Robust Structure Without Predictability: The “Compass Rose” Pattern of the Stock Market
发现将每日股票收益率与滞后一日收益率作图时，会出现从原点辐射的等距线条，形成“罗盘玫瑰”模式，该模式由离散性引起，但无法用于获利，且可能影响ARCH模型估计和混沌检验。
ABSTRACT Plotting daily stock returns against themselves with one day's lag reveals a striking pattern. Evenly spaced lines radiate from the origin; the thickest lines point in the major directions of the compass. This “compass rose” pattern appears in every stock. It is caused by discreteness. However, counter‐examples demonstrate that the existence of exchange‐imposed tick sizes (e.g. eighths) is neither necessary nor sufficient for the compass rose. The compass rose cannot be used to make abnormal profits: it is structure without predictability. Among other consequences, the compass rose may bias estimation of ARCH models, and tests for chaos.