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Sum of squared ACF and the Ljung–Box statistics

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  • Hassani, Hossein
  • Yeganegi, Mohammad Reza

Abstract

The Ljung–Box test is one of the most important tests for time series diagnostics and model selection. The Hassani’s −12 Theorem, however, indicates that the sum of sample autocorrelation function is always −12 for any stationary time series with arbitrary length. In this paper, Hassani’s −12 Theorem is used to assess the sensitivity of the Ljung–Box test results to the number of lags. Bitcoin price return data is also used to examine the applicability of the theoretical results obtained here. The results confirm sensitivity of the Ljung–Box test to the number of lags involved in the test and therefore it should be used with extra caution.

Suggested Citation

  • Hassani, Hossein & Yeganegi, Mohammad Reza, 2019. "Sum of squared ACF and the Ljung–Box statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 81-86.
    • Handle: RePEc:eee:phsmap:v:520:y:2019:i:c:p:81-86
    DOI: 10.1016/j.physa.2018.12.028
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    References listed on IDEAS

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    1. Hassani, Hossein, 2010. "A note on the sum of the sample autocorrelation function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1601-1606.
    2. Hassani, Hossein & Leonenko, Nikolai & Patterson, Kerry, 2012. "The sample autocorrelation function and the detection of long-memory processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6367-6379.
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    Cited by:

    1. Hassani, Hossein & Yeganegi, Mohammad Reza, 2020. "Selecting optimal lag order in Ljung–Box test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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    4. Hassani, Hossein & Leonenko, Nikolai & Patterson, Kerry, 2012. "The sample autocorrelation function and the detection of long-memory processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6367-6379.

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