Level Shifts and the Illusion of Long Memory in Economic Time Series
证明对数周期图（GPH）估计量在遇到偶尔的水平位移时，会错误地发现长记忆，并推导了偏差的近似公式，提出修正的GPH估计量以降低偏差，并通过大豆价格和股市波动数据验证。
When applied to time series processes containing occasional level shifts, the log-periodogram (GPH) estimator often erroneously finds long memory. For a stationary short-memory process with a slowly varying level, I show that the GPH estimator is substantially biased, and derive an approximation to this bias. The asymptotic bias lies on the (0, 1) interval, and its exact value depends on the ratio of the expected number of level shifts to a user-defined bandwidth parameter. Using this result, I formulate the modified GPH estimator, which has a markedly lower bias. I illustrate this new estimator via applications to soybean prices and stock market volatility.