A slowly decaying autocorrelation function indicates a non-stationary time series
A slowly decaying autocorrelation function is a well-established indicator of long memory and non-stationarity in time series analysis, often modeled using fractionally integrated or integrated processes.
The retrieved papers include foundational discussions on non-stationary time series, memory parameters, and autocorrelation behaviors (such as slow declines or long memory associated with non-stationarity like unit roots or fractional integration). No papers contradict the premise that slow autocorrelation decay is tied to non-stationarity.
Clifford M. Hurvich, Bonnie K. Ray. ESTIMATION OF THE MEMORY PARAMETER FOR NONSTATIONARY OR NONINVERTIBLE FRACTIONALLY INTEGRATED PROCESSES. 1995. https://doi.org/10.1111/j.1467-9892.1995.tb00221.x
Paper [0] discusses fractionally integrated processes where memory parameters correspond to non-stationary behavior and long-range persistence characterized by slow decay.
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O. D. Anderson. PARTIAL AUTOCORRELATION PROPERTIES FOR NON‐STATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODELS. 1992. https://doi.org/10.1111/j.1467-9892.1992.tb00122.x
Paper [5] examines partial autocorrelation properties in non-stationary autoregressive moving-average models, noting behaviors like slow linear declines from unity.
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