다단계 통계 회귀 거래 전략

/*backtest
start: 2024-07-31 00:00:00
end: 2025-07-29 08:00:00
period: 1d
basePeriod: 1d
exchanges: [{"eid":"Futures_Binance","currency":"ETH_USDT"}]
*/

//@version=5
strategy("Multi-Layer Statistical Regression Strategy - Optimized", overlay=true)

// === MULTI-LAYER REGRESSION INPUTS ===
// Linear Regression Layers
lr_short_length = input.int(20, "Short-Term LR Length", minval=10, maxval=50, step=2)
lr_medium_length = input.int(50, "Medium-Term LR Length", minval=30, maxval=100, step=5)
lr_long_length = input.int(100, "Long-Term LR Length", minval=50, maxval=200, step=10)

// === 优化后的统计验证参数 (降低严格程度) ===
min_r_squared = input.float(0.45, "Min R-Squared Threshold", minval=0.2, maxval=0.8, step=0.05)
slope_threshold = input.float(0.00005, "Min Slope Significance", minval=0.00001, maxval=0.001, step=0.00001)
correlation_min = input.float(0.5, "Min Correlation", minval=0.3, maxval=0.8, step=0.05)

// Lookback/Look-Forward Analysis
validation_lookback = input.int(30, "Validation Lookback", minval=10, maxval=60, step=5)
prediction_horizon = input.int(10, "Prediction Horizon", minval=5, maxval=20, step=1)

// Ensemble Weights
weight_short = input.float(0.4, "Short-Term Weight", minval=0.1, maxval=0.6, step=0.1)
weight_medium = input.float(0.35, "Medium-Term Weight", minval=0.1, maxval=0.6, step=0.05)
weight_long = input.float(0.25, "Long-Term Weight", minval=0.1, maxval=0.6, step=0.05)

// === 优化后的风险管理参数 ===
position_size_pct = input.float(50.0, "Position Size %", minval=10.0, maxval=100.0, step=5.0)
max_daily_loss = input.float(12.0, "Max Daily Loss %", minval=5.0, maxval=25.0, step=2.5)
confidence_threshold = input.float(0.55, "Signal Confidence Threshold", minval=0.4, maxval=0.8, step=0.05)

// === 新增：信号强度分级 ===
use_graded_signals = input.bool(true, "Use Graded Signal Strength")
strong_signal_threshold = input.float(0.7, "Strong Signal Threshold", minval=0.6, maxval=0.9, step=0.05)

// === STATISTICAL FUNCTIONS ===
// Calculate Linear Regression with full statistics
linear_regression_stats(src, length) =>
    var float sum_x = 0
    var float sum_y = 0
    var float sum_xy = 0
    var float sum_x2 = 0
    var float sum_y2 = 0
    
    // Reset sums
    sum_x := 0
    sum_y := 0
    sum_xy := 0
    sum_x2 := 0
    sum_y2 := 0
    
    // Calculate sums for regression
    for i = 0 to length - 1
        x = i + 1
        y = src[i]
        if not na(y)
            sum_x := sum_x + x
            sum_y := sum_y + y
            sum_xy := sum_xy + x * y
            sum_x2 := sum_x2 + x * x
            sum_y2 := sum_y2 + y * y
    
    n = length
    
    // Calculate regression coefficients
    denominator = n * sum_x2 - sum_x * sum_x
    slope = denominator != 0 ? (n * sum_xy - sum_x * sum_y) / denominator : 0
    intercept = (sum_y - slope * sum_x) / n
    
    // Calculate correlation coefficient (R)
    correlation = (n * sum_xy - sum_x * sum_y) / 
                  math.sqrt((n * sum_x2 - sum_x * sum_x) * (n * sum_y2 - sum_y * sum_y))
    
    // Calculate R-squared
    r_squared = correlation * correlation
    
    // Current regression value
    current_lr = intercept + slope * n
    
    // Projected value (look-forward)
    projected_lr = intercept + slope * (n + prediction_horizon)
    
    [current_lr, slope, r_squared, correlation, projected_lr]

// === 优化后的统计显著性测试 (更灵活) ===
is_statistically_significant(r_squared, correlation, slope_abs, grade = "normal") =>
    if grade == "relaxed"
        r_squared >= (min_r_squared * 0.8) and math.abs(correlation) >= (correlation_min * 0.8) and math.abs(slope_abs) >= (slope_threshold * 0.5)
    else if grade == "strict"
        r_squared >= (min_r_squared * 1.2) and math.abs(correlation) >= (correlation_min * 1.1) and math.abs(slope_abs) >= (slope_threshold * 1.5)
    else
        r_squared >= min_r_squared and math.abs(correlation) >= correlation_min and math.abs(slope_abs) >= slope_threshold

// === MULTI-LAYER REGRESSION ANALYSIS ===
// Short-term layer
[lr_short, slope_short, r2_short, corr_short, proj_short] = linear_regression_stats(close, lr_short_length)
sig_short = is_statistically_significant(r2_short, corr_short, slope_short, "normal")
sig_short_strong = is_statistically_significant(r2_short, corr_short, slope_short, "strict")

// Medium-term layer  
[lr_medium, slope_medium, r2_medium, corr_medium, proj_medium] = linear_regression_stats(close, lr_medium_length)
sig_medium = is_statistically_significant(r2_medium, corr_medium, slope_medium, "relaxed")
sig_medium_strong = is_statistically_significant(r2_medium, corr_medium, slope_medium, "normal")

// Long-term layer
[lr_long, slope_long, r2_long, corr_long, proj_long] = linear_regression_stats(close, lr_long_length)
sig_long = is_statistically_significant(r2_long, corr_long, slope_long, "relaxed")

// === LOOKBACK VALIDATION ===
validate_prediction_accuracy() =>
    var array<float> accuracy_scores = array.new<float>()
    
    if bar_index >= validation_lookback
        historical_slope = (close - close[prediction_horizon]) / prediction_horizon
        predicted_slope = slope_short[prediction_horizon]
        
        error = math.abs(historical_slope - predicted_slope)
        accuracy = math.max(0, 1 - error * 10000)
        
        array.push(accuracy_scores, accuracy)
        if array.size(accuracy_scores) > validation_lookback
            array.shift(accuracy_scores)
    
    array.size(accuracy_scores) > 5 ? array.avg(accuracy_scores) : 0.5

validation_accuracy = validate_prediction_accuracy()

// === 优化后的集成信号生成 ===
// Individual layer signals (directional)
signal_short = sig_short ? (slope_short > 0 ? 1 : -1) : 0
signal_medium = sig_medium ? (slope_medium > 0 ? 1 : -1) : 0  
signal_long = sig_long ? (slope_long > 0 ? 1 : -1) : 0

// Weighted ensemble score
ensemble_score = (signal_short * weight_short + 
                  signal_medium * weight_medium + 
                  signal_long * weight_long)

// === 多级信号置信度计算 ===
// 基础一致性评分
agreement_score = math.abs(signal_short + signal_medium + signal_long) / 3.0

// 统计置信度 (使用加权平均)
stat_confidence = (r2_short * weight_short + 
                   r2_medium * weight_medium + 
                   r2_long * weight_long)

// 验证置信度
validation_confidence = validation_accuracy

// 整体置信度 (调整权重比例)
overall_confidence = (agreement_score * 0.3 + 
                     stat_confidence * 0.5 + 
                     validation_confidence * 0.2)

// 信号强度分级
signal_strength = math.abs(ensemble_score)
is_strong_signal = overall_confidence > strong_signal_threshold and (sig_short_strong or sig_medium_strong)

// === POSITION MANAGEMENT ===
trend_direction = ensemble_score > 0 ? 1 : ensemble_score < 0 ? -1 : 0

// 基于信号强度的仓位调整
confidence_multiplier = if use_graded_signals
    if is_strong_signal
        1.0 + (overall_confidence - strong_signal_threshold) * 0.5
    else
        0.7 + (overall_confidence / strong_signal_threshold) * 0.3
else
    overall_confidence > confidence_threshold ? 1.0 : overall_confidence / confidence_threshold

base_position_value = strategy.equity * (position_size_pct / 100)
adjusted_position_value = base_position_value * confidence_multiplier
position_units = adjusted_position_value / close

// Daily loss tracking
var float daily_start_equity = strategy.equity 
if ta.change(time("1D"))
    daily_start_equity := strategy.equity

current_daily_loss = daily_start_equity > 0 ? (daily_start_equity - strategy.equity) / daily_start_equity * 100 : 0
halt_trading = current_daily_loss > max_daily_loss

// === 优化后的入场/退出逻辑 ===
// 更灵活的入场条件
long_condition_basic = ensemble_score > 0.2 and overall_confidence > confidence_threshold and sig_short
long_condition_strong = ensemble_score > 0.4 and overall_confidence > strong_signal_threshold and sig_short and sig_medium

short_condition_basic = ensemble_score < -0.2 and overall_confidence > confidence_threshold and sig_short  
short_condition_strong = ensemble_score < -0.4 and overall_confidence > strong_signal_threshold and sig_short and sig_medium

// 入场信号生成
long_signal = use_graded_signals ? (long_condition_strong or long_condition_basic) : long_condition_strong
short_signal = use_graded_signals ? (short_condition_strong or short_condition_basic) : short_condition_strong

// 策略执行
if long_signal and not halt_trading and strategy.position_size <= 0
    signal_type = long_condition_strong ? "Strong Long" : "Basic Long"
    strategy.entry("Long", strategy.long, qty=position_units, 
                   comment=signal_type + ": " + str.tostring(overall_confidence, "#.##"))

if short_signal and not halt_trading and strategy.position_size >= 0
    signal_type = short_condition_strong ? "Strong Short" : "Basic Short"
    strategy.entry("Short", strategy.short, qty=position_units,
                   comment=signal_type + ": " + str.tostring(overall_confidence, "#.##"))

// 降低初始化门槛
if strategy.position_size == 0 and not halt_trading and barstate.isconfirmed
    if ensemble_score > 0.15 and overall_confidence > (confidence_threshold * 0.8)
        strategy.entry("InitLong", strategy.long, qty=position_units * 0.8, comment="Init Long")
    else if ensemble_score < -0.15 and overall_confidence > (confidence_threshold * 0.8)
        strategy.entry("InitShort", strategy.short, qty=position_units * 0.8, comment="Init Short")

// Emergency exit
if halt_trading and strategy.position_size != 0
    strategy.close_all(comment="Daily Loss Limit")

// === 增强的可视化 ===
// Plot regression lines with transparency based on significance
plot(lr_short, "Short-Term LR", color=sig_short_strong ? color.blue : color.new(color.blue, 50), linewidth=2)
plot(lr_medium, "Medium-Term LR", color=sig_medium_strong ? color.orange : color.new(color.orange, 50), linewidth=2)
plot(lr_long, "Long-Term LR", color=color.new(color.purple, 30), linewidth=1)

// Background with graded confidence
bg_color = if overall_confidence > strong_signal_threshold
    ensemble_score > 0 ? color.new(color.green, 85) : color.new(color.red, 85)
else if overall_confidence > confidence_threshold
    ensemble_score > 0 ? color.new(color.green, 92) : color.new(color.red, 92)
else
    color.new(color.gray, 97)

bgcolor(bg_color)

// Enhanced signal markers
plotshape(long_condition_strong, "Strong Long", shape.triangleup, location.belowbar, 
          color=color.green, size=size.large)
plotshape(long_condition_basic and not long_condition_strong, "Basic Long", shape.triangleup, location.belowbar, 
          color=color.new(color.green, 40), size=size.small)

plotshape(short_condition_strong, "Strong Short", shape.triangledown, location.abovebar, 
          color=color.red, size=size.large)
plotshape(short_condition_basic and not short_condition_strong, "Basic Short", shape.triangledown, location.abovebar, 
          color=color.new(color.red, 40), size=size.small)