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

Hossein Hassani (), Masoud Yarmohammadi and Leila Marvian Mashhad
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Hossein Hassani: The Research Institute of Energy Management and Planning (RIEMP), University of Tehran, Tehran 19395-4697, Iran
Masoud Yarmohammadi: Department of Statistics, Payame Noor University, Tehran 19395-4697, Iran
Leila Marvian Mashhad: Department of Statistics, Payame Noor University, Tehran 19395-4697, Iran

Risks, 2023, vol. 11, issue 6, 1-15

Abstract: 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 − 1 2 theorem demonstrates that the sum of the sample ACF is always − 1 2 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.

Keywords: long-memory process; sum of sample autocorrelation function; Hassani’s ? 1 2 theorem; spectral density; time series; autocorrelation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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