-->To Mike --> Re: [amibroker] Re: Aronson Detrending Market {Was Detrending... log}, AmiBroker Email List Archive

2008/3/3, Mike <sfclimbers@xxxxxxxxx>:

Louis,

The first script (Detrend.afl) will detrend the market. Nothing more
to do. If you want to chart the results, open the symbol in a chart
and plot the Close using line format (i.e. not bar or candlesticks).
You will see what appears like an oscillator centered on zero, since
all the values average out. Similarly, if you plotted a histogram, of
the Close values, you would get a normal distribution centered at
zero.

You must code your own strategy into the second script, replacing the
example buy/sell/short/cover with your own logic.

If you are not using a separate symbol to base your signals on, you
can remove the SetForeign/RestorePrice arrays. The parts that are
most important are the setting of trade delays (since the detrended
market data was produced with that assumption) and the generating of
a new composite.

SetTradeDelays(1, 1, 1, 1);

...

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);

Once your buy/sell/cover/short logic is in place, there is nothing
more to do, the resulting composite (e.g. ~SP-500Return) will already
have every thing you need. If you were to plot a histogram of the
Close values, you want to see a normal distribution centered on a
value greater than zero, indicating better than chance results.

Since the second script is *your* trading logic, yes, when running it
the buy/sell signals and all AmiBroker performance data are relevant.
If the system does not perform well based on your personal criteria,
then you really don't care whether or not it is statistically
significant, because you wouldn't want to trade it anyway!

The only thing that you need to do with the two composites is to
compare the results.

Take the mean of the detrended market (e.g. use excel to add all
Close values found in ~SP-500 and divide by the number of values) and
compare it to the mean of your strategy results (again, add all Close
values of ~SP-500Results and divide by the number of values).

If a t-test shows them to be statistically significant, you *might*
be on to something. According to Aronson (by my interpretation) you
would then have to correct for data mining bias.

Note that this is just one approach. Others prefer the much simpler
walk forward analysis and visually evaluating the equity curve. Walk
forward and equity curve evaluation will rule out most of your ideas
long before you ever need to start doing the statistical validation.

Delaying the statistics until after you've got a nice walk forward
equity curve will get you on your way much quicker. Though, if
possible it would still be preferable to do the statistics at that
time.

Walk forward is built in to the most recent release of AmiBroker, and
also available in the free edition of Intelligent Optimizer (see IO
under Files section of this forum). My understanding is that
AmiBroker and IO treat the handling of trades accross boundries
differently, so don't be surprised if you get slightly different
results between them.

Again, I'm no statistician, I wrote the code quickly in the late
hours of the night, and I may not have understood correctly the
process described in the book. So, use all of this as a starting
point, but don't accept any of it as Gospel.

Mike

--- In amibroker@xxxxxxxxxxxxxxx, "Louis Préfontaine"
<rockprog80@xxx> wrote:
>
> Hi again Mike,
>
> Ok I tried the formula without the "setbacktestmode" and it seems
to work.
> I did use the first formula to get the log results of spx.xo (S&P
500) from
> January 9 2007 to December 31, 2007. Then I added all the results
and
> divided by the number of days. -->But what do I do with this
number then?
> (I know it's the number I want to substract from each day result,
but od I
> have to do it manually?)
>
> Then I applied the second formula to the same spx.xo for the same
days.
> When clicking on "backtesting" buying/selling orders were issued.
Are those
> relevant, or do I simply need to look at what's in the new
~spx.xoReturn?
> (I changed DTX--X for spx.xo everywhere in the formula). And when
I open
> this ~spx.xoReturn I get the detrended results but how to use them
with the
> actual stock? I mean: I get all those 0. 000x numbers; how can I
actually
> use my trading system to test my positive/negative bias with this?
>
> Thank you a lot for your help. Your formulas really rock. Thanks!
>
> Louis
>
>
>
> 2008/3/2, Mike <sfclimbers@xxx>:

> >
> > 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 amibroker@xxxxxxxxxxxxxxx <amibroker%
40yahoogroups.com>, "Louis
> > Préfontaine"
> > <rockprog80@> 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 <rockprog80@>:
> > > >
> > > > 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 = "" == 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 <sfclimbers@>:
> >
> > > > >
> > > > > 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 amibroker@xxxxxxxxxxxxxxx <amibroker%

40yahoogroups.com><amibroker%40yahoogroups.com>,
> > > > > "louisprefontaine" <rockprog80@>
> > > > > wrote:
> > > > > >
> > > > > > Anybody can help?
> > > > > >
> > > > > > Thanks,
> > > > > >
> > > > > > Louis
> > > > > >
> > > > > > --- In amibroker@xxxxxxxxxxxxxxx <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
> > > > > > >
> > > > > >
> > > > >
> > > > >
> > > > >
> > > >
> > > >
> > >
> >
> >
> >
>