Registered User
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I created a Percentage True with formula (C>XAVGC200), but I found for many stocks it shows as "Not Enough Data", for example, VRNT. However, there is no problem to plot exponential moving average to the price chart for VRNT. So for VRNT, it should have enough data, right? I do not know what is going wrong. Could you give me a hint? Thanks!
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Worden Trainer
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Hmm... odd. I am not sure why this is but I will look into it.
In the meantime, can you give me an idea what you are trying to find out with this procedure? I might have a workaround for you.
- Craig
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Registered User
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An Exponential Moving Average (EMA) requires data in the amount of about 5 times the period for good accuracy.
Thus, an EMA of period 200 requires about 1000 data values. If there is not that much data available, as in the case of VRNT, the missing data has to be filled in with something and the filter output depends on what that "something" is.
So, the Custom Percent True Indicator is giving an appropriate response and the question should be redirected to how the EMA on the Price chart is calculated.
Thanks,
Jim Murphy
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Seeing that an exponential moving average only needs today and the day before to calculate (a 2-period XMA only needs, in theory, three days) I can see how any stock with 201 days has enough data to calculate the XMA on the chart.
The PCF cannot be building from the first day and calculating the average on a day-by-day basis. I can see where the PCF version is using something like what bustermu mentions above.
I will find out more information tomorrow and share it here.
- Craig
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QUOTE (Craig_S) Seeing that an exponential moving average only needs today and the day before to calculate (a 2-period XMA only needs, in theory, three days) I can see how any stock with 201 days has enough data to calculate the XMA on the chart.
It is true that an EMA needs only today's input and yesterday's output to calculate today's output. That is not the same as saying that an EMA needs only today's input and yesterday's input to calculate today's output.
An EMA of period 2 on C is:
(2/3)*(1*C0+(1/3)*C1+(1/3)^2*C2+(1/3)^3*C3+(1/3)^4*C4+...)
If you use only three inputs, C0,C1,C2, most would consider the results unsatisfactory no matter how you calculate the output.
Thanks,
Jim Murphy
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bustermu,
Three inputs would produce unsatisfactory results if the output was an approximation, but that is not the case here. The output of an Exponential Moving Average on a financial chart is not an approximation if it uses all of the data for the symbol. There is no reason an EMA can't (or shouldn't for that matter) go all the way back to the beginning of a symbol's data as long as the result is adjusted for the sum of the coefficients. The relative weights of the data will still be correct, and requiring bars be available equal to 1, 5, or 7 times the Period is both arbitrary and artificial under such circumstances (it's not quite as artificial if the available data doesn't go back to the actual beginning of the symbol's data).
Since the Exponential Moving Averages in TeleChart do require bars of data equal to 1 times the Period for the Indicator and 5 times the Period for Custom Indicators and Personal Criteria Formulas, it still makes sense to look into why.
-Bruce
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Registered User
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QUOTE (Craig_S) Hmm... odd. I am not sure why this is but I will look into it.
In the meantime, can you give me an idea what you are trying to find out with this procedure? I might have a workaround for you.
Thanks! I am trying to mark a stock on the bottom part of chart if it is above both 100EMA and 200EMA with high volume. I like the % True indicator since it is very easy to see when browsing the charts.
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Registered User
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Bruce,
I have seen no evidence that TC2005 uses all of the available data to calculate an EMA. I doubt that TC2005 uses data from 1915 to calculate say an EMA of period 20 for today on DJ-30 when on Zoom = 9. Maybe, but why bother?
An EMA of period P on C is not plotted in TC2005 until P+1 data points are available and that is too soon. No harm is done if users are made aware of how the calculation is done.
If an EMA is calculated by using the difference equation, it has to be initialized with something and whatever that something is influences the output significantly to begin with but not much after about 5*P input data points.
"The output of an Exponential Moving Average on a financial chart is not an approximation if it uses all of the data for the symbol."
That would require a precise definition of an EMA for the case where only a finite amount of data is available. The most obvious way to do this is to let the initial output be the initial input data point and use the difference equation:
EMA = ((P-1)/(P+1))*EMA.1 + (2/(P+1))*C
for all subsequence outputs. This corresponds to initializing with the initial data point.
How should the coefficients be adjusted? I assume you need to adjust them so that the result still fits whatever definition of the EMA is above. Please give us an example of how the coefficients should be adjusted for P = 2 and for the first say 3 inputs. Notice that if the coefficients are adjusted the way Jim Dean does it, the result is no longer an EMA, but an approximation.
Thanks,
Jim Murphy
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bustermu,
I can pretty much assure you TeleChart doesn't use all of the available data to calculate an Exponential Moving Average. I don't think we disagree on this point.
QUOTE (bustermu) That would require a precise definition of an EMA for the case where only a finite amount of data is available. The most obvious way to do this is to let the initial output be the initial input data point and use the difference equation:
EMA = ((P-1)/(P+1))*EMA.1 + (2/(P+1))*C
for all subsequence outputs. This corresponds to initializing with the initial data point.
Let's look at that method using P=99 and a hypothetical 3-Day old IPO with the somewhat unusual Prices of 100, 1 and 1000 for its first three days....
Day 1: 98/100*100+2/100*100=100
Day 2: 98/100*100+2/100*1=98.2
Day 3: 98/100*98.2+2/100*1000=116.236
That's completely useless drivel (it puts too much weight on Day 1) even if it is correct based on the pencil and paper method originally used to derive an EMA. The reason to use an EMA in the modern era isn't ease of hand calculation, it is because the older data is less import than the newer data and decays in a somewhat natural way. And for that, only one thing is important, each data point is weighted (P+1)/(P-1) more than the previous data point.
QUOTE (bustermu) How should the coefficients be adjusted? I assume you need to adjust them so that the result still fits whatever definition of the EMA is above. Please give us an example of how the coefficients should be adjusted for P = 2 and for the first say 3 inputs. Notice that if the coefficients are adjusted the way Jim Dean does it, the result is no longer an EMA, but an approximation.
I'll use the same P=99 used above for consistency, but that shouldn't make much difference.
Day 1: ((100/98)^0*100)/((100/98)^0)=100
Day 2: ((100/98)^0*100+(100/98)^1*1)/((100/98)^0+(100/98)^1)=50
Day 3: ((100/98)^0*100+(100/98)^1*1+(100/98)^2*1000)/((100/98)^0+(100/98)^1+(100/98)^2)=373.085
You can call this method an approximation if you want, but the results actually make sense and I see it as the real thing. I see the other method, original or not, as an approximation requiring more terms to come up with usable results and best saved for when a shortcut is required to do the calculations by hand.
-Bruce
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Registered User
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Bruce,
The limited numerical evidence I have looked at leads me to believe that plots of EMA's on closing prices are calculated exactly as indicated in the post above.
This is exactly the EMA output one would get if all missing past data were filled in with oldest available data point. This is not the same as filling in with zeros or some SMA of data points, for example.
Users should be aware that this is done.
Thanks,
Jim Murphy
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zliu9999,
I can't think of a reasonable workaround, but that doesn't necessarily mean somebody else won't come up with something.
bustermu,
Knowing how the Exponential Moving Average in TeleChart is calculated is desirable if it plots an EMA when the number of available data points does not exceed the Period of the EMA by whatever factor is required for the desired accuracy. The reason an Exponential Moving Average Indicator will plot when only 1xPeriod points of data are available instead of 5xPeriod points is being looked into. Other than that, the rest of this post isn’t really applicable to anything TeleChart attempts to do currently.
I think seeding EMA = ((P-1)/(P+1))*EMA.1 + (2/(P+1))*C with either a Simple Moving Average or zero is far from optimal when attempting to plot an EMA on early data after an IPO. Seeding with zero produces a result where the EMA of 1 and 1 is less than 1. Seeding with an SMA of the early data points (including an SMA of Period 1) produces results where some data points are not weighted exactly (P+1)/(P-1) more than the previous data point (early data points receive more weight than they should). Whatever the seed, I see EMA = ((P-1)/(P+1))*EMA.1 + (2/(P+1))*C as a shortcut (albeit an almost necessary shortcut when the calculations are done by hand) that produces a really good approximation with enough data.
The quality of the approximation means the exact method used doesn't make much difference if enough data is both available and used for the calculations. The obvious problem with the previous statement is determining how much data is enough. The number of data points and the desired accuracy are pretty much arbitrary. So not plotting an EMA all the way back to the oldest data point when that point is visible on the chart is an artificial limitation considering it is possible to just weight each data point (P+1)/(P-1) more than the previous data point. It only becomes necessary when using EMA = ((P-1)/(P+1))*EMA.1 + (2/(P+1))*C in order to prevent plotting an EMA without the desired accuracy.
-Bruce
Personal Criteria Formulas
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Worden Trainer
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zliu9999
Why not:
1. Create an EasyScan with the PCFs and scan those charts KNOWING where they are relative to the MAs
or
2. Take the PCFs and add them to your WatchList tab OR on the data bar. If you see TRUE there you know.
Customize the Information Displayed in the WatchList
Customize the Data Bar to display selected data points
- Craig
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Registered User
Joined: 12/19/2004
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Yes, I can add it into data bar or screen from PCF. But the major disadvantage of them is that they do not show historical behaviour. For example, using % True indicator I can easily check during the past year how many times this stock matches my buying condition. That is the reason I like % True indicator most.
Is it possible that you fix the issue related to EMA using in % True and we can download the latest TeleChart online. Since you already are able to plot 200 EMA in price chart, I guess it is not difficult to put the same algorithm to the % True indicator.
Thanks!
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Registered User
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Bruce,
The filter you are proposing has been implimented as a fixed length Finite Impulse Response (FIR) filter for approximating the output of an EMA many times by you and Jim Dean. Please see:
Exponential moving averages of formulas in pcfs
There, I make the comment:
"I have never seen this before, but it makes perfectly good sense and it is quite simple and easy to do analytically. More importantly, it stops the weighting of the last (earliest) term from being greater than that of the previous term."
An EMA is a Linear Time Invariant (LTI) Moving Average. The filter you describe is a Linear Time Varying (LTV) Moving Average. The linear difference equation for the EMA has constant coefficients. The linear difference equation for the filter you describe has time varying coefficients.
The output of your filter asymptoticly approaches the output of the corresponding EMA as time increases and should be much preferred to the EMA for inputs of relatively short duration. As far as I am concerned, the filter deserves its own standing aside from its relation to the EMA.
Do you know of others who have used the filter, or are you and Jim Dean the only ones?
Thanks,
Jim Murphy
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 Gold Customer
Joined: 5/4/2005
Posts: 74
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Bruce L:
I find this exchange between you and bustermu interesting ... always something to be learned,
Just to be sure I understand your IPO example in your post of 7.24 @ 3:18 p.m., should not the coefficient of the "1000" term in the numerator be (100/98)^2 rather than (100/98)^1?
And do we care that the coefficient (P+1)/(P-1) be used? All the EMA form requires is that the the exponential coefficient (say "a" in the Infinite Impulse Response filter (i.e. the recursive form) lie in the range 0<a<1 and can be selected for various desired results such a MMSE, etc. My understanding is that the EMA form EMA = ((P-1)/(P+1))*EMA.1 + (2/(P+1))*C
is a hangover from the hand computation days when a linearly weighted moving average (WMA) of period "P" was used to seed the EMA recursive form. Note the similarities bewteen the WMA and EMA recursive expressions. The coefficients are "almost" identical.
markacz
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markacz,
Yes, the example fragment should be (100/98)^2 (fixing now). Thank you. Anyway, I'm not particularly well versed in the history of technical analysis, but it would certainly seem likely the (P-1)/(P+1) exponential coefficient is a hangover from the hand computation days.
-Bruce
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Worden Trainer
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QUOTE (zliu9999) Is it possible that you fix the issue related to EMA using in % True and we can download the latest TeleChart online. Since you already are able to plot 200 EMA in price chart, I guess it is not difficult to put the same algorithm to the % True indicator.
I could be wrong, but I find it more likely any such fix will see the number of data points required to plot a 200-Period Exponential Moving Average increasing instead of the number of data points required to calculate a 200-Period EMA as part of a Personal Criteria Formula or Custom Indicator decreasing.
-Bruce
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... of course just sorting your WatchList by the Visual Difference of the Price and the Average is a simple workaround:
Comparing indicators using Visual Difference sorts
- Craig
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Registered User
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markacz,
The assignment the period P to the EMA is discussed in:
Lag Efficient Moving Average
This assignment causes the EMA and the SMA of the same period P to have the same Lag and also the same Noise Bandwidth (Smoothing). My guess is that the equal Lag relation is due to Jack K. Hutson, although I have never seen his paper on the subject. Comparing filters based on equal Noise Bandwidth occurred long before EMA's were introduced to Technical Analysis.
As far as I know, the assignment of the period P to the EMA has nothing to do with the WMA. I have never seen anyone initialize an EMA with a WMA and do not know of a reason to ever do so. Wells Wilder initializes the EMA with an SMA, but I know of no reason for doing so. You are certainly correct in your implication that there is no reason whatsoever for the period P of an EMA to be constrained to integer values.
I have never seen anyone write a recursive equation for the WMA as they do for the SMA and the EMA. It would not save any computation as far as I can see. Are you sure you did not mean SMA every where you wrote WMA?
Thanks,
Jim Murphy
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bustermu:
I have read ... somewhere in my distant past ... that WMA's were also used for "seeding" the EMA because the WMA is not computation intensive and yields a set of filter outputs whose transfer function weights the present more than the past. The WMA IIR for is quite similar to that of the EMA IIR. The "C" coefficient is indeed 2/(P+1) and the EMA.1 coefficient is "similar". The WMA requires more calculation than the SMA ... but hardly, because the data stream is multiplied by n, n-1, n-2, .... 1.; no exponentiation is required. And as you have noted, I have read most often that the SMA was used.
I have read your prior post in comparing the EMA and SMA and selecting coefficients to equate lag and bandwidth. Makes sense to me, however, I have never seen any papers specifying the EMA coefficients based on your derivations or any other for that matter.
Actually, I have never come across any paper specifically identifying the origin of the coefficients. It might be interesting to transform the EMA to the frequency domain using Z transforms to examine the magnitude (bandwidth) and phase (lag) of the EMA ... althought it seems like too much work to me.
The paper I mentioned above that referenced the WMA did not state as fact that the origin of the EMA coefficients was attributed to the WMA but alluded to it as likely due to the similarity of the IIR form. (I wish I could recall the paper/article ... it's been too long ago).
If you are interested, I could provide you with the WMA IIR.
regards,
markacz
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QUOTE (bustermu) Do you know of others who have used the filter, or are you and Jim Dean the only ones?
While it took some research to find an example of anybody else using it, I do now (and I'm sure additional research would find others, the standard EMA algorithm is just too flawed for use with limited data and the fix too obvious). John C. Gunther published an article in Dr. Dobb's Journal (September 1998) called Discontiguous Exponential Averaging which includes the technique as part of a more extensive set of algorithms designed to produce Exponential Moving Averages corrected for both initialization bias and irregularly spaced data.
We've already discussed correcting the initialization bias. The handling of irregularly spaced data also has obvious uses in technical analysis. As an added bonus, the article also covers Discontiguous Exponential Regression Analysis and has a Sidebar by the same author, What Averaging Window?, also related to the current discussion.
-Bruce
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Gold Customer
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Bruce L:
Thanks for the reference .. I intend to read it.
With regards to bustermu's reference to the use of of truncated (finite impulse response filters FIR), in the Digital Signal Processing (DSP) area (I designed sonar systems prior to my retirement) FIR filters, like that you used in your IPO example, are typically implemented. Incidentally, the the similarity between signal processing and processing stock data is striking. I'm sure there are people applying FFT's, Kalman filters, etc. to processing stock data to extract information. Progress in that application would be interesting to survey. However, takes too much time away from trading.
regards,
markacz
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Registered User
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Bruce,
Thanks for the reference. How you found it, I don't know since you have to read the program to know how the initialization is handled.
It is interesting that when Gunther's maxDT = infinity, the result is an EMA initialized with the initial input data point. When maxDT = 1, the result is the Moving Average you describe. The results stated would not be immediately obvious to the uninitiated.
If you come across additional references, please let us know.
Thanks,
Jim Murphy
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QUOTE (bustermu) How you found it, I don't know since you have to read the program to know how the initialization is handled.
I actually did quite a few other searches first, so when exponential averaging algorithm brought up the article as the first result, "...the initial estimates from exponential smoothing are often unreliable -- with only a few data points, you can't get meaningful averages" was enough to get me to read it all the way through.
QUOTE (bustermu) It is interesting that when Gunther's maxDT = infinity, the result is an EMA initialized with the initial input data point. When maxDT = 1, the result is the Moving Average you describe. The results stated would not be immediately obvious to the uninitiated.
And who knows, I might have missed it if the article hadn't said, "For a data sequence dominated by large random variations, a maxDt of 1 might be more appropriate. Note that the algorithm of Listing Three reduces to Listing Two when maxDt=INFINITY." Then again, maybe not since the algorithm at least looked like it would produce the appropriate results with the correct settings. All it took to know for sure was to install the CPAN module into Perl and run some quick tests.
-Bruce
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Registered User
Joined: 3/15/2005
Posts: 95
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What is the bottom line? How far off is the EMA on the stock chart? I know it will depend upon the data but I need some guidelines as to whether the EMA is usable or should be ignored.
Thanks
bradsticker
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bradsticker,
While certainly not exhaustive, with every symbol I've tested, for Periods running from 2 to 500, for points on the chart where an Exponential Moving Average requiring 5xPeriod points of data will plot, the EMA requiring 1xPeriod of data produces exactly the same results in the Data Box for every point I checked. This is true even when the EMAs are plotted one at a time under circumstances where the the EMA requiring 5xPeriod points of data first starts on the left edge of the chart.
This leads me to the possibly incorrect conclusion that even though the charted Exponential Moving Average Indicator only requires 1xPeriod points of data, it will use 5xPeriod points of data if available (even when another indicator requiring more data is not being charted). So while I think the reason why an Exponential Moving Average plots with only 1xPeriod points of data is worth looking into (and this is being done), I also think the current Exponential Moving Average Indicator is quite usable. If you are still concerned, in many cases, a Custom Indicator can be used in place of the Moving Average Indicator on the charts.
-Bruce
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Worden Trainer
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The bottom line, bradsticker, is the charted EMA is as close to a true total history EMA you will ever see in a computer charting program. If there is a difference in the value of the EMA in TeleChart and if you did it every day by hand for the entire history of the stock... it would be so minimal as to be negligible.
I don't believe these gents are discussing whether the charted EMA's are valid or not... they are discussing some hardcore theory that has (IMHO) gone well beyond the realm of charting in TeleChart (but is still a great read for us math heads).
- Craig
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Registered User
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Thanks! I feel more confident now in using the EMA.
bradsticker
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Registered User
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There is a very noticable and significant difference in an EMA of period 19 using P+1 = 20 terms and one using 5*P+1 = 96 terms. The difference is not so significant when P is small. That is because less than 5*P terms are required for the usual fixed accuracy when P is small.
For TC2005, when you see an EMA on C plotted starting P+1 days after the beginning of the data for a stock, you are looking at a basically meaningless curve and it should be ignored until you are about 5*P away from the beginning of the data.
Please do the following setup:
Zoom = 9
Top Window
Price - Bar Chart
__Moving Average - 500 bars - Exponential (Invisible)
Custom Indicator
Check "Plot using price scale"
Smoothing Average 19 Exponential
Formula C
Be sure there are no other indicators, visible or not. Continuously remove and replace the EMA500 and watch the Custom EMA19 on the left-side of the screen jump each time you do. This is likely due to not using enough terms for the Custom EMA19 unless forced to do so by the presence of the EMA500. This would be easily verified, but I have not done so.
Here are two rules to observe:
1) Ignore the EMA of period P plot within 5*P of the begining of the data.
2) Keep the EMA500 invisible above on all Templates.
I have never observed any problems with EMA's when these rules are observed.
Thanks,
Jim Murphy
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Registered User
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QUOTE (bustermu) There is a very noticable and significant difference in an EMA of period 19 using P+1 = 20 terms and one using 5*P+1 = 96 terms.
If you would like to observe this difference, please do the following setup:
Top Window
Price - Bar Chart
__Moving Average - 19 bars - Exponential
Custom Indicator
Check "Plot using price scale"
Indicator Formula
0.1
*(C0+0.9
*(C1+0.9
*(C2+0.9
*(C3+0.9
*(C4+0.9
*(C5+0.9
*(C6+0.9
*(C7+0.9
*(C8+0.9
*(C9+0.9
*(C10+0.9
*(C11+0.9
*(C12+0.9
*(C13+0.9
*(C14+0.9
*(C15+0.9
*(C16+0.9
*(C17+0.9
*(C18+0.9
*(C19/0.1))))))))))))))))))))
The Custom Indicator uses 1*P+1 = 20 terms and the Moving Average uses 5*P+1 = 96 terms or close enough to it so that you cannot observe the difference. Please observe the difference in the two moving averages.
Thanks,
Jim Murphy
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Gold Customer
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bustermu:
You're right ... quite a difference. However, if you select "use price scale" for your custom indicator, the difference is zilch.
markacz
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Registered User
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markacz,
If you look at both posts again, I did say:
Check "Plot using price scale"
If you got agreement in either, you have not followed the setup description or you need to look at another Symbol.
If you are looking at the setup with the EMA500 and EMA19 and the ENA19 does not move as described, you are not on Zoom 9 or you have another indicator present.
If you are looking at the setup with the two EMA19's and they agree, look at another Symbol.
Thanks,
Jim Murphy
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Gold Customer
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bustermu:
I neglected to use ZOOM=9. And you're right, on ZOOM=9, the differences are noticeable ... but I'm not surprised. You're essentially comparing an IIR with a FIR filter. However, on ZOOM=5 the difference is still zilch for the 20 or so stocks I viewed.
What's interesting, when viewing on ZOOM=9, you can establish an EMA length that minimizes the difference between the EMAxx and the custom FIR.
e.g
Symbol: SM
Setup: As you described above
View the difference
Adjust the EMA19 to EMA 16.
View the difference again ... zilch.
markacz
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Registered User
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Let's not loose sight of the purpose of my post with the Custom EMA19 using 20 days of input. It is not to compare the EMA19 to the 20 day approximation of an EMA19. We already know 20 days is not enough, and, fortunately, no EMA19 in TC2005 behaves like the curve you see.
The purpose of the post is to show the value of the EMA19 re-initialized 19 days ago relative to the value of the EMA19 not re-initialized. If one thinks they are close enough for their purposes, then use the plot of the EMAP P+1 days after the initial data of a Symbol. If not, wait until about 5*P days after the initial data of the Symbol.
Again, there is no EMA19 in TC2005 that actually behaves like the Custom Indicator you see.
Thanks,
Jim Murphy
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