On the Sample Autocorrelation Function’s Absolute Summability

Hassani, Hossein; Yeganegi, Mohammad Reza; Mehreyan, Sedigheh Zamani; Sayyareh, Abdolreza

doi:10.1142/s0219477522500043

Fluct. Noise Lett.

2021

DOI: 10.1142/s0219477522500043

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On the Sample Autocorrelation Function’s Absolute Summability

Hossein Hassani

Mohammad Reza Yeganegi

Sedigheh Zamani Mehreyan

et al.

Abstract: The sample ACF is the most common basic tool in analyzing time-series data. This paper provides a theoretical proof that, under some regularity conditions, sample ACF of a given stationary time series is not absolutely summable. Furthermore, it shows that under some mild conditions, the number of positive and negative sample ACFs and their absolute summation tend to infinity as the length of time series increases. The theoretical results are supported by practical evidence from a simulation study.

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Cited by 3 publications

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“…The property of S ACF being constant and equal to −1 2 for any stationary time series has important implications for time series analysis and modeling (see, for example, Silva 2015 andHassani et al 2021).…”

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confidence: 99%

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Hassani,

Yarmohammadi,

Mashhad

2023

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Long-memory models are frequently used in finance and other fields to capture long-range dependence in time series data. However, correctly identifying whether a process has long memory is crucial. This paper highlights a significant limitation in using the sample autocorrelation function (ACF) to identify long-memory processes. While the ACF establishes the theoretical definition of a long-memory process, it is not possible to determine long memory by summing the sample ACFs. Hassani’s −12 theorem demonstrates that the sum of the sample ACF is always −12 for any stationary time series with any length, rendering any diagnostic or analysis procedures that include this sum open to criticism. The paper presents several cases where discrepancies between the empirical and theoretical use of a long-memory process are evident, based on real and simulated time series. It is critical to be aware of this limitation when developing models and forecasting. Accurately identifying long-memory processes is essential in producing reliable predictions and avoiding incorrect model specification.

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mentioning

confidence: 99%

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Hassani,

Yarmohammadi,

Mashhad

2023

Risks

Self Cite

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Two New Estimators for the Autocorrelation Function Through Singular Spectrum Analysis

Mahmoudvand

2024

Fluct. Noise Lett.

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It is around a century that sample autocorrelation function has been introduced and used as a standard tool in time series analysis. A vast literature can be found on the statistical properties of the sample autocorrelation function. However, it has been highlighted recently that the sum of the sample autocorrelation function over the lags 1 to [Formula: see text] is −0.5 for all time series of length T. This property produces a big concern for the cases in which all available sample autocorrelations are used in the inference. This paper provides two new alternative for estimating the autocorrelation function. These estimators come from the idea of singular spectrum analysis which is a non-parametric technique for time series analysis. The paper utilizes a simulation study to illustrate the performance of the new approach. The results suggest that further improvement to the sample autocorrelation is possible and the new methods provide an attractive alternative to the classical approach.

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Unraveling Time Series Dynamics: Evaluating Partial Autocorrelation Function Distribution and Its Implications

Hassani,

Marvian,

Yarmohammadi

et al. 2024

MCA

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The objective of this paper is to assess the distribution of the Partial Autocorrelation Function (PACF), both theoretically and empirically, emphasizing its crucial role in modeling and forecasting time series data. Additionally, it evaluates the deviation of the sum of sample PACF from normality: identifying the lag at which departure occurs. Our investigation reveals that the sum of the sample PACF, and consequently its components, diverges from the expected normal distribution beyond a certain lag. This observation challenges conventional assumptions in time series modeling and forecasting, indicating a necessity for reassessment of existing methodologies. Through our analysis, we illustrate the practical implications of our findings using real-world scenarios, highlighting their significance in unraveling complex data patterns. This study delves into 185 years of monthly Bank of England Rate data, utilizing this extensive dataset to conduct an empirical analysis. Furthermore, our research paves the way for future exploration, offering insights into the complexities and potential revisions in time series analysis, modeling, and forecasting.

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On the Sample Autocorrelation Function’s Absolute Summability

Cited by 3 publications

References 19 publications

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Two New Estimators for the Autocorrelation Function Through Singular Spectrum Analysis

Unraveling Time Series Dynamics: Evaluating Partial Autocorrelation Function Distribution and Its Implications

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