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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 metastock 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 in the FFT function 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 confusing terminology.
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
> ----------
> From: A.J. Maas[SMTP:anthmaas@xxxxxxxxx]
> Reply To: metastock@xxxxxxxxxxxxx
> Sent: 27 February 2000 21:23
> To: Metastock-List
> Subject: Re: === Looping constructs.
>
> 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
>
>
> ----------------------------------------
> 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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