量化择时系列研究之一：基于稀疏自编码器的指数择时模型

Quantitative Models and Construction Methods - Model Name: Sparse Auto Encoder (SAE) Model Construction Idea: The model aims to compress high-dimensional features into low-dimensional sparse coding while ensuring the reconstructed features retain most of the original information. It also incorporates autoregressive loss and sparsity penalties to enhance robustness and reduce overfitting [7][8][9] Model Construction Process: 1. Encoding: Compress input features into sparse coding $ \text{code}{i}=\text{Encoder}(x{i}) $ Here, $ x_{i} $ represents input features, and $ \text{code}{i} $ is the compressed sparse coding [8] 2. Decoding: Reconstruct features from sparse coding $ \hat{x}{i}=\text{Decoder}(code_{i}) $ $ \hat{x}{i} $ represents reconstructed features, which should closely resemble $ x{i} $ [8] 3. Prediction: Predict future index returns using hidden layer features $ \hat{y}{i}=\text{Predictor}(res{i}) $ $ \hat{y}{i} $ represents the predicted future returns [8] 4. Loss Function: Combines prediction error, reconstruction error, and sparsity penalty $Loss=\frac{1}{N}\sum\nolimits_{i=1}^{N}\left(\mathcal{J}(y_{i},{\hat{y}}_{i})+\lambda_{1}\mathcal{L}\left(x_{i},{\hat{x}}_{i}\right)+\lambda_{2}SparseLoss(code_{i})\right)$ $ \mathcal{J} $ measures prediction error, $ \mathcal{L} $ measures reconstruction error, and $ SparseLoss $ applies sparsity penalties using KL divergence or vector norms [9][12] Evaluation: The model effectively selects features, enhances robustness, and learns the "true" patterns of index movements [11] - Wavelet Transform for Noise Reduction Construction Idea: Decompose time-series data into multiple components to isolate noise and retain meaningful information [19][20] Construction Process: 1. Select parent wavelet $ \varphi $ and mother wavelet $ \psi $ $ \varphi{jk}=2^{-j/2}\varphi(2^{-j}-k) $ $ \psi_{jk}=2^{-j/2}\psi(2^{-j}-k) $ Parent wavelet captures low-frequency trends, while mother wavelet captures high-frequency fluctuations [19][20] 2. Reconstruct time-series data using wavelet coefficients $x(t)=\sum\nolimits_{k}s_{j,k}\varphi_{j,k}+\sum\nolimits_{k}d_{j,k}\psi_{j,k}+\ldots+\sum\nolimits_{k}d_{1,k}\psi_{1,k}$ Coefficients $ S_{J,k} $ and $ d_{j,k} $ are calculated as: $ S_{J,k}=\int\varphi_{J,k}x(s)ds $ $ d_{j,k}=\int\psi_{J,k}x(s)ds $ [20] Evaluation: Reduces overfitting risks by filtering out noise and retaining meaningful components [21] Model Backtesting Results - SAE Model Performance on CSI 500 Index: - Multi-strategy annualized return: 43.86% - Long-only annualized return: 23.30% - Short-only annualized return: 16.68% - Sharpe ratio: 2.07 (multi-strategy), 1.39 (long-only), 1.28 (short-only) - Maximum drawdown: -14.00% (multi-strategy), -16.04% (long-only), -14.30% (short-only) [29][33][34] Performance on CSI 1000 Index: - Multi-strategy annualized return: 51.21% - Long-only annualized return: 26.00% - Short-only annualized return: 20.01% - Sharpe ratio: 1.41 (long-only), 1.27 (short-only) - Maximum drawdown: -22.08% (long-only), -19.85% (short-only) [43][46][47] Performance on CSI 2000 Index: - Multi-strategy annualized return: 32.40% - Long-only annualized return: 32.56% - Sharpe ratio: 1.62 (long-only) - Maximum drawdown: -25.59% (long-only) [55][56] Performance on CSI All Share Index: - Multi-strategy annualized return: 18.74% - Long-only annualized return: 18.83% - Sharpe ratio: 1.26 (long-only) - Maximum drawdown: -16.95% (long-only) [55][56] Quantitative Factors and Construction Methods - Input Features Construction Idea: Use common technical indicators and derived metrics from daily K-line data as model inputs [16][18] Construction Process: 1. Technical Indicators: - RSI: $ RSI=(N\text{-day absolute closing price increase})/(N\text{-day absolute closing price decrease}) $ - OBV: $ OBV=\text{sum of closing price change signs} \times \text{turnover rate} $ - MACD: $ DIF=12\text{-day EMA}-26\text{-day EMA} $ $ DEA=DIF\text{'s 9-day EMA} $ $ MACD=DIF-DEA $ [16][17] 2. Derived Metrics: Rolling averages, relative positions of moving averages, volatility metrics, and other derived indicators [16][18] Evaluation: The feature set is comprehensive but not optimized, as no additional filtering was applied to avoid overfitting [18] Factor Backtesting Results - RSI, OBV, MACD Performance: Incorporated into the SAE model, contributing to the overall strategy performance across indices [16][18] Key Observations - The SAE model performs better on smaller-cap indices like CSI 2000 and CSI 1000 compared to CSI 500, indicating its effectiveness in smaller market segments [62] - Multi-strategy returns are balanced between long and short positions, with no significant bias toward either direction [42][54] - The model's robustness and sparsity design mitigate overfitting risks and enhance generalization across different market conditions [11][21] - Setting appropriate thresholds for signal generation improves strategy stability and reduces transaction costs [66]