HEMA - A Fast And Efficient Estimate Of The Hull Moving AverageIntroduction
The Hull moving average (HMA) developed by Alan Hull is one of the many moving averages that aim to reduce lag while providing effective smoothing. The HMA make use of 3 linearly weighted (WMA) moving averages, with respective periods p/2 , p and √p , this involve three convolutions, which affect computation time, a more efficient version exist under the name of exponential Hull moving average (EHMA), this version make use of exponential moving averages instead of linearly weighted ones, which dramatically decrease the computation time, however the difference with the original version is clearly noticeable.
In this post an efficient and simple estimate is proposed, the estimation process will be fully described and some comparison with the original HMA will be presented.
This post and indicator is dedicated to LucF
Estimation Process
Estimating a moving average is easier when we look at its weights (represented by the impulse response), we basically want to find a similar set of weights via more efficient calculations, the estimation process is therefore based on fully understanding the weighting architecture of the moving average we want to estimate.
The impulse response of an HMA of period 20 is as follows :
We can see that the first weights increases a bit before decaying, the weights then decay, cross under 0 and increase again. More recent closing price values benefits of the highest weights, while the oldest values have negatives ones, negative weighting is what allow to drastically reduce the lag of the HMA. Based on this information we know that our estimate will be a linear combination of two moving averages with unknown coefficients :
a × MA1 + b × MA2
With a > 0 and b < 0 , the lag of MA1 is lower than the lag of MA2 . We first need to capture the general envelope of the weights, which has an overall non-linearly decaying shape, therefore the use of an exponential moving average might seem appropriate.
In orange the impulse response of an exponential moving average of period p/2 , that is 10. We can see that such impulse response is not a bad estimate of the overall shape of the HMA impulse response, based on this information we might perform our linear combination with a simple moving average :
2EMA(p/2) + -1SMA(p)
this gives the following impulse response :
As we can see there is a clear lack of accuracy, but because the impulse response of a simple moving is a constant we can't have the short increasing weights of the HMA, we therefore need a non-constant impulse response for our linear combination, a WMA might be appropriate. Therefore we will use :
2WMA(p/2) + -1EMA(p/2)
Note that the lag a WMA is inferior to the lag of an EMA of same period, this is why the period of the WMA is p/2 . We obtain :
The shape has improved, but the fit is poor, which mean we should change our coefficients, more precisely increasing the coefficient of the WMA (thus decreasing the one of the EMA). We will try :
3WMA(p/2) + -2EMA(p/2)
We then obtain :
This estimate seems to have a decent fit, and this linear combination is therefore used.
Comparison
HMA in blue and the estimate in fuchsia with both period 50, the difference can be noted, however the estimate is relatively accurate.
In the image above the period has been set to 200.
Conclusion
In this post an efficient estimate of the HMA has been proposed, we have seen that the HMA can be estimated via the linear combinations of a WMA and an EMA of each period p/2 , this isn't important for the EMA who is based on recursion but is however a big deal for the WMA who use recursion, and therefore p indicate the number of data points to be used in the convolution, knowing that we use only convolution and that this convolution use twice less data points then one of the WMA used in the HMA is a pretty great thing.
Subtle tweaking of the coefficients/moving averages length's might help have an even more accurate estimate, the fact that the WMA make use of a period of √p is certainly the most disturbing aspect when it comes to estimating the HMA. I also described more in depth the process of estimating a moving average.
I hope you learned something in this post, it took me quite a lot of time to prepare, maybe 2 hours, some pinescripters pass an enormous amount of time providing content and helping the community, one of them being LucF, without him i don't think you'll be seeing this indicator as well as many ones i previously posted, I encourage you to thank him and check his work for Pinecoders as well as following him.
Thanks for reading ! Indicator
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Multi SMA EMA WMA HMA BB (5x8 MAs Bollinger Bands) MAX MTF - RRBMulti SMA EMA WMA HMA 4x7 Moving Averages with Bollinger Bands MAX MTF by RagingRocketBull 2019
Version 1.0
All available MAX MTF versions are listed below (They are very similar and I don't want to publish them as separate indicators):
ver 1.0: 4x7 = 28 MTF MAs + 28 Levels + 3 BB = 59 < 64
ver 2.0: 5x6 = 30 MTF MAs + 30 Levels + 3 BB = 63 < 64
ver 3.0: 3x10 = 30 MTF MAs + 30 Levels + 3 BB = 63 < 64
ver 4.0: 5(4+1)x8 = 8 CurTF MAs + 32 MTF MAs + 20 Levels + 3 BB = 63 < 64
ver 5.0: 6(5+1)x6 = 6 CurTF MAs + 30 MTF MAs + 24 Levels + 3 BB = 63 < 64
ver 6.0: 4(3+1)x10 = 10 CurTF MAs + 30 MTF MAs + 20 Levels + 3 BB = 63 < 64
Fib numbers: 8, 13, 21, 34, 55, 89, 144, 233, 377
This indicator shows multiple MAs of any type SMA EMA WMA HMA etc with BB and MTF support, can show MAs as dynamically moving levels.
There are 4 MA groups + 1 BB group, a total of 4 TFs * 7 MAs = 28 MAs. You can assign any type/timeframe combo to a group, for example:
- EMAs 9,12,26,50,100,200,400 x H1, H4, D1, W1 (4 TFs x 7 MAs x 1 type)
- EMAs 8,13,21,30,34,50,55,89,100,144,200,233,377,400 x M15, H1 (2 TFs x 14 MAs x 1 type)
- D1 EMAs and SMAs 8,13,21,30,34,50,55,89,100,144,200,233,377,400 (1 TF x 14 MAs x 2 types)
- H1 WMAs 13,21,34,55,89,144,233; H4 HMAs 9,12,26,50,100,200,400; D1 EMAs 12,26,89,144,169,233,377; W1 SMAs 9,12,26,50,100,200,400 (4 TFs x 7 MAs x 4 types)
- +1 extra MA type/timeframe for BB
There are several versions: Simple, MTF, Pro MTF, Advanced MTF, MAX MTF and Ultimate MTF. This is the MAX MTF version. The Differences are listed below. All versions have BB
- Simple: you have 2 groups of MAs that can be assigned any type (5+5)
- MTF: +2 custom Timeframes for each group (2x5 MTF) +1 TF for BB, TF XY smoothing
- Pro MTF: 4 custom Timeframes for each group (4x3 MTF), 1 TF for BB, MA levels and show max bars back options
- Advanced MTF: +4 extra MAs/group (4x7 MTF), custom Ticker/Symbols, Timeframe <>= filter, Remove Duplicates Option
- MAX MTF: +2 subtypes/group, packed to the limit with max possible MAs/TFs: 4x7, 5x6, 3x10, 4(3+1)x10, 5(4+1)x8, 6(5+1)x6
- Ultimate MTF: +individual settings for each MA, custom Ticker/Symbols
MAX MTF version tests the limits of Pinescript trying to squeeze as many MAs/TFs as possible into a single indicator.
It's basically a maxed out Advanced version with subtypes allowing for mixed types within a group (i.e. both emas and smas in a single group/TF)
Pinescript has the following limits:
- max 40 security calls (6 calls are reserved for dupe checks and smoothing, 2 are used for BB, so only 32 calls are available)
- max 64 plot outputs (BB uses 3 outputs, so only 61 plot outputs are available)
- max 50000 (50kb) size of the compiled code
Based on those limits, you can only have the following MAs/TFs combos in a single script:
1. 4x7, 5x6, 3x10 - total number of MTF MAs must always be <= 32, and you can still have BB and Num Levels = total MAs, without any compromises
2. 5(4+1)x8, 6(5+1)x6, 4(3+1)x10 - you can use the Current Symbol/Timeframe as an extra (+1) fixed TF with the same number of MTF MAs
- you don't need to call security to display MAs on the Current Symbol/Timeframe, so the total number of MTF MAs remains the same and is still <= 32
- to fit that many MAs into the max 64 plot outputs limit you need to reduce the number of levels (not every MA Group will have corresponding levels)
Features:
- 4x7 = 28 MAs of any type
- 4x MTF groups with XY step line smoothing
- +1 extra TF/type for BB MAs
- 2 MA subtypes within each group/TF
- 4x7 = 28 MA levels with adjustable group offsets, indents and shift
- supports any existing type of MA: SMA, EMA, WMA, Hull Moving Average (HMA)
- custom tickers/symbols for each group
- show max bars back option
- show/hide both groups of MAs/levels/BB and individual MAs
- timeframe filter: show only MAs/Levels with TFs <>= Current TF
- hide MAs/Levels with duplicate TFs
- support for custom TFs that are not available in free accounts: 2D, 3D etc
- support for timeframes in H: H, 2H, 4H etc
Notes:
- Uses timeframe textbox instead of input resolution dropdown to allow for 240 120 and other custom TFs
- Uses symbol textbox instead of input symbol to avoid establishing multiple dummy security connections to the current ticker - otherwise empty symbols will prevent script from running
- Possible reasons for missing MAs on a chart:
- there may not be enough bars in history to start plotting it. For example, W1 EMA200 needs at least 200 bars on a weekly chart.
- for charts with low/fractional prices i.e. 0.00002 << 0.001 (default Y smoothing step) decrease Y smoothing as needed (set Y = 0.0000001) or disable it completely (set X,Y to 0,0)
- for charts with high price values i.e. 20000 >> 0.001 increase Y smoothing as needed (set Y = 10-20). Higher values exceeding MAs point density will cause it to disappear as there will be no points to plot. Different TFs may require diff adjustments
- PulseWire Replay Mode UI and Pinescript security calls are limited to TFs >= D (D,2D,W,MN...) for free accounts
- attempting to plot any TF < D1 in Replay Mode will only result in straight lines, but all TFs will work properly in history and real-time modes. This is not a bug.
- Max Bars Back (num_bars) is limited to 5000 for free accounts (10000 for paid), will show error when exceeded. To plot on all available history set to 0 (default)
- Slow load/redraw times. This indicator becomes slower, its UI less responsive when:
- Pinescript Node.js graphics library is too slow and inefficient at plotting bars/objects in a browser window. Code optimization doesn't help much - the graphics engine is the main reason for general slowness.
- the chart has a long history (10000+ bars) in a browser's cache (you have scrolled back a couple of screens in a max zoom mode).
- Reload the page/Load a fresh chart and then apply the indicator or
- Switch to another Timeframe (old TF history will still remain in cache and that TF will be slow)
- in max possible zoom mode around 4500 bars can fit on 1 screen - this also slows down responsiveness. Reset Zoom level
- initial load and redraw times after a param change in UI also depend on TF. For example: D1/W1 - 2 sec, H1/H4 - 5-6 sec, M30 - 10 sec, M15/M5 - 4 sec, M1 - 5 sec. M30 usually has the longest history (up to 16000 bars) and W1 - the shortest (1000 bars).
- when indicator uses more MAs (plots) and timeframes it will redraw slower. Seems that up to 5 Timeframes is acceptable, but 6+ Timeframes can become very slow.
- show_last=last_bars plot limit doesn't affect load/redraw times, so it was removed from MA plot
- Max Bars Back (num_bars) default/custom set UI value doesn't seem to affect load/redraw times
- In max zoom mode all dynamic levels disappear (they behave like text)
- Dupe check includes symbol: symbol, tf, both subtypes - all must match for a duplicate group
- For the dupe check to work correctly a custom symbol must always include an exchange prefix. BB is not checked for dupes
Good Luck! Feel free to learn from/reuse the code to build your own indicators.
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Multi SMA EMA WMA HMA BB (4x5 MAs Bollinger Bands) Adv MTF - RRBMulti SMA EMA WMA HMA 4x5 Moving Averages with Bollinger Bands Advanced MTF by RagingRocketBull 2019
Version 1.0
This indicator shows multiple MAs of any type SMA EMA WMA HMA etc with BB and MTF support, can show MAs as dynamically moving levels.
There are 4 MA groups + 1 BB group, a total of 4 TFs * 5 MAs = 20 MAs. You can assign any type/timeframe combo to a group, for example:
- EMAs 12,26,50,100,200 x H1, H4, D1, W1 (4 TFs x 5 MAs x 1 type)
- EMAs 8,10,13,21,30,50,55,100,200,400 x M15, H1 (2 TFs x 10 MAs x 1 type)
- D1 EMAs and SMAs 8,10,12,26,30,50,55,100,200,400 (1 TF x 10 MAs x 2 types)
- H1 WMAs 7,77,89,167,231; H4 HMAs 12,26,50,100,200; D1 EMAs 89,144,169,233,377; W1 SMAs 12,26,50,100,200 (4 TFs x 5 MAs x 4 types)
- +1 extra MA type/timeframe for BB
There are several versions: Simple, MTF, Pro MTF, Advanced MTF and Ultimate MTF. This is the Advanced MTF version. The Differences are listed below. All versions have BB
- Simple: you have 2 groups of MAs that can be assigned any type (5+5)
- MTF: +2 custom Timeframes for each group (2x5 MTF) +1 TF for BB, TF XY smoothing
- Pro MTF: 4 custom Timeframes for each group (4x3 MTF), 1 TF for BB, MA levels and show max bars back options
- Advanced MTF: +2 extra MAs/group (4x5 MTF), custom Ticker/Symbols, Timeframe <>= filter, Remove Duplicates Option
- Ultimate MTF: +individual settings for each MA, custom Ticker/Symbols
Features:
- 4x5 = 20 MAs of any type
- 4x MTF groups with XY step line smoothing
- +1 extra TF/type for BB MAs
- 4x5 = 20 MA levels with adjustable group offsets, indents and shift
- supports any existing type of MA: SMA, EMA, WMA, Hull Moving Average (HMA)
- custom tickers/symbols for each group - you can compare MAs of the same symbol across exchanges
- show max bars back option
- show/hide both groups of MAs/levels/BB and individual MAs
- timeframe filter: show only MAs/Levels with TFs <>= Current TF
- hide MAs/Levels with duplicate TFs
- support for custom TFs that are not available in free accounts: 2D, 3D etc
- support for timeframes in H: H, 2H, 4H etc
Notes:
- Uses timeframe textbox instead of input resolution dropdown to allow for 240 120 and other custom TFs
- Uses symbol textbox instead of input symbol to avoid establishing multiple dummy security connections to the current ticker - otherwise empty symbols will prevent script from running
- Possible reasons for missing MAs on a chart:
- there may not be enough bars in history to start plotting it. For example, W1 EMA200 needs at least 200 bars on a weekly chart.
- price << default Y smoothing step 5. For charts with low/fractional prices (i.e. 0.00002 << 5) adjust X Y smoothing as needed (set Y = 0.0000001) or disable it completely (set X,Y to 0,0)
- PulseWire Replay Mode UI and Pinescript security calls are limited to TFs >= D (D,2D,W,MN...) for free accounts
- attempting to plot any TF < D1 in Replay Mode will only result in straight lines, but all TFs will work properly in history and real-time modes. This is not a bug.
- Max Bars Back (num_bars) is limited to 5000 for free accounts (10000 for paid), will show error when exceeded. To plot on all available history set to 0 (default)
- Slow load/redraw times. This indicator becomes slower, its UI less responsive when:
- Pinescript Node.js graphics library is too slow and inefficient at plotting bars/objects in a browser window. Code optimization doesn't help much - the graphics engine is the main reason for general slowness.
- the chart has a long history (10000+ bars) in a browser's cache (you have scrolled back a couple of screens in a max zoom mode).
- Reload the page/Load a fresh chart and then apply the indicator or
- Switch to another Timeframe (old TF history will still remain in cache and that TF will be slow)
- in max possible zoom mode around 4500 bars can fit on 1 screen - this also slows down responsiveness. Reset Zoom level
- initial load and redraw times after a param change in UI also depend on TF. For example:
D1/W1 - 2 sec, H1/H4 - 5-6 sec, M30 - 10 sec, M15/M5 - 4 sec, M1 - 5 sec.
M30 usually has the longest history (up to 16000 bars) and W1 - the shortest (1000 bars).
- when indicator uses more MAs (plots) and timeframes it will redraw slower. Seems that up to 5 Timeframes is acceptable, but 6+ Timeframes can become very slow.
- show_last=last_bars plot limit doesn't affect load/redraw times, so it was removed from MA plot
- Max Bars Back (num_bars) default/custom set UI value doesn't seem to affect load/redraw times
- In max zoom mode all dynamic levels disappear (they behave like text)
1. based on 3EmaBB, uses plot*, barssince and security functions
2. you can't set certain constants from input due to Pinescript limitations - change the code as needed, recompile and use as a private version
3. Levels = trackprice implementation
4. Show Max Bars Back = show_last implementation
5. swma has a fixed length = 4, alma and linreg have additional offset and smoothing params
6. Smoothing is applied by default for visual aesthetics on MTF. To use exact ma mtf values (lines with stair stepping) - disable it
Good Luck! You can explore, modify/reuse the code to build your own indicators.
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CryptoCoyns HullMA [v2018-12-10]CryptoCoyns Hull Moving Average
This indicator implements the Hull moving average.
The Hull Moving Average (HMA), developed by Alan Hull, is an extremely
fast and smooth moving average. In fact, the HMA almost eliminates lag
altogether and manages to improve smoothing at the same time. A longer
period HMA may be used to identify trend. If the HMA is rising, the
prevailing trend is rising, indicating it may be better to enter long
positions. If the HMA is falling, the prevailing trend is also falling,
indicating it may be better to enter short positions. A shorter period
HMA may be used for entry signals in the direction of the prevailing trend.
The Source for price can be defined. i.e. Close, Open, High, Low, etc.
The period length used can be defined.
MA Line colour is fully configurable.
If you get some value out of this indicator please consider making
a small donation to my favourite charity the Save the Childrens Fund.
Every donation will make a difference to the lives of children.
All donations over $2 are tax deductable. You can donate here:
savethechildrenfundraising.org.au
Copyright (c) 2018, Grant Cause aka CryptoCoyns
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