Range Filter [DW]

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © DonovanWall

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//@version=4
study(title="Range Filter [DW] [UT-backtester]", shorttitle="RF [DW]", overlay=true)

//This is an experimental study designed to filter out minor price action for a clearer view of trends.

//Inspired by the QQE's volatility filter, this filter applies the process directly to price rather than to a smoothed RSI.

//First, a smooth average price range is calculated for the basis of the filter and multiplied by a specified amount.
//Next, the filter is calculated by gating price movements that do not exceed the specified range.
//Lastly the target ranges are plotted to display the prices that will trigger filter movement.

//Custom bar colors are included. The color scheme is based on the filtered price trend.

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Updates:

// -> Migrated to v4.
// -> Range Filter and the bands are now calculated in a singular function.
// -> There are now two different calculation methods for the filter. Select the type you want to use via the "Filter Type" input. Type 1 is the original formula.
// -> Multiple range sizing methods are now available. You can choose from the following scales:
//    - Points
//    - Pips (Works best with forex pairs, obviously)
//    - Ticks
//    - % of Price
//    - ATR
//    - Average Change (Default. This is the original sizing method.)
//    - Standard Deviation
//    - Absolute (Absolute numerical value)
// -> Range smoothing is now optional, and you can specify your smoothing length. Smoothing only affects dynamic scales (ATR, Average Change, and Standard Deviation).
// -> Filter movement can now be determined using wicks or close. This can be specified via the "Movement Source" input.
// -> Stability Fix: Added correction for NaN values to stabilize initial states.
// -> Reorganized the script structure.
// -> Revamped the color scheme.

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Updates:

// - The Range Filter functions have now been rebuilt using Pine's awesome new array functions.

// - Standard deviation calculation has been adjusted to calculate the same as TV's built in stdev() function.

// - Rewritten filter direction and bar color variables.

// - Included an external output variable for trend information that can easily be sent to other scripts without hardcoding.
//   The output format is 1 for bullish, and -1 for bearish.
//   To use this external variable with another script, simply select it from your other script's source dropdown tab.

// - Added the ability to average range filter values based on a user defined number of filter changes.
//   This averaging method utilized the Conditional Sampling EMA function I introduced in my Resampling Filter Pack and only takes a new sample when the filter changes its value.
//   This opens up a whole new world of possible filter outputs.

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Functions
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//Conditional Sampling EMA Function 
Cond_EMA(x, cond, n)=>
    var val     = array.new_float(0)
    var ema_val = array.new_float(1)
    if cond
        array.push(val, x)
        if array.size(val) > 1
            array.remove(val, 0)
        if na(array.get(ema_val, 0))
            array.fill(ema_val, array.get(val, 0))
        array.set(ema_val, 0, (array.get(val, 0) - array.get(ema_val, 0))*(2/(n + 1)) + array.get(ema_val, 0))
    EMA = array.get(ema_val, 0)
    EMA

//Conditional Sampling SMA Function
Cond_SMA(x, cond, n)=>
    var vals = array.new_float(0)
    if cond
        array.push(vals, x)
        if array.size(vals) > n
            array.remove(vals, 0)
    SMA = array.avg(vals)
    SMA

//Standard Deviation Function
Stdev(x, n)=>
    sqrt(Cond_SMA(pow(x, 2), 1, n) - pow(Cond_SMA(x, 1, n), 2))

//Range Size Function
rng_size(x, scale, qty, n)=> 
    ATR      = Cond_EMA(tr(true), 1, n)
    AC       = Cond_EMA(abs(x - x[1]), 1, n)
    SD       = Stdev(x, n)
    rng_size = scale=="Pips" ? qty*0.0001 : scale=="Points" ? qty*syminfo.pointvalue : scale=="% of Price" ? close*qty/100 : scale=="ATR" ? qty*ATR :
               scale=="Average Change" ? qty*AC : scale=="Standard Deviation" ? qty*SD : scale=="Ticks" ? qty*syminfo.mintick : qty   

//Two Type Range Filter Function
rng_filt(h, l, rng_, n, type, smooth, sn, av_rf, av_n)=>
    rng_smooth = Cond_EMA(rng_, 1, sn)
    r          = smooth ? rng_smooth : rng_
    var rfilt  = array.new_float(2, (h + l)/2)
    array.set(rfilt, 1, array.get(rfilt, 0))
    if type=="Type 1"
        if h - r > array.get(rfilt, 1)
            array.set(rfilt, 0, h - r)
        if l + r < array.get(rfilt, 1)
            array.set(rfilt, 0, l + r)
    if type=="Type 2"
        if h >= array.get(rfilt, 1) + r
            array.set(rfilt, 0, array.get(rfilt, 1) + floor(abs(h - array.get(rfilt, 1))/r)*r)
        if l <= array.get(rfilt, 1) - r
            array.set(rfilt, 0, array.get(rfilt, 1) - floor(abs(l - array.get(rfilt, 1))/r)*r)
    rng_filt1 = array.get(rfilt, 0)
    hi_band1  = rng_filt1 + r
    lo_band1  = rng_filt1 - r
    rng_filt2 = Cond_EMA(rng_filt1, rng_filt1 != rng_filt1[1], av_n)
    hi_band2  = Cond_EMA(hi_band1, rng_filt1 != rng_filt1[1], av_n)
    lo_band2  = Cond_EMA(lo_band1, rng_filt1 != rng_filt1[1], av_n)
    rng_filt  = av_rf ? rng_filt2 : rng_filt1
    hi_band   = av_rf ? hi_band2 : hi_band1
    lo_band   = av_rf ? lo_band2 : lo_band1
    [hi_band, lo_band, rng_filt]
 
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Inputs
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//Filter Type
f_type = input(defval="Type 1", options=["Type 1", "Type 2"], title="Filter Type")

//Movement Source
mov_src = input(defval="Close", options=["Wicks", "Close"], title="Movement Source")

//Range Size Inputs
rng_qty   = input(defval=2.618, minval=0.0000001, title="Range Size")
rng_scale = input(defval="Average Change", options=["Points", "Pips", "Ticks", "% of Price", "ATR", "Average Change", "Standard Deviation", "Absolute"], title="Range Scale")

//Range Period
rng_per = input(defval=14, minval=1, title="Range Period (for ATR, Average Change, and Standard Deviation)")

//Range Smoothing Inputs
smooth_range = input(defval=true, title="Smooth Range")
smooth_per   = input(defval=27, minval=1, title="Smoothing Period")

//Filter Value Averaging Inputs
av_vals    = input(defval=false, title="Average Filter Changes")
av_samples = input(defval=2, minval=1, title="Number Of Changes To Average")

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Definitions
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//High And Low Values
h_val = mov_src=="Wicks" ? high : close
l_val = mov_src=="Wicks" ? low : close

//Range Filter Values
[h_band, l_band, filt] = rng_filt(h_val, l_val, rng_size((h_val + l_val)/2, rng_scale, rng_qty, rng_per), rng_per, f_type, smooth_range, smooth_per, av_vals, av_samples)

//Direction Conditions
var fdir = 0.0
fdir    := filt > filt[1] ? 1 : filt < filt[1] ? -1 : fdir
upward   = fdir==1 ? 1 : 0
downward = fdir==-1 ? 1 : 0

//Colors
filt_color = upward ? #05ff9b : downward ? #ff0583 : #cccccc
bar_color  = upward and (close > filt) ? (close > close[1] ? #05ff9b : #00b36b) :
             downward and (close < filt) ? (close < close[1] ? #ff0583 : #b8005d) : #cccccc

//-----------------------------------------------------------------------------------------------------------------------------------------------------------------
//Outputs
//-----------------------------------------------------------------------------------------------------------------------------------------------------------------

//Filter Plot
filt_plot = plot(filt, color=filt_color, linewidth=3, transp=0, title="Filter")

//Band Plots
h_band_plot = plot(h_band, color=#05ff9b, transp=100, title="High Band")
l_band_plot = plot(l_band, color=#ff0583, transp=100, title="Low Band")

//Band Fills
fill(h_band_plot, filt_plot, color=#00b36b, transp=85, title="High Band Fill")
fill(l_band_plot, filt_plot, color=#b8005d, transp=85, title="Low Band Fill")

//Bar Color
barcolor(bar_color)

//External Trend Output
plot(fdir, transp=100, editable=false, display=display.none, title="External Output - Trend Signal")


strategy = fdir
plot(strategy, "Strategy Signal", display=display.none)