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<p>Predicting meteorological and hydrological variables, such as drought, is vital for managing their adverse impacts on various sectors. Since hydrological data often exhibit periodicity, selecting appropriate periodic time-series methods for prediction is preferable to stationary techniques. This study investigates the comparative performance of Periodic Autoregressive Fractionally Integrated Moving Average (PARFIMA) and Periodically Correlated (PC) models in predicting the periodic Standardized Precipitation Evapotranspiration Index (SPEI) on monthly and seasonally time scales. For this purpose, meteorological data from 12 stations in Iran, spanning diverse climatic conditions, were used over 50 years (1970–2019). The results indicated that the Periodic Autoregressive (PAR (20)) was the optimal PC model across all stations and all time scales. Conversely, PARFIMA models with varying parameters (monthly: <i>p</i> = 2–5, d = 0–0.455, q = 0–2; seasonal: <i>p</i> = 0–5, d = 0–0.339, q = 0–5) provided the best fit among fractionally integrated models. Performance assessment using <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({R}^{2}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left|\text{T}-\text{S}\text{t}\text{a}\text{t}\text{i}\text{s}\text{t}\text{i}\text{c}\text{s}\right|\)</EquationSource> </InlineEquation> (TS) indices between observed and simulated SPEI (1970–2014) demonstrated the superior predictive capability of PARFIMA models. This superiority was further confirmed during the validation period (2015–2019) across selected stations. The findings suggest that PARFIMA models, by accounting for long-memory fluctuations in periodic data, offer higher accuracy than standard PC models for drought prediction.</p>

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Assessing the Performance of the Periodic Autoregressive Fractionally Integrated Moving Average and Periodically Correlated Models to Predict Periodic Drought

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Abdol Rassoul Zarei,
  • Mohammad Reza Mahmoudi

摘要

Predicting meteorological and hydrological variables, such as drought, is vital for managing their adverse impacts on various sectors. Since hydrological data often exhibit periodicity, selecting appropriate periodic time-series methods for prediction is preferable to stationary techniques. This study investigates the comparative performance of Periodic Autoregressive Fractionally Integrated Moving Average (PARFIMA) and Periodically Correlated (PC) models in predicting the periodic Standardized Precipitation Evapotranspiration Index (SPEI) on monthly and seasonally time scales. For this purpose, meteorological data from 12 stations in Iran, spanning diverse climatic conditions, were used over 50 years (1970–2019). The results indicated that the Periodic Autoregressive (PAR (20)) was the optimal PC model across all stations and all time scales. Conversely, PARFIMA models with varying parameters (monthly: p = 2–5, d = 0–0.455, q = 0–2; seasonal: p = 0–5, d = 0–0.339, q = 0–5) provided the best fit among fractionally integrated models. Performance assessment using \({R}^{2}\) and \(\left|\text{T}-\text{S}\text{t}\text{a}\text{t}\text{i}\text{s}\text{t}\text{i}\text{c}\text{s}\right|\) (TS) indices between observed and simulated SPEI (1970–2014) demonstrated the superior predictive capability of PARFIMA models. This superiority was further confirmed during the validation period (2015–2019) across selected stations. The findings suggest that PARFIMA models, by accounting for long-memory fluctuations in periodic data, offer higher accuracy than standard PC models for drought prediction.