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

2008/3/25, Mike <sfclimbers@xxxxxxxxx>:

Louis,

Forget the book for a minute. Just try to understand the objective.
Until you understand what is trying to be accomplished, you will not
get anywhere.

Given two sets of daily changes, can you say with confidence that the
daily changes did not come from the same strategy?

If the average daily change from the first set of numbers is zero,
and the average daily change from the second set of numbers is NOT
zero. Then, is the strategy that generated the second set of daily
changes really better than the first? Or, was it just a lucky sample
from a strategy whose true daily change really is equal to the first
(i.e. really is zero after all).

The hypothesis is that the two sets of daily changes came from
equivalent strategies (i.e. both zero predictive ability).

The test is to calculate the probability of drawing a sample (whose
average was the non zero average found in the second set of daily
changes), assuming that the true average for the second strategy is
the same as the true average for the first strategy (i.e both true
averages equal to zero).

If the probability is less than your cutoff (e.g. 5%), then reject
the hypothesis and conclude that the strategy that returned the non
zero average daily change must be better than the one that generated
the zero average daily change (i.e. the strategy generating non zero
daily change has predictive ability).

You may find the following link helpful:
http://www.socialresearchmethods.net/kb/stat_t.php

The first script generates the first set of daily changes (log
percent change) for the period being studied. These changes were not
generated by any strategy. They are just a detrended representation
of what the market actually did.

The second script generates the second set of daily changes based on
the buy sell signal of your strategy as applied against the actual
detrended market changes. They are the results of what your strategy
would capture from the detrended market.

Running the second script will not give you a performance number per
se. It will merely allow you to calculate the second detrended
average daily return (i.e. log percent change, presumably non zero)
that must be compared to that of the first script (zero).

If you want to see the actual performance of your strategy (e.g.
compounded average return), you still need to look at the AmiBroker
backtest results.

Also, if you go back and re-read my earlier comments. After running
the first script, the High holds the total of all daily changes for
the period, the Lo holds the number of bars in the period. Dividing
the first by the second gives you the average daily change for the
period, which is then subtracted from the *individual* daily changes,
giving the *detrended* daily changes in the _Close_ such that if you
were to take the average of the Close you would get zero. The only
values you are interested in are the Close values. The rest are just
intermediary values used to calculate the Close.

The second script applies the strategy signal against the Close of
the first script to generate the second set of daily changes (again,
in the Close), the average of which you want to compare to the
results of the first.

I haven't run against the full 25 year period to compare against the
book for any given strategy. Depending on data providers, you may get
very different numbers. Particularly if Aronson used the actual
contents of the SP-500 for each year, as opposed to only the
survivors that currently appear in today's index.

Mike

--- In amibroker@xxxxxxxxxxxxxxx, "Louis Préfontaine"
<rockprog80@xxx> wrote:
>
> Hi Mike,
>
> I took a break from the detrending procedure because I thought I
had a lot
> to learn before been able to apply it. Now I think I am ready for
some more
> testing. I know you took a lot of time to explain how you were
able to do
> build the detrending process, and so I will try not to make
yourself repeat
> yourself.
>
> I did exactly what Aronson did to try the method. I used the
S&P500 from
> November 1980 (November 1, 1980) to Junes 2005 (June 30, 2005) and
used the
> 91 days channel breakout:
>
> Buy=C>Ref (HHV (C,91),-1);
> Sell= C< Ref (LLV (C,91),-1);
> Short=Sell;
> Cover=Buy;
>
> I used Yahoo data and used your detrend script:
>
> 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());
>
> The values I got (in the new file created by your script) are the
following:
>
>
> Hi: 2.21199
> Lo: 0.000355397
>
> And that's why I am stuck.
>
> I tried to apply the 91-days channel breakout to the new file, but
after
> reflexion it makes no sense because the Hi value in that file is a
constant
> while in "real life" it isn't. So I am kind of stucked there, still
> wondering how to apply the rule to the "detrended" data.
>
> If you could help me with that, I would appreciate a lot!
>
> Thanks,
>
> Louis
>
> p.s. For anyone actually trying to do this yourself without having
read
> Aronson, Aronson says the result is +-4% annualized on detrended
data.
>
>
>
>
>
>
>
>
> 2008/3/3, Mike <sfclimbers@xxx>:

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