Low Frequency Fourier Transform Trend Following Moving Average Strategy

/*backtest
start: 2023-11-27 00:00:00
end: 2023-11-29 02:00:00
period: 1m
basePeriod: 1m
exchanges: [{"eid":"Futures_Binance","currency":"BTC_USDT"}]
*/

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © 03.freeman

//@version=4
strategy("FTSMA", overlay=true )
src=input(close,"Source")
slowMA=input(200,"Slow MA period")
mediumMA=input(20,"Mid MA period")
fastMA=input(5,"Fast MA period")
plotSMA=input(true,"Use MA")
sin1=input(1,"First sinusoid",minval=1)
sin2=input(2,"Second sinusoid",minval=1)
sin3=input(3,"Third sinusoid",minval=1)
smoothinput = input('EMA', title = "MA Type", options =['EMA', 'SMA', 'ALMA','FRAMA','RMA', 'SWMA', 'VWMA','WMA','LinearRegression'])
linearReg=input(false, "Use linear regression?")
linregLenght=input(13, "Linear regression lenght")
linregOffset=input(0, "Linear regression offset")

//------FRAMA ma---------
ma(src, len) =>
    float result = 0
    int len1 = len/2
    frama_SC=200
    frama_FC=1
    e = 2.7182818284590452353602874713527
    w = log(2/(frama_SC+1)) / log(e) // Natural logarithm (ln(2/(SC+1))) workaround
    H1 = highest(high,len1)
    L1 = lowest(low,len1)
    N1 = (H1-L1)/len1
    H2_ = highest(high,len1)
    H2 = H2_[len1]
    L2_ = lowest(low,len1)
    L2 = L2_[len1]
    N2 = (H2-L2)/len1
    H3 = highest(high,len)
    L3 = lowest(low,len)
    N3 = (H3-L3)/len
    dimen1 = (log(N1+N2)-log(N3))/log(2)
    dimen = iff(N1>0 and N2>0 and N3>0,dimen1,nz(dimen1[1]))
    alpha1 = exp(w*(dimen-1))
    oldalpha = alpha1>1?1:(alpha1<0.01?0.01:alpha1)
    oldN = (2-oldalpha)/oldalpha
    N = (((frama_SC-frama_FC)*(oldN-1))/(frama_SC-1))+frama_FC
    alpha_ = 2/(N+1)
    alpha = alpha_<2/(frama_SC+1)?2/(frama_SC+1):(alpha_>1?1:alpha_)
    frama = 0.0
    frama :=(1-alpha)*nz(frama[1]) + alpha*src
    result := frama
    result

// ----------MA calculation - ChartArt and modified by 03.freeman-------------
calc_ma(src,l) => 
    _ma = smoothinput=='SMA'?sma(src, l):smoothinput=='EMA'?ema(src, l):smoothinput=='WMA'?wma(src, l):smoothinput=='LinearRegression'?linreg(src, l,0):smoothinput=='VWMA'?vwma(src,l):smoothinput=='RMA'?rma(src, l):smoothinput=='ALMA'?alma(src,l,0.85,6):smoothinput=='SWMA'?swma(src):smoothinput=='FRAMA'?ma(sma(src,1),l):na
    
//----------------------------------------------


//pi = acos(-1)
// Approximation of Pi in _n terms --- thanks to e2e4mfck
f_pi(_n) =>
    _a = 1. / (4. * _n + 2)
    _b = 1. / (6. * _n + 3)
    _pi = 0.
    for _i = _n - 1 to 0
        _a := 1 / (4. * _i + 2) - _a / 4.
        _b := 1 / (6. * _i + 3) - _b / 9.
    _pi := (4. * _a) + (4. * _b) - _pi
pi=f_pi(20)

//---Thanks to xyse----https://www.tradingview.com/script/UTPOoabQ-Low-Frequency-Fourier-Transform/
//Declaration of user-defined variables
N = input(defval=64, title="Lookback Period", type=input.integer, minval=2, maxval=600, confirm=false, step=1, options=[2,4,8,16,32,64,128,256,512,1024,2048,4096])

//Real part of the Frequency Domain Representation
ReX(k) =>
    sum = 0.0
    for i=0 to N-1
        sum := sum + src[i]*cos(2*pi*k*i/N)
    return = sum
    
//Imaginary part of the Frequency Domain Representation
ImX(k) =>
    sum = 0.0
    for i=0 to N-1
        sum := sum + src[i]*sin(2*pi*k*i/N)
    return = -sum

//Get sinusoidal amplitude from frequency domain  
ReX_(k) =>
    case = 0.0
    if(k!=0 and k!=N/2)
        case := 2*ReX(k)/N
    if(k==0)
        case := ReX(k)/N
    if(k==N/2)
        case := ReX(k)/N
    return = case
    
 //Get sinusoidal amplitude from frequency domain  
ImX_(k) =>
    return = -2*ImX(k)/N
    
//Get full Fourier Transform
x(i, N) =>
    sum1 = 0.0
    sum2 = 0.0
    for k=0 to N/2
        sum1 := sum1 + ReX_(k)*cos(2*pi*k*i/N)
    for k=0 to N/2
        sum2 := sum2 + ImX_(k)*sin(2*pi*k*i/N)
    return = sum1+sum2
    
//Get single constituent sinusoid
sx(i, k) =>
    sum1 = ReX_(k)*cos(2*pi*k*i/N)
    sum2 = ImX_(k)*sin(2*pi*k*i/N)
    return = sum1+sum2
//Calculations for strategy
SLOWMA = plotSMA?calc_ma(close+sx(0,sin1),slowMA):close+sx(0,sin1)
MEDMA = plotSMA?calc_ma(close+sx(0,sin2),mediumMA):close+sx(0,sin2)
FASTMA = plotSMA?calc_ma(close+sx(0,sin3),fastMA):close+sx(0,sin3)

SLOWMA := linearReg?linreg(SLOWMA,linregLenght,linregOffset):SLOWMA
MEDMA := linearReg?linreg(MEDMA,linregLenght,linregOffset):MEDMA
FASTMA := linearReg?linreg(FASTMA,linregLenght,linregOffset):FASTMA

//Plot 3 Low-Freq Sinusoids
plot(SLOWMA, color=color.green)
plot(MEDMA, color=color.red)
plot(FASTMA, color=color.blue)

//  Strategy: (Thanks to JayRogers)
// === STRATEGY RELATED INPUTS ===
// the risk management inputs
inpTakeProfit   = input(defval = 0, title = "Take Profit Points", minval = 0)
inpStopLoss     = input(defval = 0, title = "Stop Loss Points", minval = 0)
inpTrailStop    = input(defval = 0, title = "Trailing Stop Loss Points", minval = 0)
inpTrailOffset  = input(defval = 0, title = "Trailing Stop Loss Offset Points", minval = 0)

// === RISK MANAGEMENT VALUE PREP ===
// if an input is less than 1, assuming not wanted so we assign 'na' value to disable it.
useTakeProfit   = inpTakeProfit  >= 1 ? inpTakeProfit  : na
useStopLoss     = inpStopLoss    >= 1 ? inpStopLoss    : na
useTrailStop    = inpTrailStop   >= 1 ? inpTrailStop   : na
useTrailOffset  = inpTrailOffset >= 1 ? inpTrailOffset : na

longCondition = FASTMA>MEDMA and close > SLOWMA             //crossover(FASTMA, MEDMA) and close > SLOWMA
if (longCondition)
    strategy.entry("Long Entry", strategy.long)

shortCondition = FASTMA<MEDMA and close < SLOWMA            //crossunder(FASTMA, MEDMA) and close < SLOWMA
if (shortCondition)
    strategy.entry("Short Entry", strategy.short)

// === STRATEGY RISK MANAGEMENT EXECUTION ===
// finally, make use of all the earlier values we got prepped
strategy.exit("Exit Buy", from_entry = "Long Entry", profit = useTakeProfit, loss = useStopLoss, trail_points = useTrailStop, trail_offset = useTrailOffset)
strategy.exit("Exit Sell", from_entry = "Short Entry", profit = useTakeProfit, loss = useStopLoss, trail_points = useTrailStop, trail_offset = useTrailOffset)