Articles | Volume 12, issue 1
https://doi.org/10.5194/ascmo-12-73-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/ascmo-12-73-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Comparing climate time series – Part 6: Testing equality of autoregressive parameters without assuming equality of noise variances
Department of Atmospheric, Oceanic, and Earth Sciences, George Mason University, Fairfax, Virginia, USA
Michael K. Tippett
Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York, USA
Related authors
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 10, 1–27, https://doi.org/10.5194/ascmo-10-1-2024, https://doi.org/10.5194/ascmo-10-1-2024, 2024
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This paper introduces a method to assess whether two data sets come from the same source. Current methods do not adequately consider spatial and temporal correlations and their annual cycles in a comprehensive test. This method addresses that gap, thereby providing a new and rigorous tool for evaluating the realism of climate simulations and measuring changes in variability over time.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 187–203, https://doi.org/10.5194/ascmo-8-187-2022, https://doi.org/10.5194/ascmo-8-187-2022, 2022
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Most climate time series contain annual and diurnal cycles. However, an objective criterion for deciding whether two time series have statistically equivalent annual and diurnal cycles is lacking, particularly if the residual variability is serially correlated. Such a criterion would be helpful in deciding whether a new version of a climate model better simulates such cycles. This paper derives an objective rule for such decisions based on a rigorous statistical framework.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 97–115, https://doi.org/10.5194/ascmo-8-97-2022, https://doi.org/10.5194/ascmo-8-97-2022, 2022
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A common problem in climate studies is to decide whether a climate model is realistic. Such decisions are not straightforward because the time series are serially correlated and multivariate. Part II derived a test for deciding wether a simulation is statistically distinguishable from observations. However, the test itself provides no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between stochastic processes.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 7, 73–85, https://doi.org/10.5194/ascmo-7-73-2021, https://doi.org/10.5194/ascmo-7-73-2021, 2021
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After a new climate model is constructed, a natural question is whether it generates realistic simulations. Here,
realisticdoes not mean that the detailed patterns on a particular day are correct, but rather that the statistics over many years are realistic. Past approaches to answering this question often neglect correlations in space and time. This paper proposes a method for answering this question that accounts for correlations in space and time.
Kelsey Malloy and Michael K. Tippett
Nat. Hazards Earth Syst. Sci., 26, 433–448, https://doi.org/10.5194/nhess-26-433-2026, https://doi.org/10.5194/nhess-26-433-2026, 2026
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Tornado outbreaks—many tornadoes in short succession—have major impacts, but it is hard to accurately assess their risk because they are rare. We used weather model data to create hundreds of thousands of realistic but unseen tornado outbreak scenarios. With this event set, we estimated U.S. and local outbreak risk and detected clear links to La Niña and upward outbreak activity in recent years.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 10, 1–27, https://doi.org/10.5194/ascmo-10-1-2024, https://doi.org/10.5194/ascmo-10-1-2024, 2024
Short summary
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This paper introduces a method to assess whether two data sets come from the same source. Current methods do not adequately consider spatial and temporal correlations and their annual cycles in a comprehensive test. This method addresses that gap, thereby providing a new and rigorous tool for evaluating the realism of climate simulations and measuring changes in variability over time.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 187–203, https://doi.org/10.5194/ascmo-8-187-2022, https://doi.org/10.5194/ascmo-8-187-2022, 2022
Short summary
Short summary
Most climate time series contain annual and diurnal cycles. However, an objective criterion for deciding whether two time series have statistically equivalent annual and diurnal cycles is lacking, particularly if the residual variability is serially correlated. Such a criterion would be helpful in deciding whether a new version of a climate model better simulates such cycles. This paper derives an objective rule for such decisions based on a rigorous statistical framework.
Michael K. Tippett, Chiara Lepore, and Michelle L. L’Heureux
Weather Clim. Dynam., 3, 1063–1075, https://doi.org/10.5194/wcd-3-1063-2022, https://doi.org/10.5194/wcd-3-1063-2022, 2022
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The El Niño–Southern Oscillation (ENSO) and Arctic Oscillation (AO) are phenomena that affect the weather and climate of North America. Although ENSO hails from from the tropical Pacific and the AO high above the North Pole, the spatial patterns of their influence on a North American tornado environment index are remarkably similar in computer models. We find that when ENSO and the AO act in concert, their impact is large, and when they oppose each other, their impact is small.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 97–115, https://doi.org/10.5194/ascmo-8-97-2022, https://doi.org/10.5194/ascmo-8-97-2022, 2022
Short summary
Short summary
A common problem in climate studies is to decide whether a climate model is realistic. Such decisions are not straightforward because the time series are serially correlated and multivariate. Part II derived a test for deciding wether a simulation is statistically distinguishable from observations. However, the test itself provides no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between stochastic processes.
Timothy DelSole and Michael K. Tippett
Adv. Stat. Clim. Meteorol. Oceanogr., 7, 73–85, https://doi.org/10.5194/ascmo-7-73-2021, https://doi.org/10.5194/ascmo-7-73-2021, 2021
Short summary
Short summary
After a new climate model is constructed, a natural question is whether it generates realistic simulations. Here,
realisticdoes not mean that the detailed patterns on a particular day are correct, but rather that the statistics over many years are realistic. Past approaches to answering this question often neglect correlations in space and time. This paper proposes a method for answering this question that accounts for correlations in space and time.
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We derived a new statistical test that can compare climate models and observations more broadly than before, while allowing for both natural fluctuations and human influences. Tests on global temperature data show that most climate models differ from observations in important ways.
We derived a new statistical test that can compare climate models and observations more broadly...