@InProceedings{8902339,
  author = {B. Berthelot and É. Grivel and P. Legrand and J. -M. André and P. Mazoyer and T. Ferreira},
  booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},
  title = {Filtering-based Analysis Comparing the DFA with the CDFA for Wide Sense Stationary Processes},
  year = {2019},
  pages = {1-5},
  abstract = {The detrended fluctuation analysis (DFA) is widely used to estimate the Hurst exponent. Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. It also confirms that they can be seen as ad hocwavelet based techniques.},
  keywords = {covariance analysis;filtering theory;time series;wavelet transforms;CDFA;wide sense stationary processes;detrended fluctuation analysis;Hurst exponent;wavelet based approaches;strong expertise;signal processing;theoretical analysis;fluctuation function;normalized covariance function;wide-sense-stationary processes;correlation function;ad hocwavelet based techniques;continuous-DFA;Market research;Correlation;Signal processing;Estimation;Europe;Time series analysis;Fourier transforms;filter;interpretation;Hurst;DFA;CDFA.},
  doi = {10.23919/EUSIPCO.2019.8902339},
  issn = {2076-1465},
  month = {Sep.},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570533530.pdf},
}

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Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. It also confirms that they can be seen as ad hocwavelet based techniques.","keywords":"covariance analysis;filtering theory;time series;wavelet transforms;CDFA;wide sense stationary processes;detrended fluctuation analysis;Hurst exponent;wavelet based approaches;strong expertise;signal processing;theoretical analysis;fluctuation function;normalized covariance function;wide-sense-stationary processes;correlation function;ad hocwavelet based techniques;continuous-DFA;Market research;Correlation;Signal processing;Estimation;Europe;Time series analysis;Fourier transforms;filter;interpretation;Hurst;DFA;CDFA.","doi":"10.23919/EUSIPCO.2019.8902339","issn":"2076-1465","month":"Sep.","url":"https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570533530.pdf","bibtex":"@InProceedings{8902339,\n author = {B. Berthelot and É. Grivel and P. Legrand and J. -M. André and P. Mazoyer and T. Ferreira},\n booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},\n title = {Filtering-based Analysis Comparing the DFA with the CDFA for Wide Sense Stationary Processes},\n year = {2019},\n pages = {1-5},\n abstract = {The detrended fluctuation analysis (DFA) is widely used to estimate the Hurst exponent. Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. 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