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# Exponential Moving Average - Lag

Discussion in 'Technical Analysis' started by jimns, Apr 14, 2008.

1. ### jimns

As is discussed in this forum and elsewhere, any moving average has a lag.

For instance, a simple moving average (SMA) has a lag of half its length so, according to Alexander Elder (Trading for a Living, Section 25. Moving Averages), a SMA would ideally be plotted half its length to the left by setting the Displace input to that amount.

And, according to John Ehlers (Signal Analysis Concepts), an exponential moving average (EMA) has a lag of (L - 1) / 2 where L is the Length input for the EMA indicator. That means that a 13 period EMA would ideally be plotted directly under period 7 ( [13 - 1] / 2 = 6 ) ( 13 - 6 = 7 ) rather than under period 13 and a 10 period EMA would ideally be plotter directly under period 5 or 6 ( [10 - 1] / 2 = 4.5 ) ( 10 - 4.5 = 5.5 ) rather than under period 10.

But according to Elder, a 10 period EMA should be plotted underneath the 7th or 8th period.

So my first question is this - - is Ehlers formula right?

And finally - - should we really be displacing EMA indicators in this way? I can imagine doing that and then mentally extrapolating an extension to the present period - but does anyone actually do that or recommend it, especially for intraday trading?

So here are the questions restated - -

1. Ehlers and Elder seem to disagree - is Ehlersâ (L - 1) / 2 the correct formula for calculating EMA lag?

2. Is there any value to plotting EMAs displaced to the left by the lag as Elder suggests instead of the traditional way (under the current period bar)?

2. ### MandelbrotSet

Moving averages only work in trending markets.

And for them, it doesn't matter what type of moving average or periodicity you use ... they will also show a trend.

3. ### murray t turtle

Did a speed read on Dr Elders moving average chapter.

Amoung the more practical things i had underlined;
====================================
a] EMA
b] support & resistance zones/EMA
c] but they lead to whipsaws in ranges,aka sideways trends;
[only if you use them in a strict mechanical sense.,i noticed over years]

As far as DR Elders 10sma;
plotted underneath the 5 or 6th day, tested lots of ma,
but never used it that way. Each to his own

Multiple ma are great guidlines;
with discretion.

And i like strongstock uptrends like oil/gas.....;

The lag is in the bar itself. The indicator cannot calculate a number until it is reported in real time. I don't see how any displacement can compensate for lag. Price at any moment in time is the only true criteria.

I don't see where either one of their formulas would make a substantive difference interpreting price movement. You're still left with decision-making in real time notwithstanding the lag of indicators - which is inherent in all indicators.

Perhaps you can expand on what you are trying to accomplish.

Interesting post, however.

5. ### jimns

Don't know if you've read Ehlers paper on Signal Analysis Concepts, but you can find it here. In his paper, Ehlers explains that a simple moving average (SMA) reduces a number of periods to a single point that lags one half the width of the observation window. He then goes on to discuss the lag in an exponential moving average (EMA) and, from his formulas one can derive the following formula for EMA lag: Lag = ( L - 1 ) / 2 where L = length of the EMA.

On the other hand, in Trading for a Living Section 25, Elder says "The proper way to plot a simple moving average is to lag it behind prices by half its length. For example, a 10-day simple MA properly belongs in the middle of a 10-day period, and it should be plotted underneath the 5th or 6th day. An exponential moving average is more heavily weighted toward the latest data, and a 10-day EMA should be plotted underneath the 7th or 8th day. Most software packages allow you to lag a moving average."

So what am I trying to accomplish?

I'd like to understand whether anyone lags their EMA as Elder suggests, is there really any value to doing it that way, etc.? And I'd like to understand how the EMA lag is supposed to be calculated since Ehlers and Elder seem to disagree about that.

6. ### yoohoo

What benefit can be achieved from a lagging indicator unless you are going to use mirrors as a signal? This idea never sat well with me - I could see that it worked but I wasn't interested in that - I was interested in when and how often it didn't work.

Anyway, imo Hurst was way ahead in understanding cycles - is that the reason for lagging a MA, to try to identify some pattern that would be useful to predict future PA? If so it's a very limited and therefore risky idea.

If you want to move from MA's into cycles and get real projections for future behaviour with a 90% success rate study Millard... he's miles ahead of anyone else (including MESA/Bressert etc.)

I know I might be a bit off target here, but I think I see your end objective and your approach leaves too much mathematical space between past, present and future market behaviour to be consistently successful. Iâm not trying to rain on your parade, just offering a field of research that might yield more fruit.

7. ### jimns

yoohoo

I agree with you about cycles - but that's another topic for another day perhaps?

I, like you, havenât seen the merit to plotting lagged EMA's or SMA's as Elder suggests so I'd just wanted to better understand what he was suggesting and why.

But Iâm beginning to think that Elder is simply saying this - The lagged data point is all we really have when we calculate a SMA or EMA and to plot that point without the lag creates the incorrect illusion that the SMA or EMA data point is underneath the current bar.

Regardless of how we use SMA or EMA, maybe he is saying that itâs just incorrect and misleading to plot an SMA or EMA under the current bar. I can imagine plotting a lagged MA and then mentally/visually extrapolating the probable next few bars - but Iâve never heard of anyone doing that - have you? And if so, is there any other value to it or are there any rules or subtleties that we might want to be aware of?

And if there is some value to plotting my favored EMAs this way, Iâm still left with the confusion between Ehlers and Elder about just how the EMA lag is supposed to be calculated.

8. ### yoohoo

You ask... "I can imagine plotting a lagged MA and then mentally/visually extrapolating the probable next few bars - but Iâve never heard of anyone doing that - have you? And if so, is there any other value to it or are there any rules or subtleties that we might want to be aware of?"

Yes, that was my point with Millard... in addition to cycles his work on MA projections is the best I've encountered... that's where he is 90% accurate - in the future.

Cycles are cycles are cycles. Millard simply allows us to experiment with cycles like no else ever has. But then to combine them with new MA formulas and projection techniques - utterly amazing what you con do with it.

9. ### jimns

Yoohoo

That's very interesting. Can you suggest where I might start with Millard?

jimns