellow, styleLine);
> Plot(upper, "DTX--X Upper", colorGreen, styleDashed);
> Plot(center, "DTX--X MA", colorPink, styleLine);
> Plot(lower, "DTX--X Lower", colorRed, styleDashed);
>
> RestorePriceArrays();
>
> BuyPrice = SellPrice = ShortPrice = CoverPrice = Open;
>
> PlotShapes(shapeUpArrow * Buy, colorGreen, 0, Close, -30);
> PlotShapes(shapeDownArrow * Sell, colorRed, 0 , Close, -30);
> PlotShapes(shapeHollowDownArrow * Short, colorRed, 0 , Close, -40) ;
> PlotShapes(shapeHollowUpArrow * Cover, colorGreen, 0, Close, -40);
>
> isLong = Flip(Buy, Sell);
> isShort = Flip(Short, Cover);
> market = Foreign("~" + Name(), "C", false);
>
> AddToComposite(IIF(isLong, 1 * market, 0), "~" + Name()
> + "Return", "C", atcFlagDefaults | atcFlagEnableInBackTest);
> AddToComposite(IIF(isShort, -1 * market, 0), "~" + Name()
> + "Return", "C", atcFlagDefaults | atcFlagEnableInBackTest);
>
> --- In [email protected] <amibroker%40yahoogroups.com>, "Louis
> Préfontaine"
> <[EMAIL PROTECTED]> wrote:
> >
> > Hi again,
> >
> > I've searched thru the manual and I think that += is simply a
> shortcut. I
> > wrote total = total+ raw[i]; instead and there is no more error!
> >
> > I did exactly as you said and got the sign with those huge bars all
> topping
> > at 0.267615. I think I understand what you say, but what is OI?
> >
> > The thing is: I am not sure how to use this. I think what I need
> is to make
> > an average of all this data and then subtract this average from
> each day log
> > of the actual stock to detrend. Am I correct? Would you be kind
> enough to
> > give me some tips about how to use this new information to actually
> backtest
> > one of my rules and see how it performs when it is detrended?
> >
> > Thanks a lot!
> >
> > Louis
> >
> > 2008/3/2, Louis Préfontaine <[EMAIL PROTECTED]>:
> > >
> > > Hi Mike,
> > >
> > > Thank you so much for your reply!
> > >
> > > This is EXACTLY what I am looking for, from the Aronson's book!
> > >
> > > I can't wait to make it work... Right now there is a small
> problem with
> > > the formula... I get an error message for this parti total += raw
> [i]; Ln12:
> > > col:8:Error 30. Syntax error.
> > >
> > > I tried to change the += for = or == and it works... Is it
> possible that
> > > the AB version that I have doesn't recognize the +=? Or maybe
> there is an
> > > error with the +=? Is it possible to get to the same result in
> any other
> > > way?
> > >
> > > Thanks a lot!
> > >
> > > Louis
> > >
> > > 2008/3/2, Mike <[EMAIL PROTECTED]>:
>
> > > >
> > > > Hi,
> > > >
> > > > Based on your formula, I assume that you are referring to
> Chapter 1
> > > > of David Aronson's book: Evidence Based Technical Analysis.
> > > >
> > > > That being the case, I am providing a script below.
> > > >
> > > > However, I believe that the formula that you originally posted
> is not
> > > > correct. Aronson's formula calls for multiplying your boolean
> > > > strategy signal (i.e. +1 for long vs. -1 for short) by the
> detrended
> > > > daily returns, *not* the Close by the returns!
> > > >
> > > > Also, the book does not go into detail for tri-state strategies
> (i.e.
> > > > long/neutral/short) nor for long/neutral or short/neutral
> strategies.
> > > > I'm assuming that plugging in a signal value of 0 would be
> acceptable
> > > > for a neutral position, but haven't researched that yet. So,
> just be
> > > > careful how you use the data once you've detrended it.
> > > >
> > > > Anyway, here is a script that I believe will detrend the market
> > > > returns as per the book. Currently, the script is intended for
> > > > detrending a single symbol. I have not yet got around to making
> it
> > > > work against a watchlist of symbols (coming soon).
> > > >
> > > > 1. Copy paste the script below to a file on your machine (say
> > > > c:\Program Files\AmiBroker\Formulas\Custom\Detrend.afl). Make
> sure
> > > > that you correct any formatting that gets messed up from this
> post,
> > > > such that AmiBroker likes everything. Use the Tools | Verify
> Syntax
> > > > menu from the code editor.
> > > >
> > > > 2. Open a chart on the symbol that you want to detrend. For
> example;
> > > > Aronson used the SP-500 for all his tests.
> > > >
> > > > 3. Open the Automatic Analysis Window
> > > >
> > > > 4. Click the "Pick" button and select the script that you just
> saved
> > > > (i.e. Detrend.afl).
> > > >
> > > > 5. Select "current symbol" for the Apply To.
> > > >
> > > > 6. Select "from" for the Range, and enter a from date and a to
> date
> > > > (e.g. from 1/1/2007 to 12/31/2007).
> > > >
> > > > 7. Click on Backtest
> > > >
> > > > A new symbol will be added to your system having the same name
> as the
> > > > original, but prefixed with a "~", for example "~SP-500". This
> symbol
> > > > will appear in Market 253 and contain detrended market
> information
> > > > for the range selected (e.g. all of 2007 as above) and zeros
> for all
> > > > other dates.
> > > >
> > > > For each bar in the detrended symbol, the information will be
> > > > arranged as follows:
> > > >
> > > > Open: The unadjusted log daily return (i.e. log(Open2/Open1)).
> > > >
> > > > High: The total sum of all unadjusted log daily returns.
> > > >
> > > > Low: The average of all unadjusted log daily returns (i.e. ALR).
> > > >
> > > > Close: The detrended log daily return (i.e. log(Open2/Open1) -
> ALR).
> > > >
> > > > OI: The number of bars over which the data has been detrended.
> > > >
> > > > Note: As per Aronson, Open2 refers to the Open two days from
> now,
> > > > Open1 refers to the Open one day from now, ALR refers to the
> average
> > > > log return over the period being detrended.
> > > >
> > > > Note: I have used the natural logarithm in my code (i.e. ln), as
> > > > opposed to the base 10 logarithm (i.e. log10). I don't know if
> that
> > > > makes a difference.
> > > >
> > > > Note: To find your detrended strategy results, you still must
> write
> > > > your own code to calculate which of the detrended daily returns
> your
> > > > strategy would pick up, and which sign to use (+/-) when
> multiplying
> > > > by the detrended return for that day.
> > > >
> > > > Note: I ran this script against SP-500 for the entire year of
> 2007.
> > > > With my data source, the average detrended log daily return
> (i.e. all
> > > > the Close values of ~SP-500 divided by 251 actual trading days)
> ended
> > > > up being -6.00797E-10 which is effectively zero. So, I'm
> assuming
> > > > that it works.
> > > >
> > > > Corrections and enhancements welcomed :)
> > > >
> > > > Mike
> > > >
> > > > procedure Detrend(compositeName) {
> > > > local range; range = Status("barinrange");
> > > > local raw; raw = log(Ref(Open, 2)/Ref(Open, 1));
> > > > local total; total = 0;
> > > > local count; count = 0;
> > > > local offset; offset = 0;
> > > >
> > > > for (i = 0; i < BarCount; i++) {
> > > > if (range[i]) {
> > > > if (NOT IsNull(raw[i])) {
> > > > count++;
> > > > total += raw[i];
> > > > }
> > > > }
> > > > }
> > > >
> > > > if (count > 0) {
> > > > AddToComposite(IIF(range, raw, Null), "~" + compositeName, "O",
> > > > atcFlagDefaults | atcFlagEnableInBackTest);
> > > >
> > > > offset = total/count;
> > > > raw = IIF(IsNull(raw), offset, raw);
> > > >
> > > > AddToComposite(IIF(range, raw - offset, Null), "~" +
> > > > compositeName, "C", atcFlagDefaults | atcFlagEnableInBackTest);
> > > > AddToComposite(IIF(range, total, Null), "~" +
> compositeName, "H",
> > > > atcFlagDefaults | atcFlagEnableInBackTest);
> > > > AddToComposite(IIF(range, offset, Null), "~" +
> > > > compositeName, "L", atcFlagDefaults | atcFlagEnableInBackTest);
> > > > AddToComposite(IIF(range, count, Null), "~" +
> compositeName, "I",
> > > > atcFlagDefaults | atcFlagEnableInBackTest);
> > > > } else {
> > > > AddToComposite(Null, "~" + compositeName, "X", atcFlagDefaults |
> > > > atcFlagEnableInBackTest);
> > > > }
> > > > }
> > > >
> > > > Buy = Sell = Short = Cover = 0;
> > > > Detrend(Name());
> > > >
> > > > --- In [email protected]
> > > > <amibroker%40yahoogroups.com><amibroker%40yahoogroups.com>,
> > > > "louisprefontaine" <rockprog80@>
> > > > wrote:
> > > > >
> > > > > Anybody can help?
> > > > >
> > > > > Thanks,
> > > > >
> > > > > Louis
> > > > >
> > > > > --- In [email protected]
> > > > > <amibroker%40yahoogroups.com><amibroker%
> 40yahoogroups.com>, "Louis
> > > > Préfontaine" <rockprog80@>
> > > > > wrote:
> > > > > >
> > > > > > I am trying to build a formula to "detrend" the market.
> > > > > >
> > > > > > What I want to set is something like this
> > > > > >
> > > > > > Close of day 0 * ( log (open day2/open day 1) - average log
> > > > > return of
> > > > > > every day of the data available.
> > > > > >
> > > > > > Anybody can do that?
> > > > > >
> > > > > > Thanks,
> > > > > >
> > > > > > Louis
> > > > > >
> > > > >
> > > >
> > > >
> > > >
> > >
> > >
> >
>
>
>
