 # Hull Moving Average Turning Points and Concavity (2nd Derivatives)

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#### mashume

##### Well-known member
VIP
This thread has exhausted its substantive discussion of this indicator so it has been locked
This thread is still available for reading. If looking for specific information in this thread, here is a great hack for searching many-paged threads.

As I was looking at the Hull Moving Average, it occurred to me that taking the local minimums and maximums might not be the most effective use of it's smooth nature. Nor did it seem that a moving average cross over would provide timely signals.

And then I remembered that I used to teach physics and calculus and decided to look at rates of change and that lead me to...

CONCAVITY

which is nothing but the second derivative of the function (if you remember or not) and so this indicator was born.

It is in two parts -- the upper which is the Hull Moving Average with the addition of colored segments representing concavity and turning points: maxima, minima and inflection. The last of these are of the greatest interest. The second part is a plot of the calculation used in finding the turning points (which is roughly the second derivative of the HMA function, where zero crosses are the inflection points. ### UPPER INDICATOR

Upper HMA colors:
• Green: Concave Up but HMA decreasing. The 'mood' has changed and the declining trend of the HMA is slowing. Long trades were entered at the turning point
• Light Green: Concave up and HMA increasing. Price is increasing, and since the curve is still concave up, it is accelerating upward.
• Orange: Concavity is now downward, and though price is still increasing, the rate has slowed, perhaps the mood has become less enthusiastic. We EXIT the trade (long) when this phase starts. Very little additional upward price movement is likely.
• Red: Concave down and HMA decreasing. Not good for long trades, but get ready for a turning point to enter long on again.

Upper Label Colors:
these are useful for getting ready to enter a trade, or exit a trade and serve as warnings that a turning point may be reached soon
• Green: Concave up and divergence (the distance from the expected HMA value to the actual HMA value is increasing). That is, we're moving away from a 2nd derivative zero crossover.
• Yellow: Concave up but the divergence is decreasing (heading toward a 2nd derivative zero crossover); it may soon be time to exit the trade.
• Red: Concave down and the absolute value of the divergence is increasing (moving away from crossover)
• Pink: Concave down but approaching a zero crossover from below (remember that that is the entry signal, so pink means 'get ready').
Arrows are provided as Buy and Sell and could perhaps be scanned against.

### LOWER INDICATOR

For those who prefer less cluttered uppers, I offer the plot of the divergence from expected HMA values; analogous to the second derivative in that the zero crossovers are of interest, as is the slope of the line. The further from zero, the stronger the curve of the concavity, and the more likely to reach a local minima or maxima in short order.

### Miscelaneous

If you find that there are too many buy and sell signals, you can change the length of the HMA (I find 34 a happy medium, though 55 and sometimes 89 can be appropriate). You can also play with the value of the lookback, though that will slow down signals.

This works well on Daily timeframes as well as intraday candles.

I set it up with High + Low / 2 as the default so that it shouldn't wait for close prices. That may not be appropriate to how you wish to trade.

Mashume

UPPER:
https://tos.mx/cgKFdmm

LOWER:
https://tos.mx/p0k7ims

### UPPER CODE V4

Code:
``````#
# Hull Moving Average Concavity and Turning Points
#  or
# The Second Derivative of the Hull Moving Average
#
# Author: Seth Urion (Mashume)
# Version: 2020-05-01 V4
#
# Now with support for ToS Mobile
#
# Faster, but not necessarily mathematically as good as the first
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare upper;

input price = HL2;
input HMA_Length = 55;
input lookback = 2;

input stddev_len = 21;

plot HMA = HullMovingAvg(price = price, length = HMA_Length);

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

plot turning_point = if concavity != concavity then HMA else double.nan;

HMA.AssignValueColor(color = if concavity == -1 then
if HMA > HMA then color.dark_orange else color.red else
if HMA < HMA then color.dark_green else color.green);

HMA.SetLineWeight(3);

turning_point.SetLineWeight(4);
turning_point.SetPaintingStrategy(paintingStrategy = PaintingStrategy.POINTS);
turning_point.SetDefaultColor(color.white);

plot MA_Max = if HMA[-1] < HMA and HMA > HMA then HMA else Double.NaN;
MA_Max.SetDefaultColor(Color.WHITE);
MA_Max.SetPaintingStrategy(PaintingStrategy.SQUARES);
MA_Max.SetLineWeight(3);

plot MA_Min = if HMA[-1] > HMA and HMA < HMA then HMA else Double.Nan;
MA_Min.SetDefaultColor(Color.WHITE);
MA_Min.SetPaintingStrategy(PaintingStrategy.TRIANGLES);
MA_Min.SetLineWeight(3);

plot sell = if turning_point and concavity == -1 then high else double.nan;
sell.SetDefaultColor(Color.DARK_ORANGE);
sell.SetPaintingStrategy(PaintingStrategy.ARROW_DOWN);
sell.SetLineWeight(3);

plot buy = if turning_point and concavity == 1 then low else double.nan;

def divergence = HMA - next_bar;

addLabel(yes, concat("DIVERGENCE: " , divergence * 10000), color = if concavity < 0 then if divergence > divergence then Color.dark_RED else color.PINK else if divergence < divergence then color.dark_green else color.dark_orange);

def divergence_stddev = StandardDeviation(price = divergence, length = stddev_len);
addLabel(yes, concat("STDDEV: " , divergence_stddev * 10000), color = if absValue(divergence) > absValue(divergence_stddev) then color.blue else color.dark_gray);

###################
#
#
###################

###################
#
# 2020-05-01
#
# MOBILE TOS SUPPORT
#
# Each color of the HMA needs to be a separate plot as ToS Mobile
# lacks the ability to assign colors the way ToS Desktop does.
# I recommend a plain colored HMA behind the line
# Set the line color of the HMA above to gray or some neutral
#
# CCD_D -> ConCave Down and Decreasing
# CCD_I -> ConCave Down and Increasing
# CCU_D -> ConCave Up and Decreasing
# CCU_I -> ConCave Up and Increasing
#
###################
plot CCD_D = if concavity == -1 and HMA < HMA then HMA else double.nan;
CCD_D.SetDefaultColor(Color.RED);
CCD_D.SetLineWeight(3);

plot CCD_I = if concavity == -1 and HMA >= HMA then HMA else double.nan;
CCD_I.SetDefaultColor(Color.DARK_ORANGE);
CCD_I.SetLineWeight(3);

plot CCU_D = if concavity == 1 and HMA <= HMA then HMA else double.nan;
CCU_D.SetDefaultColor(COLOR.DARK_GREEN);
CCU_D.SetLineWeight(3);

plot CCU_I = if concavity == 1 and HMA > HMA then HMA else double.nan;
CCU_I.SetDefaultColor(COLOR.GREEN);
CCU_I.SetLineWeight(3);

#zscore @codydog
input zlength = 13;
input vlevel = 0.00;
def min = lowest(divergence, zlength);
def max = highest(divergence, zlength);
def Zscore = (divergence - Average(divergence, zlength)) / StDev(divergence, zlength);
# addlabel(1,"Zscore Div= " + round(zscore,2), if zscore > vlevel and zscore < 3 then color.blue else if zscore > 3 then color.red else if zscore < -vlevel and zscore > -3 then color.red else if zscore < -3 then color.blue else color.black);``````

### UPPER CODE

Code:
``````#
# Hull Moving Average Concavity and Turning Points
#  or
# The Second Derivative of the Hull Moving Average
#
# Author: Seth Urion (Mashume)
# Version: 2020-02-23 V3
# Faster, but not necessarily mathematically as good as the first
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare upper;

input price = HL2;
input HMA_Length = 21;
input lookback = 2;

plot HMA = HullMovingAvg(price = price, length = HMA_Length);

# def delta_per_bar =
# (fold n = 0 to lookback with s do s + getValue(HMA, n, lookback - 1)) / lookback;

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

plot turning_point = if concavity != concavity then HMA else double.nan;

HMA.AssignValueColor(color = if concavity == -1 then
if HMA > HMA then color.dark_orange else color.red else
if HMA < HMA then color.dark_green else color.green);

HMA.SetLineWeight(3);

turning_point.SetLineWeight(4);
turning_point.SetPaintingStrategy(paintingStrategy = PaintingStrategy.POINTS);
turning_point.SetDefaultColor(color.white);

plot MA_Max = if HMA[-1] < HMA and HMA > HMA then HMA else Double.NaN;
MA_Max.SetDefaultColor(Color.WHITE);
MA_Max.SetPaintingStrategy(PaintingStrategy.SQUARES);

#####

### LOWER CODE

Code:
``````#
# Hull Moving Average Concavity Divergence
#  or
# The Second Derivative of the Hull Moving Average
#
# Author: Seth Urion (Mashume)
# Version: 2020-02-23 V3
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare lower;

input price = OPEN;

input HMA_length = 55;
input lookback = 2;

def HMA = HullMovingAvg(length = HMA_length, price = price);

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

plot zero = 0;
zero.setdefaultcolor(color.gray);
zero.setpaintingstrategy(PaintingStrategy.DASHES);

plot divergence = HMA - next_bar;
divergence.setDefaultColor(Color.LIME);
divergence.SetLineweight(2);

plot cx_up = if divergence crosses above zero then 0 else double.nan;
cx_up.SetPaintingStrategy(PaintingStrategy.POINTS);
cx_up.SetDefaultColor(Color.LIGHT_GREEN);
cx_up.SetLineWeight(4);

plot cx_down = if divergence crosses below zero then 0 else double.nan;
cx_down.SetPaintingStrategy(PaintingStrategy.POINTS);
cx_down.SetDefaultColor(Color.RED);
cx_down.SetLineWeight(4);``````

### NEW VERSION 4

Now with Mobile!
https://tos.mx/NXqbYE9

Last edited by a moderator:
• • QUIKTDR1, shgreenejr, MM325 and 53 others

#### chillc15

##### New member
@mashume I would personally like to say thank you for your input and find this a very interesting take on the Hull and a better representation of a moving average that I have ever seen. The ability for the trader to see possible turning points is most impressive. Understandably we all know or should know that most indicators and moving averages alike are lagging but yours puts a new spin and element into the mix.

The Hull MA can be a useful tool but I do find like others it has its limitations and can overshoot etc. I (personal taste) find the ALMA to be the smoothest of the smooth when it comes to a MA. It has its limitations as well but utilizing other indicators like support and resistance and price action etc works for me.

My question to you is using your formulas, is it possible to apply the same principles and math to the ALMA MA for an upper study MA.

Thank you again.

Last edited:

#### mailbagman2000

##### Member
VIP
Great indicator, is there anyway to backtest and show profit and loss? or run as a scan?

#### mashume

##### Well-known member
VIP

I have a laundry list of things in this post:
1. Variations to scripts
2. Scanner
3. Testing

### Script Variations

@chillc15, I'm intrigued by the Arnaud Legoux MA, and so here is a variant of the upper study that will allow you to choose between Hull, Simple, Exponential, Williams, and ALMA. I haven't gone through the various permutations, but bear in mind that the 'overshoot' and smoothing of the Hull is part of what makes the turning point signal so attractive.

@Miket Used your posted code for the ALMA. Hope you're good with this use. Thanks!

Code:
``````#
# Multiple Moving Average Concavity and Turning Points
#  or
# The Second Derivative of the A Moving Average
#
# via useThinkScript
# request from chillc15
# Added Arnaud Legoux MA and other Moving Averages
#
# Author: Seth Urion (Mahsume)
# Version: 2020-02-22 V2
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare upper;

input price = HL2;
input MA_Length = 21;
input lookback = 2;

input MovingAverage = {default "HMA", "EMA", "SMA", "WMA", "ALMA"};

script ALMA {
# Attributed to Miket
# https://tos.mx/9mznij
input Data = close;
input Window = 9;
input Sigma = 6;
input Offset = 0.85;

def m = (Offset * (Window - 1));
def s = Window/Sigma;

def SumVectorData = fold y = 0 to Window with WS do WS + Exp(-(sqr(y-m))/(2*sqr(s))) * getvalue(Data, (Window-1)-y);
def SumVector = fold z = 0 to Window with CW do CW + Exp(-(sqr(z-m))/(2*sqr(s)));

plot ALMA = SumVectorData / SumVector;
}

plot MA;
switch (MovingAverage) {
case EMA:
MA = MovAvgExponential(price, length = MA_Length);
case SMA:
MA = simpleMovingAvg(price, length = MA_Length);
case WMA:
MA = wma(price, length = MA_Length);
case ALMA:
MA = ALMA(Data = price, window = MA_Length);
default:
MA = HullMovingAvg(price = price, length = MA_Length);
}

def delta = MA - MA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = MA + delta_per_bar;

def concavity = if MA > next_bar then 1 else -1;

plot turning_point = if concavity[-1] != concavity then MA else double.nan;

MA.AssignValueColor(color = if concavity == -1 then
if MA > MA then color.dark_orange else color.red else
if MA < MA then color.dark_green else color.green);

MA.SetLineWeight(3);

turning_point.SetLineWeight(4);
turning_point.SetPaintingStrategy(paintingStrategy = PaintingStrategy.POINTS);
turning_point.SetDefaultColor(color.white);

plot MA_Max = if MA[-1] < MA and MA > MA then MA else Double.NaN;
MA_Max.SetDefaultColor(Color.WHITE);
MA_Max.SetPaintingStrategy(PaintingStrategy.SQUARES);
MA_Max.SetLineWeight(3);

plot MA_Min = if MA[-1] > MA and MA < MA then MA else Double.Nan;
MA_Min.SetDefaultColor(Color.WHITE);
MA_Min.SetPaintingStrategy(PaintingStrategy.TRIANGLES);
MA_Min.SetLineWeight(3);

plot sell = if turning_point and concavity == 1 then high else double.nan;
sell.SetDefaultColor(Color.DARK_ORANGE);
sell.SetPaintingStrategy(PaintingStrategy.ARROW_DOWN);
sell.SetLineWeight(3);

plot buy = if turning_point and concavity == -1 then low else double.nan;

def divergence = MA - next_bar;

addLabel(yes, concat("DIVERGENCE: " , divergence), color = if concavity < 0 then if divergence > divergence then Color.RED else color.PINK else if divergence < divergence then color.green else color.yellow);``````

### SCANS

@mailbagman2000 , Scans, yes...

This scan relies on the upper study being called "Concavity" and is entered on the scan page as a custom.
Code:
``Concavity("hma length" = 55, price = CLOSE)."buy" is true within 2 bars``

Scan 2 -- Stocks approaching possible Buy signals
I thought that, since the lower indicator crossovers can generate signals, that an 'early warning' scan might be of interest. We can scan for any HMA that has a negative convergence, and look for a decrease in the distance below zero. It may be a long way off, it may never get there, but we are alerted before the trade entry.

Code:
``````script ConcavityDivergence {
#
# Hull Moving Average Concavity Divergence
#  or
# The Second Derivative of the Hull Moving Average
#
# Author: Seth Urion (Mahsume)
# Version: 2020-02-21 Initial Public
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare lower;

input price = HL2;

input HMA_length = 34;
input lookback = 2;

def HMA = HullMovingAvg(length = HMA_length, price = price);

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

plot zero = 0;
zero.setdefaultcolor(color.gray);
zero.setpaintingstrategy(PaintingStrategy.DASHES);

plot divergence = displacer(-1, HMA - next_bar);
divergence.setDefaultColor(Color.LIME);
divergence.SetLineweight(2);

plot cx_up = if divergence crosses above zero then 0 else double.nan;
cx_up.SetPaintingStrategy(PaintingStrategy.POINTS);
cx_up.SetDefaultColor(Color.LIGHT_GREEN);
cx_up.SetLineWeight(4);

plot cx_down = if divergence crosses below zero then 0 else double.nan;
cx_down.SetPaintingStrategy(PaintingStrategy.POINTS);
cx_down.SetDefaultColor(Color.RED);
cx_down.SetLineWeight(4);

}

def signal = ConcavityDivergence("hma length" = 55)."concavity";
def HMA = ConcavityDivergence("hma length" = 55)."HMA";
def next = ConcavityDivergence("hma length" = 55)."next_bar";

plot buy = signal < 0 and (HMA - next) > (HMA - next);``````

### TESTING

I used the built-in strategy feature of thinkorswim, with block sizes of 100. All tests were run on 1 year Daily charts, with an HMA length of 55 and set price to CLOSE

First SPX
Strategy: \$77,372
Delta + \$21772 Strategy: \$5202
Delta: + \$3483 Last BA
Strategy: \$14393
Delta: + \$23715 SHORT TIME FRAMES
I did not take time today to test shorter timeframes, though I imagine the results would be good. If there is interest, I'll try to post up some another time.

If you've read this far, thank you.

Last edited:
• • kking, jerome, iAskQs and 29 others

#### toopoor88

##### Member
@mashume Hi, possibly you can link the strategy. For some reason when I try to copy it for a scan or backtest it doesn't work for me .

#### mashume

##### Well-known member
VIP
• StockJockey

#### StockJockey

##### New member
Mashume your script is nothing short of amazing. Thank you , Thank You sir! Is there anyway that I can have the Strategy Version to use without the "addorder" I tested all 3 versions of your script and the strategy version works best for me. I cannot use the strategy version with addorder during the "Normal Market Hours" on thinkorswim , If I disable the Long Enter and Long Exit the visuals disappear. can you please help? TIA !

#### mashume

##### Well-known member
VIP
@StockJockey --

Per your request, below is the exact code from the study, with the buy and sell order mechanics replaced with plots. Hope that gets toward what you wanted.

-mashume

Code:
``````input price = HL2;
input HMA_Length = 21;
input lookback = 2;

def HMA = HullMovingAvg(price = price, length = HMA_Length);

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

def turning_point = if concavity[-1] != concavity then HMA else Double.NaN;

Plot buy = if turning_point and concavity == -1 then low else double.nan;

plot buy = if turning_point and concavity == -1 then low else double.nan;

plot sell = if  turning_point and concavity == 1 then high else double.nan;
sell.SetDefaultColor(Color.DARK_ORANGE);
sell.SetPaintingStrategy(PaintingStrategy.ARROW_DOWN);
sell.SetLineWeight(3);``````

Last edited:
• #### Poc

##### New member
Thanks. Fantastic, spending the weekend playing with chart settings and indicator settings. One request: Add an offset variable for the buy and sell signals to adjust the distance away from the price chart and the indicator. With shorter time frame charts, the arrows tighten down right to the indicator plot and the appearance gets busy.

#### toopoor88

##### Member
@mashume any chance adding a sound alert to the lower and upper?

#### JB7

##### New member
See image, One way to use it is with 30 min ORB/Fib(10-min HK chart) so that we have level to risk off. It seems to be working good, entry when Hull is Red and we break a level. I need help with a scanner and sound alert for this setup, any help is appreciated.

• • Nick, raynzer, scottstots and 2 others

#### mashume

##### Well-known member
VIP
The Upper Indicator code above has had the following lines added to the end:

Code:
``````Alert(condition = buy, text = "Buy", "alert type" = Alert.BAR, sound = Sound.Chimes);

I have NOT yet 'shared' a version with these alerts, but can at some point. This was just a quick fix for those who want them before the morning open. • • jerome, iAskQs, Dman and 1 other person

#### toopoor88

##### Member
I just wanted to give a fair warning that the indicator is roughly 1-2 bars behind when it produces some of its signals. So what you see in the report will be off. For example, was just watching a Futures contract on a 15 min chart for kicks and giggles, and when the signal appeared to buy, it was 2 bars ago making it almost impossible to enter any trades when it says too. Tested it again on Eur/Usd and other stocks using OnDemand. It's still not bad from what I am seeing but if the market is choppy you might get hurt really bad.

• BenTen

#### mashume

##### Well-known member
VIP
TL;DR; There is no Holy Grail.

@BenTen I had noticed that. And I've been trying to come up with a solution...

Part of the issue stems from the indicator relying on the next bar to determine whether the concavity has flipped; the signal will always be at least a bar in the past if CLOSE is used.

I've been trying to do the maths to solve the HMA for a the next minimum value that would cause a flip on say a daily aggregation (or anything higher than current) and plot that line on an intraday chart. It's just a matter of rearranging the equations for the HMA to solve for the most recent price, given the value the HMA needs to reach for a concavity flip (which is a known value).

With all that said, I did whip up a version of the lower study that is a bar faster than the old version. It doesn't line up with the old version of the upper, and so I've got a new upper too.

HOWEVER. There is no Holy Grail of Indicators. The power of the turning point lies behind a mist of only being able to know it has turned one bar into the future... we can't know we've turned with certainty (even with an intraday study as described above) without the next value.

### NEW LOWER

Code:
``````#
# Hull Moving Average Concavity Divergence
#  or
# The Second Derivative of the Hull Moving Average
#
# Author: Seth Urion (Mahsume)
# Version: 2020-02-23 V3
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare lower;

input price = OPEN;

input HMA_length = 55;
input lookback = 2;

def HMA = HullMovingAvg(length = HMA_length, price = price);

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

plot zero = 0;
zero.setdefaultcolor(color.gray);
zero.setpaintingstrategy(PaintingStrategy.DASHES);

plot divergence = HMA - next_bar;
divergence.setDefaultColor(Color.LIME);
divergence.SetLineweight(2);

plot cx_up = if divergence crosses above zero then 0 else double.nan;
cx_up.SetPaintingStrategy(PaintingStrategy.POINTS);
cx_up.SetDefaultColor(Color.LIGHT_GREEN);
cx_up.SetLineWeight(4);

plot cx_down = if divergence crosses below zero then 0 else double.nan;
cx_down.SetPaintingStrategy(PaintingStrategy.POINTS);
cx_down.SetDefaultColor(Color.RED);
cx_down.SetLineWeight(4);``````

### NEW UPPER

Code:
``````#
# Hull Moving Average Concavity and Turning Points
#  or
# The Second Derivative of the Hull Moving Average
#
# Author: Seth Urion (Mahsume)
# Version: 2020-02-23 V3
# Faster, but not necessarily mathematically as good as the first
#
# This code is licensed (as applicable) under the GPL v3
#
# ----------------------

declare upper;

input price = HL2;
input HMA_Length = 21;
input lookback = 2;

plot HMA = HullMovingAvg(price = price, length = HMA_Length);

# def delta_per_bar =
# (fold n = 0 to lookback with s do s + getValue(HMA, n, lookback - 1)) / lookback;

def delta = HMA - HMA[lookback + 1];
def delta_per_bar = delta / lookback;

def next_bar = HMA + delta_per_bar;

def concavity = if HMA > next_bar then 1 else -1;

plot turning_point = if concavity != concavity then HMA else double.nan;

HMA.AssignValueColor(color = if concavity == -1 then
if HMA > HMA then color.dark_orange else color.red else
if HMA < HMA then color.dark_green else color.green);

HMA.SetLineWeight(3);

turning_point.SetLineWeight(4);
turning_point.SetPaintingStrategy(paintingStrategy = PaintingStrategy.POINTS);
turning_point.SetDefaultColor(color.white);

plot MA_Max = if HMA[-1] < HMA and HMA > HMA then HMA else Double.NaN;
MA_Max.SetDefaultColor(Color.WHITE);
MA_Max.SetPaintingStrategy(PaintingStrategy.SQUARES);
MA_Max.SetLineWeight(3);

plot MA_Min = if HMA[-1] > HMA and HMA < HMA then HMA else Double.Nan;
MA_Min.SetDefaultColor(Color.WHITE);
MA_Min.SetPaintingStrategy(PaintingStrategy.TRIANGLES);
MA_Min.SetLineWeight(3);

plot sell = if turning_point and concavity == -1 then high else double.nan;
sell.SetDefaultColor(Color.DARK_ORANGE);
sell.SetPaintingStrategy(PaintingStrategy.ARROW_DOWN);
sell.SetLineWeight(3);

plot buy = if turning_point and concavity == 1 then low else double.nan;

def divergence = HMA - next_bar;

addLabel(yes, concat("DIVERGENCE: " , divergence), color = if concavity < 0 then if divergence > divergence then Color.RED else color.PINK else if divergence < divergence then color.green else color.yellow);

### CAVIAT LECTOR

Be aware that these do not backtest as well as the original versions, perhaps because mathematically they do not represent the turning points as well... I'm not sure why.

As always,
mashume

#### toopoor88

##### Member
@mashume Can you again link the Strat for the new upper, please.

#### toopoor88

##### Member
Also to add, new version is much more realistic but its 1 bar behind sometimes, which is way better than 2. So if you were to backtest this, the results will still be off a little but not as bad as before. Example: Today S&P 500 futures the top indicator stated a buy at 3251.75 on a 15 min chart a buy but that would be impossible as when it triggered it was trading at 3260. Just giving you some feedback to help you fine-tune this thing.

#### codydog

##### Active member
@mashume - Thanks for the work - its very generous and sometimes requires a thick skin as folks feel free to comment/criticize because you haven't posted their winning lottery ticket!

I dont know if you've seen this, but I posted an open source study that compared the favorite moving averages and detailed which worked best for various markets. Here's the link - https://drive.google.com/file/d/0B81LU8RSctNyUzVRcmNXLU9vT3p6SlI3NlpOWjNoOWNVUThF/view , page 43,44 summarize their findings.

Also, don't know if you're familiar with Leavitt Convolution but its a little faster than Hull and seems to work when I plugged it into your work.

Let me know if I can be of any help.

Thanks, again

#### asragov

##### Member
2019 Donor
VIP
Thanks so much - could you please (re) explain how to make a scan with the "improved" 1-bar behind version?

#### mashume

##### Well-known member
VIP
@asragov et al,

UPPER
https://tos.mx/ljjgn40

LOWER
https://tos.mx/Y8VY8RA

Upper includes alert, lower does not.

@codydog, thank you for your kind words. I'm intrigued with the Leavitt Convolution... Homework. I do this a lot for the maths I'm afraid. It means a lot that the tool I've shared here is both somewhat useful, but also extensible -- that the math behind it works given any reasonable input.

SCANS
AFTER loading the new versions, and being careful with the names. %-\ You should be able to create new filter scans.
In the scans tab:
2. Choose Study
3. In the left-most dropdown which defaults to ADX Crossover or something select Custom...
4. Click ThinkScript Editor near the top of the window
5. Paste this code:
Code:
``Concavity("hma length" = 55)."buy" is true within 1 bars``

or this code:

Code:
``````def signal = ConcavityDivergence("hma length" = 55)."concavity";
def HMA = ConcavityDivergence("hma length" = 55)."HMA";
def next = ConcavityDivergence("hma length" = 55)."next_bar";

plot buy = signal < 0 and (HMA - next) > (HMA - next);``````

Adjust as needed. The second won't show you things that are at a BUY, it shows things that currently have negative concavity, but the moving in a direction that may signal a buy sooner or later (if at all, of course).

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