Quadratic Fitting Trading Signals Strategy

This strategy fits a quadratic curve to high/low points of bars to generate trading signals when price breaks through the fitted lines. It attempts to identify key support/resistance levels mathematically for…

Pine ScriptArbitrage Machine learning Pairs & stat-arb SMA Volume Pivots / S&R

Author: ChaoZhang
Complexity: Intermediate · 114 lines
Parameters: 11
Backtest bar: 1h · intraday
Tested on: BTC/USDT · futures

Jump to code View in vault Original on FMZ

Overview

Strategy Logic

The key components and rules are:

Curve fitting on high/low points using quadratic regression.
Buy signal when close breaks above upper band.
Sell signal when close breaks below lower band.
N periods verification to avoid false breaks.
No fixed exit rules, optimize exits via backtesting.

The strategy tries to identify key prices mathematically and trade the breakouts, a typical breakout system.

Advantages

Compared to other breakout systems, the main advantages are:

Mathematical fitting is more objective than subjective judgment.
Novel approach combining technical analysis and statistical models.
Multi-period verification avoids false breaks.
Backtesting can optimize exits and holding period.
Easy to implement with flexible adjustments.
Model updates automatically without manual intervention.
Can test parameter robustness across products and timeframes.
Potential to optimize further with machine learning.
Overall novel approach with exploratory value.

Risks

However, the risks are:

Fitting performance depends on parameter tuning, overfitting risk.
Fitted lines lag, cannot completely avoid losses.
No volume confirmation, risk of being trapped.
Statistical arbitrage is challenging for persistent alpha.
Limited backtest period, need to verify robustness.
Multi-market adaptability requires validation.
Fixed size lacks dynamic adjustment.
Need strict evaluation of reward/risk ratios.

Enhancements

Based on the analysis, enhancements may involve:

Test parameter robustness across market regimes.
Add volume confirmation indicators.
Optimize entry/exit logic for higher quality signals.
Build dynamic position sizing models.
Incorporate stops to limit losses.
Optimize risk management strategies.
Rolling window backtest validation.
Evaluate multi-market stability.
Leverage machine learning for model optimization.

Conclusion

In summary, this strategy has some innovative value and experimentation merit. But the long-term viability of statistical arbitrage remains unproven. Comprehensive in-sample testing on robustness, risk/reward is key to prevent overfitting and maintain adaptability.

Parameters

Name	Default	What it controls
v_input_1	true	═══════════════ From ═══════════════
v_input_2	true	Month
v_input_3	true	Day
v_input_4	2019	Year
v_input_5	true	════════════════ To ════════════════
v_input_6	31	Month
v_input_7	12	Day
v_input_8	9999	Year
v_input_9	true	══════════════ Config ══════════════
v_input_10	6	p
v_input_11	30	length

Source Pine Script

/*backtest
start: 2023-08-23 00:00:00
end: 2023-09-22 00:00:00
period: 1h
basePeriod: 15m
exchanges: [{"eid":"Futures_Binance","currency":"BTC_USDT"}]
*/

//@version=4
//
// ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ //

strategy(title = " Strategy Quadratic Semaphore ",
         shorttitle = "SQS",
         overlay = true,
         precision = 8,
         calc_on_order_fills = true,
         calc_on_every_tick = true,
         backtest_fill_limits_assumption = 0,
         default_qty_type = strategy.fixed,
         default_qty_value = 2,
         initial_capital = 10000,
         pyramiding=5,
         currency = currency.USD,
         linktoseries = true)

//
// ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ //

backTestSectionFrom = input(title = "═══════════════ From ═══════════════", defval = true, type = input.bool)

FromMonth         = input(defval = 1, title = "Month", minval = 1)
FromDay           = input(defval = 1, title = "Day", minval = 1)
FromYear          = input(defval = 2019, title = "Year", minval = 2014)

backTestSectionTo = input(title = "════════════════ To ════════════════", defval = true, type = input.bool)
ToMonth           = input(defval = 31, title = "Month", minval = 1)
ToDay             = input(defval = 12, title = "Day", minval = 1)
ToYear            = input(defval = 9999, title = "Year", minval = 2014)

Config            = input(title = "══════════════ Config ══════════════", defval = true, type = input.bool)
p = input(6)
length = input(30)
//
backTestPeriod() => (time > timestamp(FromYear, FromMonth, FromDay, 00, 00)) and (time < timestamp(ToYear, ToMonth, ToDay, 23, 59))
//
//
// ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ //

x1 = bar_index
x2 = sqrt(x1)
y = high
//
S11 = sum(x2,length) - sqrt(sum(x1,length)) / length  
S12 = sum(x1*x2,length) - (sum(x1,length) * sum(x2,length)) / length  
S22 = sum(sqrt(x2),length) - sqrt(sum(x2,length)) / length            
Sy1 = sum (y*x1,length) - (sum(y,length) * sum(x1,length)) / length   
Sy2 = sum (y*x2,length) - (sum(y,length) * sum(x2,length)) / length   
//
max1 = sma(x1,length) 
max2 = sma(x2,length)
may = sma(y,length)
b2 = ((Sy1 * S22) - (Sy2*S12))/(S22*S11 - sqrt(S12))
b3 = ((Sy2 * S11) - (Sy1 * S12))/(S22 * S11 - sqrt(S12))
b1 = may - b2*max1 - b3*max2
qr = b1 + b2*x1 + b3*x2
//
yl = low
//
Sy1l = sum(yl*x1,length) - (sum(yl,length) * sum(x1,length)) / length  
Sy2l = sum(yl*x2,length) - (sum(yl,length) * sum(x2,length)) / length  
//
mayl = sma(yl,length)
b2l = ((Sy1l * S22) - (Sy2l*S12))/(S22*S11 - sqrt(S12))
b3l = ((Sy2l * S11) - (Sy1l * S12))/(S22 * S11 - sqrt(S12))
b1l = mayl - b2l*max1 - b3l*max2
qrl = b1l + b2l*x1 + b3l*x2
//
period = round(p/2)+1
hh = qr[period]
ll = qrl[period]
countH = 0
countL = 0
buy=0
sell=0
//
for i = 1 to period-1
    if qr[i]<hh
        countH:=countH+1
    if qrl[i]>ll
        countL:=countL+1

for i = period+1 to p+1
    if qr[i]<hh
        countH:=countH+1
    if qrl[i]>ll
        countL:=countL+1

if countH==p
    pivotH = high[period]
    buy := 1
    
if countL==p
    pivotL = low[period]
    sell := 1
//    
plotshape(buy == 1 , text='?', style=shape.arrowup, location=location.belowbar, color=#32CD32, textcolor=color.white, offset=0, transp=0,size=size.auto)
plotshape(sell == 1 , text='?', style=shape.arrowdown, location=location.abovebar, color=#FF0000, textcolor=color.white, offset=0, transp=0,size=size.auto)
//

if (backTestPeriod())
    strategy.entry("long", true, 1, when = buy == 1)
    strategy.entry("short", false, 1, when = sell == 1)

Published by ChaoZhang on the FMZ strategy square · last modified 2023-09-23. Collected in the Quant Trading Vault. Unvalidated research: re-test with your own data and costs before trusting it.

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