Power spectrum and detrended fluctuation analysis: application to daily temperatures

Area of Science:

• * Physics
• * Time Series Analysis
• * Climate Science

Background:

• * Fluctuation analysis (FA) and detrended fluctuation analysis (DFA) are statistical methods used to quantify variability in time series data.
• * These methods are often expressed in terms of power spectral density and autocovariance, crucial for understanding underlying processes.
• * Previous research has explored their diagnostic potential, particularly in analyzing geophysical data like temperature records.

Purpose of the Study:

• * To evaluate the diagnostic capabilities of FA and DFA on model power spectral densities.
• * To apply FA and DFA to 20th-century ambient temperature data.
• * To resolve the debate regarding the low-frequency behavior of temperature data's power spectral density, specifically distinguishing between power law, stretched exponential, and Weibull distribution models.

Main Methods:

• * Analysis of power spectral density and autocovariance functions.
• * Application of fluctuation analysis (FA) and detrended fluctuation analysis (DFA) to synthetic and real-world time series data.
• * Comparison of model fits (power law, stretched exponential, Weibull distribution) to empirical data.

Main Results:

• * Both FA and DFA identify algebraic singularities in power spectral density at low frequencies, correlating with autocovariance decay.
• * Detrended fluctuation analysis (DFA) demonstrates a superior ability to capture scaling behavior in intermediate frequency regimes compared to FA.
• * Neither FA nor DFA could reliably differentiate between power law, stretched exponential, or Weibull distribution models when applied to 20th-century ambient temperature data.

Conclusions:

• * FA and DFA are valuable for characterizing spectral properties and identifying singularities in time series.
• * DFA offers enhanced sensitivity for detecting scaling behaviors in power spectral densities.
• * Despite their utility, FA and DFA have limitations in definitively distinguishing between complex low-frequency spectral models for ambient temperature data.