Asymptotic decorrelation of between-scale wavelet coefficients of generalized fractional process

Gonzaga, Alex; Kawanaka, Akira

doi:10.1016/j.dsp.2005.11.003

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…However, the following theorem shows that for sufficiently large L the covariance function, cov d Y jt , d Y j t , may be approximated by zero for j = j . It generalizes similar results for fractionally differenced process in Fan (2003) and in Craigmile and Percival (2005), and for generalized fractional process in Gonzaga and Kawanaka (2006). We use the fact that 0 ≤ H j,L ( f ) 2 ≤ 2 j for any f , and …”

Section: A Wavelet Whittle Estimatormentioning

confidence: 55%

A wavelet Whittle estimator of generalized long-memory stochastic volatility

Gonzaga

Hauser

2010

Stat Methods Appl

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Section: A Wavelet Whittle Estimatormentioning

confidence: 55%

A wavelet Whittle estimator of generalized long-memory stochastic volatility

Gonzaga

Hauser

2010

Stat Methods Appl

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“…As such, non-orthogonal WTs produce intra-scale autocorrelation, and the wider the scale the more autocorrelation. Inversely, orthogonal WTs optimally sample the time domain, so that the autocorrelation between adjacent intra-scale coefficients is approximately zero [70,72,73]. Therefore, in orthogonal WTs, wider scales produce fewer coefficients than narrower scales.…”

Section: Choice Of the Continuous Wavelet Transformmentioning

confidence: 99%

The Significance of Neural Inter-Frequency Correlations

Savolainen

2021

Preprint

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It is of great interest in neuroscience to determine what frequency bands in the brain contain common information. However, to date, a comprehensive statistical approach to this question has been lacking. As such, this work presents a novel statistical significance test for correlated power across frequency bands in non-stationary time series. The test accounts for biases that often go untreated in time-frequency analysis, i.e. intra-frequency autocorrelation, inter-frequency non-dyadicity, and multiple testing under dependency. It is used to test all of the inter-frequency correlations between 0.2 and 8500 Hz in continuous intracortical extracellular neural recordings, using a very large, publicly available dataset. The results show that neural processes have signatures across a very broad range of frequency bands. In particular, LFP frequency bands as low as 20 Hz were found to almost always be significantly correlated to kHz frequency ranges. This test also has applications in a broad range of fields, e.g. biological signal processing, economics, finance, climatology, etc. It is useful whenever one wants to robustly determine whether short-term components in a signal are robustly related to long-term trends, or what frequencies contain common information.

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“…As such, non-orthogonal WTs produce intra-scale autocorrelation, and the wider the scale the more autocorrelation. Inversely, orthogonal WTs optimally sample the time domain, so that the autocorrelation between adjacent intra-scale coefficients is approximately zero 48 , 71 , 72 . Therefore, in orthogonal WTs, wider scales produce fewer coefficients than narrower scales.…”

Section: Introductionmentioning

confidence: 99%

The significance of neural inter-frequency power correlations

Savolainen

2021

Sci Rep

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It is of great interest in neuroscience to determine what frequency bands in the brain have covarying power. This would help us robustly identify the frequency signatures of neural processes. However to date, to the best of the author’s knowledge, a comprehensive statistical approach to this question that accounts for intra-frequency autocorrelation, frequency-domain oversampling, and multiple testing under dependency has not been undertaken. As such, this work presents a novel statistical significance test for correlated power across frequency bands for a broad class of non-stationary time series. It is validated on synthetic data. It is then used to test all of the inter-frequency power correlations between 0.2 and 8500 Hz in continuous intracortical extracellular neural recordings in Macaque M1, using a very large, publicly available dataset. The recordings were Current Source Density referenced and were recorded with a Utah array. The results support previous results in the literature that show that neural processes in M1 have power signatures across a very broad range of frequency bands. In particular, the power in LFP frequency bands as low as 20 Hz was found to almost always be statistically significantly correlated to the power in kHz frequency ranges. It is proposed that this test can also be used to discover the superimposed frequency domain signatures of all the neural processes in a neural signal, allowing us to identify every interesting neural frequency band.

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Asymptotic decorrelation of between-scale wavelet coefficients of generalized fractional process

Cited by 6 publications

References 17 publications

A wavelet Whittle estimator of generalized long-memory stochastic volatility

A wavelet Whittle estimator of generalized long-memory stochastic volatility

The Significance of Neural Inter-Frequency Correlations

The significance of neural inter-frequency power correlations

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