Level Shifts and the Illusion of Long Memory in Economic Time Series

Level Shifts and the Illusion of Long Memory in Economic Time Series. Smith, A. Journal of Business and Economic Statistics, 23(3):321–335, Taylor & Francis, 2005.

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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.

@article{smith2005level,
  title={Level Shifts and the Illusion of Long Memory in Economic Time Series},
  author={Smith, Aaron},
  journal={Journal of Business and Economic Statistics},
  volume={23},
  number={3},
  pages={321--335},
  year={2005},
	URL={https://files.asmith.ucdavis.edu/2005_JBES_S_levelshifts.pdf},
	keywords={econometrics},
	abstract={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.},
  publisher={Taylor \& Francis}
}

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