Strategi Momentum RSI Berbasis Interpolasi Polinomial
Penulis:ChaoZhang, Tanggal: 2024-01-12 13:46:53Tag:
Gambaran umum
Strategi ini menghasilkan sinyal perdagangan menggunakan indikator momentum RSI Delta-RSI berdasarkan interpolasi polinomial. Delta-RSI meratakan RSI melalui regresi polinomial lokal untuk mendapatkan turunan waktu urutan pertama sebagai indikator momentum. Strategi ini menggabungkan filter tambahan berdasarkan ATR, volume dan RSI untuk menyaring beberapa sinyal
Prinsip
Indikator inti dari strategi ini adalah Delta-RSI. Langkah perhitungannya adalah:
- Ambil seri waktu RSI dengan panjang rsi_l sebagai input
- Sesuaikan RSI menggunakan interpolasi polinomial dalam jendela geser dari jendela panjang
- Hitung turunan urutan pertama dari kurva yang dipasang pada titik saat ini sebagai Delta-RSI
- Melalui Delta-RSI di atas 0 menghasilkan sinyal beli, melewati di bawah 0 menghasilkan sinyal jual
- Sinyal perdagangan juga dapat dihasilkan menggunakan garis sinyal Delta-RSI
Strategi ini memfilter sinyal menggunakan filter ATR, volume dan RSI:
- Filter ATR: ATR periode N saat ini lebih tinggi dari ATR periode M menunjukkan meningkatnya volatilitas
- Filter volume: volume saat ini lebih tinggi dari N kali volume rata-rata selama M periode
- RSI filter: RSI antara ambang 1 dan ambang 2 filter area overbought/oversold
Keuntungan
Keuntungan dari strategi ini meliputi:
- Delta-RSI lebih sensitif untuk mendeteksi pembalikan tren awal
- Filter dapat menghilangkan sebagian besar sinyal palsu dan meningkatkan kualitas sinyal
- Parameter polinomial dan filter yang dapat disesuaikan sesuai dengan pasar yang berbeda
- Berpisah panjang / pendek memungkinkan akomodasi bias yang berbeda
- Kontrol Stop Loss/Take Profit per trade loss/profit
Risiko
Risiko dari strategi ini meliputi:
- Penyesuaian parameter yang buruk dapat menyebabkan terlalu halus atau terlalu menyaring
- kerugian posisi panjang/pendek
- Stop yang terlalu luas dapat meningkatkan kerugian per perdagangan
Ini dapat dikendalikan melalui optimasi parameter, penyesuaian filter dan pemberhentian yang lebih ketat.
Peluang Peningkatan
Strategi ini dapat ditingkatkan lagi dengan:
- Mengoptimalkan parameter model Delta-RSI
- Mengintegrasikan penyaringan adaptif berbasis pembelajaran mesin
- Parameter penyesuaian untuk produk yang berbeda
- Menambahkan metode kombinasi model dll untuk meningkatkan ketahanan
Kesimpulan
Dengan memanfaatkan kepekaan tinggi Delta-RSI dan mekanisme penyaringan yang ketat, strategi ini dapat meningkatkan kualitas sambil mengendalikan risiko. Optimasi parameter dan model lebih lanjut dapat memperluas tingkat keuntungan positif. Ini adalah strategi perdagangan kuantitatif yang efektif.
/*backtest
start: 2024-01-04 00:00:00
end: 2024-01-11 00:00:00
period: 1h
basePeriod: 15m
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/
// © tbiktag
//
// Delta-RSI Oscillator Strategy With Filters
//
// This is a version of the Delta-RSI Oscillator Strategy compatible with
// the Strategy Tester.
//
// This version also allows filtering the trade signals generated by Delts-RSI
// by means of volatility (defined by ATR), relative volume and RSI(14).
//
// Delta-RSI (© tbiktag) is a smoothed time derivative of the RSI designed
// as a momentum indicator. For the original publication, see link below:
// https://www.tradingview.com/script/OXQVFTQD-Delta-RSI-Oscillator/
//
// D-RSI model parameters:
// RSI Length: The timeframe of the RSI that serves as an input to D-RSI.
// Frame Length: The length of the lookback frame used for local regression.
// Polynomial Order: The order of the local polynomial function used to interpolate
// the RSI.
// Trade signals are generated based on three optional conditions:
// - Zero-crossing: bullish when D-RSI crosses zero from negative to positive
// values (bearish otherwise)
// - Signal Line Crossing: bullish when D-RSI crosses from below to above the signal
// line (bearish otherwise)
// - Direction Change: bullish when D-RSI was negative and starts ascending
// (bearish otherwise)
//
//@version=4
strategy(title="Delta-RSI Strategy with Filters", shorttitle = "D-RSI with filters", overlay = true)
// ---Subroutines---
matrix_get(_A,_i,_j,_nrows) =>
// Get the value of the element of an implied 2d matrix
//input:
// _A :: array: pseudo 2d matrix _A = [[column_0],[column_1],...,[column_(n-1)]]
// _i :: integer: row number
// _j :: integer: column number
// _nrows :: integer: number of rows in the implied 2d matrix
array.get(_A,_i+_nrows*_j)
matrix_set(_A,_value,_i,_j,_nrows) =>
// Set a value to the element of an implied 2d matrix
//input:
// _A :: array, changed on output: pseudo 2d matrix _A = [[column_0],[column_1],...,[column_(n-1)]]
// _value :: float: the new value to be set
// _i :: integer: row number
// _j :: integer: column number
// _nrows :: integer: number of rows in the implied 2d matrix
array.set(_A,_i+_nrows*_j,_value)
transpose(_A,_nrows,_ncolumns) =>
// Transpose an implied 2d matrix
// input:
// _A :: array: pseudo 2d matrix _A = [[column_0],[column_1],...,[column_(n-1)]]
// _nrows :: integer: number of rows in _A
// _ncolumns :: integer: number of columns in _A
// output:
// _AT :: array: pseudo 2d matrix with implied dimensions: _ncolums x _nrows
var _AT = array.new_float(_nrows*_ncolumns,0)
for i = 0 to _nrows-1
for j = 0 to _ncolumns-1
matrix_set(_AT, matrix_get(_A,i,j,_nrows),j,i,_ncolumns)
_AT
multiply(_A,_B,_nrowsA,_ncolumnsA,_ncolumnsB) =>
// Calculate scalar product of two matrices
// input:
// _A :: array: pseudo 2d matrix
// _B :: array: pseudo 2d matrix
// _nrowsA :: integer: number of rows in _A
// _ncolumnsA :: integer: number of columns in _A
// _ncolumnsB :: integer: number of columns in _B
// output:
// _C:: array: pseudo 2d matrix with implied dimensions _nrowsA x _ncolumnsB
var _C = array.new_float(_nrowsA*_ncolumnsB,0)
int _nrowsB = _ncolumnsA
float elementC= 0.0
for i = 0 to _nrowsA-1
for j = 0 to _ncolumnsB-1
elementC := 0
for k = 0 to _ncolumnsA-1
elementC := elementC + matrix_get(_A,i,k,_nrowsA)*matrix_get(_B,k,j,_nrowsB)
matrix_set(_C,elementC,i,j,_nrowsA)
_C
vnorm(_X,_n) =>
//Square norm of vector _X with size _n
float _norm = 0.0
for i = 0 to _n-1
_norm := _norm + pow(array.get(_X,i),2)
sqrt(_norm)
qr_diag(_A,_nrows,_ncolumns) =>
//QR Decomposition with Modified Gram-Schmidt Algorithm (Column-Oriented)
// input:
// _A :: array: pseudo 2d matrix _A = [[column_0],[column_1],...,[column_(n-1)]]
// _nrows :: integer: number of rows in _A
// _ncolumns :: integer: number of columns in _A
// output:
// _Q: unitary matrix, implied dimenstions _nrows x _ncolumns
// _R: upper triangular matrix, implied dimansions _ncolumns x _ncolumns
var _Q = array.new_float(_nrows*_ncolumns,0)
var _R = array.new_float(_ncolumns*_ncolumns,0)
var _a = array.new_float(_nrows,0)
var _q = array.new_float(_nrows,0)
float _r = 0.0
float _aux = 0.0
//get first column of _A and its norm:
for i = 0 to _nrows-1
array.set(_a,i,matrix_get(_A,i,0,_nrows))
_r := vnorm(_a,_nrows)
//assign first diagonal element of R and first column of Q
matrix_set(_R,_r,0,0,_ncolumns)
for i = 0 to _nrows-1
matrix_set(_Q,array.get(_a,i)/_r,i,0,_nrows)
if _ncolumns != 1
//repeat for the rest of the columns
for k = 1 to _ncolumns-1
for i = 0 to _nrows-1
array.set(_a,i,matrix_get(_A,i,k,_nrows))
for j = 0 to k-1
//get R_jk as scalar product of Q_j column and A_k column:
_r := 0
for i = 0 to _nrows-1
_r := _r + matrix_get(_Q,i,j,_nrows)*array.get(_a,i)
matrix_set(_R,_r,j,k,_ncolumns)
//update vector _a
for i = 0 to _nrows-1
_aux := array.get(_a,i) - _r*matrix_get(_Q,i,j,_nrows)
array.set(_a,i,_aux)
//get diagonal R_kk and Q_k column
_r := vnorm(_a,_nrows)
matrix_set(_R,_r,k,k,_ncolumns)
for i = 0 to _nrows-1
matrix_set(_Q,array.get(_a,i)/_r,i,k,_nrows)
[_Q,_R]
pinv(_A,_nrows,_ncolumns) =>
//Pseudoinverse of matrix _A calculated using QR decomposition
// Input:
// _A:: array: implied as a (_nrows x _ncolumns) matrix
//. _A = [[column_0],[column_1],...,[column_(_ncolumns-1)]]
// Output:
// _Ainv:: array implied as a (_ncolumns x _nrows) matrix
// _A = [[row_0],[row_1],...,[row_(_nrows-1)]]
// ----
// First find the QR factorization of A: A = QR,
// where R is upper triangular matrix.
// Then _Ainv = R^-1*Q^T.
// ----
[_Q,_R] = qr_diag(_A,_nrows,_ncolumns)
_QT = transpose(_Q,_nrows,_ncolumns)
// Calculate Rinv:
var _Rinv = array.new_float(_ncolumns*_ncolumns,0)
float _r = 0.0
matrix_set(_Rinv,1/matrix_get(_R,0,0,_ncolumns),0,0,_ncolumns)
if _ncolumns != 1
for j = 1 to _ncolumns-1
for i = 0 to j-1
_r := 0.0
for k = i to j-1
_r := _r + matrix_get(_Rinv,i,k,_ncolumns)*matrix_get(_R,k,j,_ncolumns)
matrix_set(_Rinv,_r,i,j,_ncolumns)
for k = 0 to j-1
matrix_set(_Rinv,-matrix_get(_Rinv,k,j,_ncolumns)/matrix_get(_R,j,j,_ncolumns),k,j,_ncolumns)
matrix_set(_Rinv,1/matrix_get(_R,j,j,_ncolumns),j,j,_ncolumns)
//
_Ainv = multiply(_Rinv,_QT,_ncolumns,_ncolumns,_nrows)
_Ainv
norm_rmse(_x, _xhat) =>
// Root Mean Square Error normalized to the sample mean
// _x. :: array float, original data
// _xhat :: array float, model estimate
// output
// _nrmse:: float
float _nrmse = 0.0
if array.size(_x) != array.size(_xhat)
_nrmse := na
else
int _N = array.size(_x)
float _mse = 0.0
for i = 0 to _N-1
_mse := _mse + pow(array.get(_x,i) - array.get(_xhat,i),2)/_N
_xmean = array.sum(_x)/_N
_nrmse := sqrt(_mse) /_xmean
_nrmse
diff(_src,_window,_degree) =>
// Polynomial differentiator
// input:
// _src:: input series
// _window:: integer: wigth of the moving lookback window
// _degree:: integer: degree of fitting polynomial
// output:
// _diff :: series: time derivative
// _nrmse:: float: normalized root mean square error
//
// Vandermonde matrix with implied dimensions (window x degree+1)
// Linear form: J = [ [z]^0, [z]^1, ... [z]^degree],
// with z = [ (1-window)/2 to (window-1)/2 ]
var _J = array.new_float(_window*(_degree+1),0)
for i = 0 to _window-1
for j = 0 to _degree
matrix_set(_J,pow(i,j),i,j,_window)
// Vector of raw datapoints:
var _Y_raw = array.new_float(_window,na)
for j = 0 to _window-1
array.set(_Y_raw,j,_src[_window-1-j])
// Calculate polynomial coefficients which minimize the loss function
_C = pinv(_J,_window,_degree+1)
_a_coef = multiply(_C,_Y_raw,_degree+1,_window,1)
// For first derivative, approximate the last point (i.e. z=window-1) by
float _diff = 0.0
for i = 1 to _degree
_diff := _diff + i*array.get(_a_coef,i)*pow(_window-1,i-1)
// Calculates data estimate (needed for rmse)
_Y_hat = multiply(_J,_a_coef,_window,_degree+1,1)
float _nrmse = norm_rmse(_Y_raw,_Y_hat)
[_diff,_nrmse]
/// --- main ---
degree = input(title="Polynomial Order", group = "Model Parameters:",
inline = "linepar1", type = input.integer, defval=3, minval = 1)
rsi_l = input(title = "RSI Length", group = "Model Parameters:",
inline = "linepar1", type = input.integer, defval = 21, minval = 1,
tooltip="The period length of RSI that is used as input.")
window = input(title="Length ( > Order)", group = "Model Parameters:",
inline = "linepar2", type = input.integer, defval=50, minval = 2)
signalLength = input(title="Signal Length", group = "Model Parameters:",
inline = "linepar2", type=input.integer, defval=9,
tooltip="The signal line is a EMA of the D-RSI time series.")
islong = input(title = "Long", group = "Allowed Entries:",
inline = "lineent",type = input.bool, defval = true)
isshort = input(title = "Short", group = "Allowed Entries:",
inline = "lineent", type = input.bool, defval= true)
buycond = input(title="Buy", group = "Entry and Exit Conditions:",
inline = "linecond",type = input.string, defval="Signal Line Crossing",
options=["Zero-Crossing", "Signal Line Crossing","Direction Change"])
sellcond = input(title="Sell", group = "Entry and Exit Conditions:",
inline = "linecond",type = input.string, defval="Signal Line Crossing",
options=["Zero-Crossing", "Signal Line Crossing","Direction Change"])
endcond = input(title="Exit", group = "Entry and Exit Conditions:",
inline = "linecond",type = input.string, defval="Signal Line Crossing",
options=["Zero-Crossing", "Signal Line Crossing","Direction Change"])
filterlong =input(title = "Long Entries", inline = 'linefilt', group = 'Apply Filters to',
type = input.bool, defval = true)
filtershort =input(title = "Short Enties", inline = 'linefilt', group = 'Apply Filters to',
type = input.bool, defval = true)
filterend =input(title = "Exits", inline = 'linefilt', group = 'Apply Filters to',
type = input.bool, defval = true)
usevol =input(title = "", inline = 'linefiltvol', group = 'Relative Volume Filter:',
type = input.bool, defval = false)
rvol = input(title = "Volume >", inline = 'linefiltvol', group = 'Relative Volume Filter:',
type = input.integer, defval = 1)
len_vol = input(title = "Avg. Volume Over Period", inline = 'linefiltvol', group = 'Relative Volume Filter:',
type = input.integer, defval = 30, minval = 1,
tooltip="The current volume must be greater than N times the M-period average volume.")
useatr =input(title = "", inline = 'linefiltatr', group = 'Volatility Filter:',
type = input.bool, defval = false)
len_atr1 = input(title = "ATR", inline = 'linefiltatr', group = 'Volatility Filter:',
type = input.integer, defval = 5, minval = 1)
len_atr2 = input(title = "> ATR", inline = 'linefiltatr', group = 'Volatility Filter:',
type = input.integer, defval = 30, minval = 1,
tooltip="The N-period ATR must be greater than the M-period ATR.")
usersi =input(title = "", inline = 'linersi', group = 'Overbought/Oversold Filter:',
type = input.bool, defval = false)
rsitrhs1 = input(title = "", inline = 'linersi', group = 'Overbought/Oversold Filter:',
type = input.integer, defval = 0, minval=0, maxval=100)
rsitrhs2 = input(title = "< RSI (14) >", inline = 'linersi', group = 'Overbought/Oversold Filter:',
type = input.integer, defval = 100, minval=0, maxval=100,
tooltip="RSI(14) must be in the range between N and M.")
issl = input(title = "SL", inline = 'linesl1', group = 'Stop Loss / Take Profit:',
type = input.bool, defval = false)
slpercent = input(title = ", %", inline = 'linesl1', group = 'Stop Loss / Take Profit:',
type = input.float, defval = 10, minval=0.0)
istrailing = input(title = "Trailing", inline = 'linesl1', group = 'Stop Loss / Take Profit:',
type = input.bool, defval = false)
istp = input(title = "TP", inline = 'linetp1', group = 'Stop Loss / Take Profit:',
type = input.bool, defval = false)
tppercent = input(title = ", %", inline = 'linetp1', group = 'Stop Loss / Take Profit:',
type = input.float, defval = 20)
fixedstart =input(title="", group = "Fixed Backtest Period Start/End Dates:",
inline = "linebac1", type = input.bool, defval = true)
backtest_start=input(title = "", type = input.time, inline = "linebac1",
group = "Fixed Backtest Period Start/End Dates:",
defval = timestamp("01 Jan 2017 13:30 +0000"),
tooltip="If deactivated, backtest staring from the first available price bar.")
fixedend = input(title="", group = "Fixed Backtest Period Start/End Dates:",
inline = "linebac2", type = input.bool, defval = false)
backtest_end =input(title = "", type = input.time, inline = "linebac2",
group = "Fixed Backtest Period Start/End Dates:",
defval = timestamp("30 Dec 2080 23:30 +0000"),
tooltip="If deactivated, backtesting ends at the last available price bar.")
if window < degree
window := degree+1
src = rsi(close,rsi_l)
[drsi,nrmse] = diff(src,window,degree)
signalline = ema(drsi, signalLength)
// Conditions for D-RSI
dirchangeup = (drsi>drsi[1]) and (drsi[1]<drsi[2]) and drsi[1]<0.0
dirchangedw = (drsi<drsi[1]) and (drsi[1]>drsi[2]) and drsi[1]>0.0
crossup = crossover(drsi,0.0)
crossdw = crossunder(drsi,0.0)
crosssignalup = crossover(drsi,signalline)
crosssignaldw = crossunder(drsi,signalline)
// D-RSI signals
drsilong = (buycond=="Direction Change"?dirchangeup:(buycond=="Zero-Crossing"?crossup:crosssignalup))
drsishort= (sellcond=="Direction Change"?dirchangedw:(sellcond=="Zero-Crossing"?crossdw:crosssignaldw))
drisendlong = (endcond=="Direction Change"?dirchangedw:(endcond=="Zero-Crossing"?crossdw:crosssignaldw))
drisendshort= (endcond=="Direction Change"?dirchangeup:(endcond=="Zero-Crossing"?crossup:crosssignalup))
// Filters
rsifilter = usersi?(rsi(close,14) > rsitrhs1 and rsi(close,14) < rsitrhs2):true
volatilityfilter = useatr?(atr(len_atr1) > atr(len_atr2)):true
volumefilter = usevol?(volume > rvol*sma(volume,len_vol)):true
totalfilter = volatilityfilter and volumefilter and rsifilter
//Filtered signals
golong = drsilong and islong and (filterlong?totalfilter:true)
goshort = drsishort and isshort and (filtershort?totalfilter:true)
endlong = drisendlong and (filterend?totalfilter:true)
endshort = drisendlong and (filterend?totalfilter:true)
// Backtest period
//backtest_start = timestamp(syminfo.timezone, startYear, startMonth, startDate, 0, 0)
//backtest_end = timestamp(syminfo.timezone, endYear, endMonth, endDate, 0, 0)
isinrange = true
// Entry price / Take profit / Stop Loss
startprice = valuewhen(condition=golong or goshort, source=close, occurrence=0)
pm = golong?1:goshort?-1:1/sign(strategy.position_size)
takeprofit = startprice*(1+pm*tppercent*0.01)
// fixed stop loss
stoploss = startprice * (1-pm*slpercent*0.01)
// trailing stop loss
if istrailing and strategy.position_size>0
stoploss := max(close*(1 - slpercent*0.01),stoploss[1])
else if istrailing and strategy.position_size<0
stoploss := min(close*(1 + slpercent*0.01),stoploss[1])
tpline = plot(takeprofit,color=color.blue,transp=100, title="TP")
slline = plot(stoploss, color=color.red, transp=100, title="SL")
p1 = plot(close,transp=100,color=color.white, title="Dummy Close")
fill(p1, tpline, color=color.green, transp=istp?70:100, title="TP")
fill(p1, slline, color=color.red, transp=issl?70:100, title="SL")
// Backtest: Basic Entry and Exit Conditions
if golong and isinrange and islong
strategy.entry("long", true )
alert("D-RSI Long " + syminfo.tickerid, alert.freq_once_per_bar_close)
if goshort and isinrange and isshort
strategy.entry("short", false)
alert("D-RSI Short " + syminfo.tickerid, alert.freq_once_per_bar_close)
if endlong
strategy.close("long", alert_message="Close Long")
alert("D-RSI Exit Long " + syminfo.tickerid, alert.freq_once_per_bar_close)
if endshort
strategy.close("short", alert_message="Close Short")
alert("D-RSI Exit Short " + syminfo.tickerid, alert.freq_once_per_bar_close)
// Exit via SL or TP
strategy.exit(id="sl/tp long", from_entry="long", stop=issl?stoploss:na,
limit=istp?takeprofit:na, alert_message="Close Long")
strategy.exit(id="sl/tp short",from_entry="short",stop=issl?stoploss:na,
limit=istp?takeprofit:na, alert_message="Stop Loss Short")
// Close if outside the range
if (not isinrange)
strategy.close_all()
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