### 完整且可运行的 Python 代码示例 以下是一个完整的 Python 示例，用于计算 MACD 并检测背离。此代码实现了 MACD 的计算、枢轴点检测以及正常规和隐藏背离的检测。 ```python # 导入必要的库 import numpy as np # 计算 EMA def calculate_ema(prices, window): alpha = 2 / (window + 1) ema = [prices[0]] # 初始化第一个值为价格的第一个值 for price in prices[1:]: next_ema = alpha * price + (1 - alpha) * ema[-1] ema.append(next_ema) return ema # 计算 MACD def calculate_macd(prices, fast_window=12, slow_window=26, signal_window=9): fast_ema = calculate_ema(prices, fast_window) slow_ema = calculate_ema(prices, slow_window) macd_line = [f - s for f, s in zip(fast_ema, slow_ema)] signal_line = calculate_ema(macd_line, signal_window) macd_histogram = [m - s for m, s in zip(macd_line, signal_line)] return macd_line, signal_line, macd_histogram # 枢轴点检测 def find_pivots(data, lookback=5): pivots_high = [] pivots_low = [] for i in range(lookback, len(data) - lookback): if data[i] > max(data[i - lookback:i]) and data[i] > max(data[i + 1:i + lookback + 1]): pivots_high.append((i, data[i])) elif data[i] < min(data[i - lookback:i]) and data[i] < min(data[i + 1:i + lookback + 1]): pivots_low.append((i, data[i])) return pivots_high, pivots_low # 背离检测 def detect_divergence(price_pivots, macd_pivots, is_high=True): divergence_points = [] for (price_idx, price_val), (macd_idx, macd_val) in zip(price_pivots, macd_pivots): if is_high: # 正常规背离 if price_val > price_pivots[0][1] and macd_val <= macd_pivots[0][1]: divergence_points.append((price_idx, price_val, macd_val)) else: # 隐藏背离 if price_val < price_pivots[0][1] and macd_val >= macd_pivots[0][1]: divergence_points.append((price_idx, price_val, macd_val)) return divergence_points # 示例数据 prices = [100, 102, 101, 103, 104, 102, 105, 106, 107, 108, 105, 103, 104] # 计算 MACD macd_line, signal_line, macd_histogram = calculate_macd(prices) # 枢轴点检测 price_pivots_high, price_pivots_low = find_pivots(prices) macd_pivots_high, macd_pivots_low = find_pivots(macd_histogram) # 正常态背离检测 regular_divergence_high = detect_divergence(price_pivots_high, macd_pivots_high, is_high=True) regular_divergence_low = detect_divergence(price_pivots_low, macd_pivots_low, is_high=False) # 隐藏背离检测 hidden_divergence_high = detect_divergence(price_pivots_high, macd_pivots_high, is_high=False) hidden_divergence_low = detect_divergence(price_pivots_low, macd_pivots_low, is_high=True) # 输出结果 print("Regular Divergence High:", regular_divergence_high) print("Regular Divergence Low:", regular_divergence_low) print("Hidden Divergence High:", hidden_divergence_high) print("Hidden Divergence Low:", hidden_divergence_low) ``` #### 代码说明 - **EMA 计算**：通过递归公式实现指数移动平均（EMA）[^1]。 - **MACD 计算**：基于 EMA 计算 MACD 线、信号线和柱状图。 - **枢轴点检测**：通过比较当前点与前后若干点的关系，检测局部高点和低点。 - **背离检测**：结合价格和 MACD 的枢轴点，检测正常规和隐藏背离。