Tóth et al. (2025) Stationarity and non-stationarity in long-term climate time series in Hungary

Identification

• Journal: Dimenziók matematikai közlemények
• Year: 2025
• Date: 2025-12-09
• Authors: Zsolt Tóth, Ernő Kulcsár, Adrienn Novotni
• DOI: 10.20312/dim.2025.04

Research Groups

• University of Sopron, Faculty of Wood Sciences and Creative Industries, Institute of Basic Sciences, Sopron, Hungary
• University of Sopron, Faculty of Wood Sciences and Creative Industries, József Cziráki Doctoral School, Sopron, Hungary

Short Summary

This study investigated the stationarity of 154 years of monthly precipitation and temperature data in four Hungarian cities, revealing regional differences in precipitation stationarity (stable in Szeged and Nyíregyháza, declining in Budapest and Sopron) but universal non-stationarity and upward trends in temperature across all locations.

Objective

• To investigate whether long-term monthly temperature and precipitation data from four Hungarian cities (Budapest, Nyíregyháza, Sopron, Szeged) between 1870 and 2023 exhibit stationarity.

Study Configuration

• Spatial Scale: Four major Hungarian cities: Budapest, Nyíregyháza, Sopron, and Szeged.
• Temporal Scale: 154 years (1870–2023), using monthly aggregated data derived from daily observations.

Methodology and Data

• Models used: Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, Autocorrelation Function (ACF), Augmented Dickey-Fuller (ADF) test, Breusch-Pagan test for heteroscedasticity, linear regression models, Bai–Perron multiple-break tests, Zivot–Andrews unit-root tests. Seasonal adjustment was performed using stl and seasadj functions in R.
• Data sources: Historical meteorological data from the Hungarian National Meteorological Service (OMSZ), consisting of original, verified, and homogenized data.

Main Results

• Precipitation:
  • Monthly precipitation data in Budapest and Sopron were found to be non-stationary at the level, showing a gradual decline (Budapest: -0.005 units of precipitation per month, p<0.001; Sopron: -0.004 units of precipitation per month, p=0.011).
  • Monthly precipitation data in Szeged and Nyíregyháza were found to be level stationary, remaining relatively stable, though with slight decreasing trends (Szeged: -0.002 units of precipitation per month, p=0.065; Nyíregyháza: -0.002 units of precipitation per month, p=0.090).
  • Trend stationarity was not rejected for precipitation in any city, suggesting the trend component is stationary.
  • A significant structural break was detected for Szeged precipitation (p=0.016), and segment-wise KPSS analysis revealed multi-phase but segment-stationary behavior for Szeged and a shift from earlier non-stationarity to later stationarity for Nyíregyháza.
• Temperature:
  • Monthly mean temperature series in all four cities were found to be non-stationary at both level and trend, exhibiting clear and statistically significant upward trends (all cities showed a positive slope of +0.001 units of temperature per month, p<0.001).
  • Significant heteroskedasticity was detected in temperature models for Szeged (p=0.044) and Nyíregyháza (p=0.014).
  • Highly significant structural breaks (p<0.001) were identified in all four temperature series, indicating multi-phase behavior consistent with long-term warming and regime shifts.
• General: Break-aware diagnostics (Bai–Perron, Zivot–Andrews) were crucial for robust inference, clarifying ambiguous full-sample KPSS outcomes and supporting a multi-phase interpretation of climate dynamics.

Contributions

• Provides a novel finding of stationarity in monthly precipitation patterns for Szeged and Nyíregyháza, contrasting with general trends of increasing variability and contributing to the limited literature on climate stationarity.
• Highlights significant regional differences in climate behavior within Hungary, particularly between eastern (Szeged, Nyíregyháza) and western (Budapest, Sopron) cities.
• Emphasizes the critical importance of employing break-aware approaches (e.g., Bai–Perron, Zivot–Andrews tests) for robust trend assessment and reliable conclusions in long-term climate time series analysis, especially for climate-sensitive applications.
• Offers a comprehensive long-term (154 years) analysis of temperature and precipitation for specific Hungarian cities, enriching the localized climate dynamics literature for the Carpathian region.

Funding

Not explicitly stated in the provided text.

Citation

@article{Tóth2025Stationarity,
  author = {Tóth, Zsolt and Kulcsár, Ernő and Novotni, Adrienn},
  title = {Stationarity and non-stationarity in long-term climate time series in Hungary},
  journal = {Dimenziók matematikai közlemények},
  year = {2025},
  doi = {10.20312/dim.2025.04},
  url = {https://doi.org/10.20312/dim.2025.04}
}