100.5 AI量化面试题：在使用LSTM预测股票价格时，如何有效处理金融时间序列的非平稳性？

- 0. 承前
- 1. 数据预处理
- - 1.1 平稳性检验
  - 1.2 数据转换
- 2. 特征工程
- - 2.1 技术指标构建
  - 2.2 时间特征提取
- 3. LSTM模型设计
- - 3.1 数据准备
  - 3.2 模型架构
- 4. 训练与验证
- - 4.1 时序交叉验证
  - 4.2 滚动预测
- 5. 回答话术

0. 承前

本文详细介绍使用LSTM处理金融时间序列时的关键技术点，包括数据预处理、特征工程、模型设计和验证方法。

如果想更加全面清晰地了解金融资产组合模型进化论的体系架构，可参考：
0. 金融资产组合模型进化全图鉴

1. 数据预处理

1.1 平稳性检验

import pandas as pd
import numpy as np
from statsmodels.tsa.stattools import adfullerdef check_stationarity(series):"""进行ADF检验判断时间序列的平稳性"""result = adfuller(series)print('ADF Statistic:', result[0])print('p-value:', result[1])print('Critical values:')for key, value in result[4].items():print('\t%s: %.3f' % (key, value))# 判断是否平稳is_stationary = result[1] < 0.05return is_stationary

1.2 数据转换

def transform_data(df):"""对数据进行转换以达到平稳性"""# 1. 对数转换df['log_price'] = np.log(df['close'])# 2. 差分df['returns'] = df['log_price'].diff()# 3. 标准化def standardize(series):return (series - series.mean()) / series.std()df['returns_standardized'] = df['returns'].rolling(window=20).apply(standardize)# 4. 百分比变化df['pct_change'] = df['close'].pct_change()return df

2. 特征工程

2.1 技术指标构建

def create_features(df):"""构建技术指标特征"""# 移动平均df['MA5'] = df['close'].rolling(window=5).mean()df['MA20'] = df['close'].rolling(window=20).mean()# 波动率df['volatility'] = df['returns'].rolling(window=20).std()# RSIdef calculate_rsi(data, periods=14):delta = data.diff()gain = (delta.where(delta > 0, 0)).rolling(window=periods).mean()loss = (-delta.where(delta < 0, 0)).rolling(window=periods).mean()rs = gain / lossreturn 100 - (100 / (1 + rs))df['RSI'] = calculate_rsi(df['close'])return df

2.2 时间特征提取

def add_time_features(df):"""添加时间相关特征"""df['dayofweek'] = df.index.dayofweekdf['quarter'] = df.index.quarterdf['month'] = df.index.monthdf['year'] = df.index.year# 季节性特征df['sin_day'] = np.sin(2 * np.pi * df.index.dayofyear/365.25)df['cos_day'] = np.cos(2 * np.pi * df.index.dayofyear/365.25)return df

3. LSTM模型设计

3.1 数据准备

def prepare_sequences(data, seq_length):"""准备LSTM输入序列"""X, y = [], []for i in range(len(data) - seq_length):X.append(data[i:(i + seq_length)])y.append(data[i + seq_length])return np.array(X), np.array(y)class TimeSeriesDataset(Dataset):def __init__(self, X, y):self.X = torch.FloatTensor(X)self.y = torch.FloatTensor(y)def __len__(self):return len(self.X)def __getitem__(self, idx):return self.X[idx], self.y[idx]

3.2 模型架构

import torch
import torch.nn as nnclass LSTMPredictor(nn.Module):def __init__(self, input_dim, hidden_dim, num_layers, dropout=0.2):super(LSTMPredictor, self).__init__()self.lstm = nn.LSTM(input_dim,hidden_dim,num_layers,batch_first=True,dropout=dropout)self.attention = nn.MultiheadAttention(hidden_dim, num_heads=4)self.fc = nn.Sequential(nn.Linear(hidden_dim, hidden_dim//2),nn.ReLU(),nn.Dropout(dropout),nn.Linear(hidden_dim//2, 1))def forward(self, x):lstm_out, _ = self.lstm(x)# 添加注意力机制attn_out, _ = self.attention(lstm_out.permute(1,0,2),lstm_out.permute(1,0,2),lstm_out.permute(1,0,2))out = self.fc(attn_out[-1])return out

4. 训练与验证

4.1 时序交叉验证

from sklearn.model_selection import TimeSeriesSplitdef time_series_cv(model, X, y, n_splits=5):tscv = TimeSeriesSplit(n_splits=n_splits)cv_scores = []for train_idx, val_idx in tscv.split(X):X_train, X_val = X[train_idx], X[val_idx]y_train, y_val = y[train_idx], y[val_idx]# 训练模型model.fit(X_train, y_train)# 评估score = model.evaluate(X_val, y_val)cv_scores.append(score)return np.mean(cv_scores), np.std(cv_scores)

4.2 滚动预测

def rolling_prediction(model, data, window_size, horizon):predictions = []for i in range(len(data) - window_size - horizon + 1):# 获取训练窗口数据train_data = data[i:i+window_size]# 训练模型model.fit(train_data)# 预测pred = model.predict(horizon)predictions.append(pred)return np.array(predictions)

5. 回答话术

在处理金融时间序列的非平稳性时，我们采用了一个系统化的方法论。首先，通过ADF检验等方法对时间序列进行平稳性检验。然后，使用对数转换、差分、标准化等方法将非平稳序列转换为平稳序列。在特征工程环节，我们构建了技术指标和时间特征来捕捉市场的多维度信息。模型设计上，我们使用了带有注意力机制的LSTM架构，能够更好地处理长期依赖关系。最后，通过时序交叉验证和滚动预测来评估模型性能，确保预测结果的可靠性。

关键技术要点：