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> Hi All
>
> I will be most grateful if someone could tell me what is meant by
> amplitude, power and spectrum as related to fourier transforms in general
> and to the FFT function in meastock in particular. And what is the
> advantage of using a detrend smoothing method as opposed to a mean
> smooting method. Further what is the precise meaning of length in the FFT
> function.
>
> In relation to a sine wave or cosine wave, I know that the amplitude is
> the greatest devation from the X-axis, and that frequency is the number of
> cycles per unit time and is the inverse of the period.
>
> I might guess that spectrum means the uncoupled combination of waves of
> which the dominant cycle over a specific time period is only one of many,
> the power is the strength of the dominant cycle and the amplitude is the
> maximum price excursion of the dominant cycle from its mean position.
> Please correct me if I am wrong as I am seeking answers to a confusing
> topic
I know that what we are trying to find out is the dominant cycle
length in days or weeks, etc, which is the same as the period. If the
amplitude of the dominant cycle can be determined in addition to this, then
that is a bonus
ade Kolade
Synopsys Limited
Tel: +44 (0)0207 250 1990
Fax: +44 (0)0207 553 4713
Email: adeniyi.kolade@xxxxxxxxxxxxxxx
www http://www.synopsys.ltd.uk
> ----------------------------------------
> 2.- Equis Support writes: {for better readability have adjusted the
> text}
>
> -The FFT() function does not plot data for all the bars in a chart.
> -The data values should be measured against the Y-axis scale on the side
> of the Chart(right)
> and represent the days of each cycle, eg determined by the numeric value
> of the indicator.
>
> -Try plotting the following formula as an indicator in your chart:
> FFT(C, 100, 1, DETREND, POWER)
> -Then scroll back to the 1st date that's plotted in Chart's most Left
> side.
> -You will now see a short plot in only the first section of the chart.
>
> -This is NOT the calculation for the whole plot, eg its based on PERIOD,
> and therefore
> the indicator only examines the 1st 100 periods of data loaded, eg it
> will leave any other
> data unexamined.
> -Since the explorer only looks at the last bar of data, it does not see
> these values.
>
> -If you enclose the above formula inside other functions, you can carry
> its values
> on to the last bar for the examined PERIOD. For example:
> Highest( FFT(C, 100, 1, DETREND, POWER) )
> -This will report on the 100th day, the highest value the FFT() function
> returned on the data
> it examined.
> -For example:
> LastValue(Highest( FFT(C, 100, 1, DETREND, POWER) )
> -This will transfer over the last report's value, reported on the 100th
> day, onto the last bar in the Chart.
>
> -This data however, is only (in the above example) the HIGHEST value of
> the
> first 100 periods loaded in the Chart (eg the Chart's 1st 100 day's of
> data records) and useless
> when a much later period needed to be examined.
> -Additional parameters to set a specific time period for when data needs
> to be examined are
> not available in program.
> ----------------------------------------
> For a better comparison, do 3a and 3b:
>
> 3a.-Drag the Fourier Tansform ind from the Indicator Builder onto the
> Chart
> -choose for parameters:
> Interpreted: RAW {since we don't want to use MSK's
> defaults}
> TimePeriods: 300
> Length : 1
> PriceField : Close
> Method : Spectrum {Power}
> Smoothing : Detrend
>
> 3b.-Drag the FastFourierTransform ind (eg the custom) onto the Chart
> -the standard build-in FFT function is written as follows:
> FUNCTION(ARRAY,PERIODS,LENGTH,SMOOTHING,METHOD)
> -for creation of the cutom ind, this should be read as:
> FFT(DA,PRDS,LEN,DETRENDorMEAN,POWERorAMPLITUDE)
> where:
> Interpreted: FFT {the function}
> TimePeriods: Prds {examend PERIOD periods}
> Length : Len {1=dly, 5=wkly}
> PriceField : DA {data array}
> Method : POWERorAMPLITUDE {Spectrum(Pwr) or Amplitude}
> Smoothing : DETRENDorMEAN {Detrend(LinReg) or Mean(MovAve)}
> -now used with the same parameters as for the standard ind would
> read
> TimPrds:=300
> FFT(C,TimPrds,1,DETREND,POWER)
> Notes:
> The settings used for the Chart's OPEN|OPTIONS, eg on Open-ing are here
> standard:
> -Load 25000 periods
> -Display 250 periods.
> It will not have much effect on calculations, if you have other settings,
> but
> a minimum Load of say 350 periods is required.
> For the above comparison the DowINDU was used (eg since its holds records
> back to 19800101, what better way to test "some" indicator!).
> ----------------------------------------
> The FFTCycles indicator (see the TAS formulas below) in MetaStock is not
> present, eg
> plain missing, and will therefore have to be created(custom).
>
> 4.-Have printed the FFTCycle attempts(converting the TAS version into a
> MSK version)
> as additional notes below the original TAS version.
>
> ===================================================
> Fast Fourier Transform and Cycle formulas as can be found in the TAS
> program.
>
> 23.1.17 FFT Fast Fourier Transform
>
> Usage: FFT( Array1 )
> Returns: Array
> Description :
> FFT(Array1) "Fast Fourier Transform" function to calculate the
> detrended power spectrum of the array Array1. The detrended
> power
> spectrum is an array [1..n] where the value of each entry is the
> amplitude of the power at the i/n'th frequency. This is
> essentially equivalent to the 'raw' power spectrum shown by
> MetaStock 3.5 and later FFT indicator.
> Example:
> Array X = FFT(CLOSE);
> would place the detrended power spectrum in array X.
>
> 23.1.18 FFTCycle Cycle via Fast Fourier Transform
>
> Usage: FFTCYCLE( Array1 )
> Returns: Array
> Description :
> FFTCycle performs a detrended FFT on array Array1 and then
> creates an array containing cycles found in order from most
> dominant to least dominant.
> The 0th entry of the result array contains the dominant cycle.
> If
> the dominent cycle length is longer than the number of data
> points in the array, no cycle was found.
> Example:
> Array X = FFTCycle(CLOSE);
> IF X[0] < QUOTE_COUNT THEN
> Writeln(`Dominant cycle is `,X[0]);
> ELSE
> WriteLn(`No dominant cycle found');
>
> ===================================================
> Fast Fourier Transform as it cannot be found in MetaStock, eg the Fourier
> Transform
> indicator is only present in program, is basicaly the FFT Function and
> therefore limited
> in use, since the Cycles formula indicator is not present, eg the Cycles
> will
> therefore have to be created as a custom indicator.
>
>
> FFTCycles indicator (Predominate cycles for FastFourierTransform)
> (version for MetaStock 6.5+)
>
> Name: FFTCycle
>
> Formula:
> {The indicator will always return the total
> amount of days a cycle has lasted. If the
> dominent cycle length is longer than the
> number of data points in the array,
> no cycle was found.
> The 0th entry of the result array contains
> the dominant cycle, eg indicator will start
> at day1 of the Chart.}
> =================================================
> {attempt 1}
> TiPrds:=300 {QUOTE_COUNT};
> FFTind:=FFT(C,TiPrds,1,DETREND,POWER);
> FFTtot:=Sum(FFTind,TiPrds);
> FrrHtot:=FFTind>(FFTtot/2)
> {Most Predominate Cycle};
> FrrLtot:=FFTind<(FFTtot/2)
> {Least Predominate Cycle};
> FrrAtot:=FFTtot-(FrrHtot+FrrLtot)
> {Average Predominate Cycle};
> CycMstSig:=HighestSince(1,C>0,FFTind);
> CycLstSig:=LowestSince(1,C>0,FFTind);
> CycPlot:= {= Array X = FFTCycle}
> If(BarsSince(C>0)<=FrrHtot,CycMstSig,
> If(BarsSince(CycMstSig)>=FrrHtot,CycLstSig,
> FrrAtot));
> If(CycPlot<TiPrds,CycPlot,-1)
> {this will only plot a small single dot on the TiPrds day in the Chart}
> ===================================================
> {finding the total amount of available Records in the data file, eg
> to overcome the error:
> "This variable or expression must contain only constant data"}
> Rcrds:=Cum(C>0);
> {Rcrds results are 5098}
> ===================================================
> {attempt 2}
> TiPrds:=300 {QUOTE_COUNT};
> FFTind:=FFT(C,TiPrds,1,DETREND,POWER);
> FFTtot:=Sum(FFTind,TiPrds)
> {total summed values after TiPrds days};
> FFTHtot:=Sum(Highest(FFTind),TiPrds)
> {total summed H values after TiPrds days};
> FFTLtot:=Sum(Lowest(FFTind),TiPrds)
> {total summed L values after TiPrds days};
> FFTAtot:=FFTHtot-FFTLtot
> {total summed Ave values after TiPrds days};
> FrrHtot:={Most Predominate Cycle}
> If(FFTHtot>=((FFTtot/3)*2)=1,FFTHtot/TiPrds,
> {Least Predominate Cycle}
> If(FFTLtot<=((FFTtot/3)*2)=1,FFTLtot/TiPrds,
> {Average Predominate Cycle}FFTAtot/TiPrds));
> FrrHtot
> {this will only plot a small single dot on the TiPrds day in the Chart}
> ====================================================
>
>
> ----- Original Message -----
> From: Theo E.M. Lockefeer
> To: metastock@xxxxxxxxxxxxx
> Sent: vrijdag 25 februari 2000 16:41
> Subject: Re: === Looping constructs.
>
>
>
> Helo Friend Ton and other friends........
>
> ----- Original Message -----
> From: A.J. Maas < anthmaas@xxxxxxxxx>
> To: Metastock-List < metastock@xxxxxxxxxxxxx>
> Sent: February 24, 2000 12:08 AM
> Subject: Re: === Looping constructs.
>
> > 1. Yes
> >
> > 2. Yes : give user definable program control back to its program
> users
> >
> > 3. -see previous FFT mailings below (incl. a reply by Equis
> Support on simular question)
> > -MESA-John Ehlers: I have created a test formula for the ITL,
> but cannot recall if it was
> > also a succes(anyone get
> back to the List with your results or findings).
>
> Ton : i plotted it and it it is invisible ?
>
> Regards Theo L.
>
>
>
>
> > -website of Dennis Meyers, Ph.D. :
> > http://www.meyersanalytics.com/
> > TASC April 1999 article (p.16) by Dennis Meyers, Ph.D. :
> > " The Discrete Fourier Transform Illustion "
> > http://www.traders.com/Abstracts_new/Meyers/Meyers9904.html
> > TASC May 1999 article (p.26) by Dennis Meyers, Ph.D. :
> > " The Endpoint Fast Fourier Transform System "
> > http://www.traders.com/Abstracts_new/Meyers/Meyers9905.html
> > TASC July 1999 Letters to S&C - 2x replies by the Editor
> > http://www.traders.com/Letters/Letters.html
> >
> > test
> > INSTANTANEOUS TREND LINE - JOHN EHLERS (Mesa version for
> MetaStock)
> >
> > DCPL:=Input("Dominant Cycle Periodical Length",1,100,30);
> > DCPLP:=Input("Dominant Cycle PerLength Period",1,1000,1);
> > DA:=MP();
> > SINDA:=Sin(DA)/DA;
> > DCSIN:=FFT(SINDA,DCPL,DCPLP,MEAN,AMPLITUDE);
> > ITLlong:=MP()+Mov(DCSIN,DCPL,S);
> > ITLlong
> >
> > Regards,
> > Ton Maas
> > ms-irb@xxxxxxxxxxxxxxxx
> > Dismiss the ".nospam" bit (including the dot) when replying.
> > Homepage http://home.planet.nl/~anthmaas
> >
> >
> --------------------------------------------------------------------------
> --------
> > ----- Original Message -----
> > From: "Kolade, Adeniyi"
> > To: < metastock@xxxxxxxxxxxxx>
> > Sent: dinsdag 22 februari 2000 17:14
> > Subject: === Looping constructs.
> >
> >
> > > Hi all
> > >
> > > Do you not think that Equis should
> > >
> > > 1 Include looping constructs in the Metastock formula language
> > >
> > > and
> > >
> > > 2 Make the tiny screen area for programming in the Explorer,
> the System
> > > Tester and the Expert Builder expandable to one page at least
> > >
> > > Further can anyone tell me how to make the FFT function works in
> an
> > > exploration. I've tried it out but it returns N/A
> > >
> > > Thanks
> > > ade Kolade
> >
> > ================================================
> >
> >
> > ----- Original Message -----
> > From: "A.J. Maas"
> > To: < metastock@xxxxxxxxxxxxx>
> > Cc: "Walter Lake"
> > Sent: woensdag 4 november 1998 0:42
> > Subject: Re: Fast Fourier Transform and FFT
> >
> >
> > > MESA + John Ehlers(see futher below)
> > > john@xxxxxxxxxxxxxxxx
> > > are now using the Instantanious Trendline wich uses the FFT and
> > > VAR etc(Adaptive) for MAs.
> > >
> > > He has just recently published it to his MESA Users Group.
> > > To join send an email with the word "subscribe" as subject to
> > > users@xxxxxxxxxxxxxxxx
> > > Subject: subscribe
> > >
> > > Regards,
> > > Ton Maas
> > >
> --------------------------------------------------------------------------
> ----
> > > From John Ehlers:
> > > The new FuturesTruth is out. We are delighted to report that
> our R-MESA
> > > is again rated as the #1 S&P daytrading system, this time for
> eight months
> > > in a row. It is also rated as the #1 trading system since
> release. SIERRA
> > > HOTEL continues to be rated as the #1 Japanese Yen system, and
> has now also
> > > garnered the #1 spot for the Deutschemark.
> > >
> > > ******* THE REALLY BIG NEWS *******
> > >
> > > We are excited to announce the release of MESA98 for Windows
> 95/98/NT.
> > > This new release comes on a CD jam-packed with other goodies,
> including a
> > > tutorial, technical articles and PowerPoint slides from my
> recent seminars.
> > > Among these are descriptions of optimum predictive filters,
> linear and
> > > nonlinear Kalman filters, multipole filters, wavelets, and
> myriad of other
> > > cycles-related technology.
> > > Some of the new features of the 32 bit-compiled MESA98 are:
> > > 1) An instantaneous trendline - obtained by completely removing
> the
> > > dominant cycle.
> > > 2) Estimate the cycle amplitude - filter attenuation of the
> cycle swing is
> > > compensated.
> > > 3) Our proprietary Sinewave Indicator that lets you anticipate
> cyclic turns.
> > > 4) Less latency - uses only .75 of a cycle for the measurement.
> > > 5) More accurate - multipole filter preprocessing.
> > > 6) Identification of Trend Modes and Cycle Modes.
> > > 7) Correlate Trend Mode and Cycle Mode signals.
> > > 8) Improved 10 bar prediction.
> > > 9) Intuitive data access to 8 data types - uses a setup wizard.
> > > 10) Output cycle measurements to and ASCII file.
> > > 11) Larger Chart Screen
> > > 12) Large portfolio capability.
> > >
> > > You can download a demo of the MESA98 program from our website
> > > www.mesasoftware.com.
> > > The cost of MESA98 is only $350. That's "out the door". No
> "ups", no
> > > "extras" (except sales tax in California, if applicable). We
> accept VISA,
> > > MC, and American Express cards.
> > > You'll be glad you added MESA98 to your arsenal of trading
> tools.
> > >
> > >
> >
> --------------------------------------------------------------------------
> --------------------
> > Van: John Ehlers < john@xxxxxxxxxxxxxxxx>
> > Aan: undisclosed reciepients
> > Onderwerp: Instantaneous Trendline
> > Datum: zondag 25 oktober 1998 23:19
> >
> > To MESA Users Group:
> > Here is a set of new indicators that you can program
> yourselves. The
> > first of these indicators I call an INSTANTANEOUS TRENDLINE. It
> works
> > because it completely removes the dominant cycle from a smoothing
> average.
> > For the mathematically inclined, the Fourier Transform of a
> rectangular
> > window (formed by a simiple average) is a Sin(X)/X distribution.
> The
> > objective is to place the first null of this distribution exactly
> at the
> > dominant cycle. For the intuitively inclined, what we are doing
> is taking
> > a simple average over the full dominant cycle period. In such an
> average,
> > there are as many sample points above the midpoint as below the
> midpoint
> > with the result that the sum of all these sample points is zero.
> > OK, so all we have to do to get an Instantaneous Trendline is
> to take a
> > simple average whose length is exactly the period of the dominant
> cycle.
> > For those of you who have TradeStation and MESA96, you just insert
> the dc
> > variable for the length of the simple moving average. For those
> of you who
> > have MetaStock or other toolbox packages, you just have to
> estimate the
> > length of the dominant cycle and insert that estimate as your
> moving
> > average period. Of course, this estimate is fixed across your
> entire
> > screen, but the dominant cycle length can be varying. So watch
> out for
> > that problem.
> > The next indicator is created by taking a moving average over
> half the
> > period of a dominant cycle. In this case, the amplitude of the
> dominant
> > cycle is attenuated by exactly 2/PI. Our objective is to restore
> the full
> > amplitude of the cyclic portion. So we take this latest moving
> average,
> > subtract the "Instantaneous Trendline", multiple the difference by
> PI/2
> > (1.57 approximately), and then add the Instantaneous trendline
> back. Since
> > the lag of a moving average is about half the moving average
> window length,
> > this modified half dominant cycle moving average will still lag
> the realy
> > cyclic swing by a quarter cycle.
> > Now, when we look at these two moving averages, we can make
> two
> > assessments. First, we now solve the age-old problem of what is
> the
> > trendline. We have create an adaptive trendline. Secondly, we
> can see the
> > cyclic swing relative to this trendline so that we can assess the
> amplitude
> > of the cyclic movement. If this cyclic amplitude is not several
> times that
> > average daily bar range, then getting an entry and exit for a
> profitable
> > cyclic move becomes a crapshoot. In other words, the signal to
> noise ratio
> > is so low that even though we have identified a good cycle, it is
> not large
> > enough to trade profitably without relying on an intraday fill.
> > Good Trading!!!
> > John
> >
> >
> >
> --------------------------------------------------------------------------
> -----------------------
> >
> > On Tue, 3 Nov 1998 16:19:00 -0600, you wrote:
> >
> > >Since the movements in the stockmarket are not truely periodic,
> is there any
> > >evidence that linear or non-linear Fourier analysis can be
> applied to the
> > >stockmarket?
> >
> > Imo, FA can answer this question: If we do some appropriate kind
> of
> > windowing, we get as a result the "amount of periodic content" vs
> > time, including information about the accompanying frequencies.
> And if
> > periodic content is high, FA can do some kind of meaningful
> > extrapolation.
> >
> > mfg rudolf stricker
> >
> >
> > ----- Original Message -----
> > From: "Lionel and Gail Issen"
> > To: < metastock@xxxxxxxxxxxxx>
> > Sent: dinsdag 3 november 1998 23:19
> > Subject: Re: Fast Fourier Transform and FFT
> >
> > > CCollins:
> > >
> > > The so called FFT in MS is a loser. The dominant cycle always
> comes up as
> > > the length of the time period of the data. The so called cycles
> bear little
> > > resemblance to anything useable. Excel spreadsheets supports
> FFT.
> > > Parenthetically I have never come across anyone who uses MS FFT
> for trading.
> > > I have met many people who collectively use almost all the rest
> of the
> > > functionality of MS,
> > >
> > > Since the movements in the stockmarket are not truely periodic,
> is there any
> > > evidence that linear or non-linear Fourier analysis can be
> applied to the
> > > stockmarket?
> > >
> > > Lionel Issen
> > >
> > > -----Oorspronkelijk bericht-----
> > > Van: C Collins
> > > Aan: metastock@xxxxxxxxxxxxx
> > > Datum: dinsdag 3 november 1998 21:27
> > > Onderwerp: Re: Fast Fourier Transform and FFT
> > >
> > >
> > > > Having recently upgraded to 6.5 and being a multiyear user
> of Metastock
> > > >2.5, 3, 5, etc, there is a part of this function which I have
> never been
> > > >able to coax into functioning. The INTERPRETED choice produces
> the findings
> > > >of long waves from 89 to 500 . Nothing I have done will show
> the smaller
> > > >waves. Also, if the choice of RAW data is made and other
> reasonable choices
> > > >(such as 100, 1, mean, amplitude) are made the result is a
> window with an
> > > >"Y-value" axis, but there is no graph of any type. Has anyone
> succeeded in
> > > >using this function. Also, has anyone ever had there hands on
> software
> > > >called "Epoch Pro" developed by John Ehlers.
> > > >
> > > >From: Manoj Abraham
> > > >> To: support@xxxxxxxxx
> > > >> Cc: metastock@xxxxxxxxxxxxx
> > > >> Subject: RE: Fast Fourier Transform and FFT
> > > >> Date: Tuesday, November 03, 1998 6:17 AM
> > > >>
> > > >> Hi,
> > > >> If Metastock can interpret the Cycles and display it I cant
> understand
> > > >> why it cannot output the value to explorer or into a custom
> indicator.
> > > >> and what is the use of FFT function built into metastock.
> > > >>
> > > >> Manoj Abraham
> > > >>
> > > >>
> > > >>
> > > >> There is not a way to create the interpreted FFT in The
> Explorer. The
> > > >> Explorer uses individual formulas and Fast Fourier Transform
> Interpreted
> > > >> is actually a long series of Raw calculations, and each Raw
> calculation
> > > >> is analyzed to determine 3 dominant cycles.
> > > >>
> > > >> Raw is only one calculation of the series. To manually
> calculate Raw
> > > >> like interpreted would have to run many Raw calculations and
> analyze the
> > > >> Raw number results in a database to determine dominant
> values. This
> > > >> series of calculations is not possible in an Exploration.
> > > >>
> > > >> Equis Support
> > > >> http://www.equis.com/
> > > >> http://www.equis.com/customer/support/
> > > >> Please include previous email answers and questions in your
> response.
> > > >>
> > > >> Equis and MetaStock and MetaStock Professional are registered
> trademarks
> > > >> of Equis International. Achelis Binary Wave, The DownLoader,
> Expert
> > > >> Advisor, OptionScope, Quotecenter, and Smart Charts are
> trademarks of
> > > >> Equis International.
> > > >>
> > > >>
> > > >> > -----Original Message-----
> > > >> > From: Manoj Abraham
> > > >> > Sent: Monday, November 02, 1998 3:11 AM
> > > >> > To: metastock@xxxxxxxxxxxxx
> > > >> > Cc: support@xxxxxxxxx
> > > >> > Subject: Fast Fourier Transform and FFT
> > > >> >
> > > >> > Hi everybody,
> > > >> >
> > > >> > Does anybody know how to get the interpreted FFT value in
> explorer.
> > > >> > When the interpreted Fourier transform is loaded the
> function says
> > > >> > Fourier Transform(Close,-1,-1.0000,Detrend,Amplitude)
> > > >> > Put the same as a new function It gives error messages.
> > > >> >
> > > >> > Manoj Abraham
> >
> >
> >
> >
> >
> >
> >
>
>
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