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根据自相关与收益频谱设计趋势跟踪系统

文章 arXiv papers · 作者: Artur Sepp et al.
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总结

本文提出一个设计和比较趋势跟踪系统的框架，涵盖欧式、美式和时间序列动量方法。对于欧式系统，研究推导了损益、自相关与波动率标准化收益漂移之间的关系。使用分数阶 ARFIMA 过程的分析表明，即使短期收益呈均值回归，长期正自相关仍可能支持盈利。从频域角度看，只要低频谱能量足够强，趋势跟踪就可能受益；漂移也可能有助于延长回看周期。

研究推导了夏普比率表达式，纳入创新项峰度，并在交易成本下考察净表现和成本最优跨度。研究还预测，白噪声条件下聚合收益呈正偏度，模拟结果支持理论结论。对流动性较高合约的测试发现，这些系统之间高度相关，且该框架有助于绩效归因。这些发现取决于模型假设和所报告的实证情境；不能保证在其他市场或未建模成本下仍能盈利。

核心观点

  • 趋势跟踪表现与波动率标准化收益的自相关、漂移和频谱有关。
  • 即使存在短期均值回归，长期正自相关仍可能支持趋势跟踪。
  • 频域分析将低频谱能量与趋势跟踪收益联系起来。
  • 交易成本会影响净夏普比率和策略的最佳跨度。
  • 在若干建模条件下，分析发现趋势跟踪收益具有结构性正偏度。

标签

趋势跟踪动量统计学风险管理回测
全文
# The Science and Practice of Trend-Following Systems


# The Science and Practice of Trend-Following Systems









We present a unified approach to designing trend-following (TF) systems and classify them into European, American, and Time Series Momentum categories. For European TF systems, we derive an exact relationship between profit-and-loss, autocorrelation, and drift in volatility-normalized returns. We analyze the expected return under fractional ARFIMA processes and show that TF systems are profitable when the long-term autocorrelation is positive, even under short-term mean reversion. In the frequency domain, the expected return is represented as a Poisson-kernel reading of the analytical or empirical spectrum of the volatility-normalized returns: the system profits at zero drift when the kernel-weighted spectral mass exceeds one, so trend-following alpha is excess spectral mass at low frequencies. Longer lookbacks benefit in addition from the squared drift of the return process. We derive the closed-form Sharpe ratio, with the excess kurtosis of the innovations entering through a single loading, and the net Sharpe ratio and cost-optimal span under trading costs. Under white noise, we derive the closed-form skewness of aggregated TF returns, which is positive at every horizon and peaks near half the filter span. Monte Carlo experiments confirm the analytical results. We show that the positive skewness of TF returns is structural under various model assumptions. Empirically, we evaluate the systems on liquid contracts, and show that all TF systems are strongly correlated and our analytical results can be applied for their performance attribution. Our results enable design, simulation, and performance attribution of TF systems from trend persistence, mean reversion, drift, and skewness.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。