Struct DFAnalysis 

pub struct DFAnalysis {
    pub alpha: f64,
    pub intercept: f64,
    pub r_squared: f64,
    pub log_n: Vec<f64>,
    pub log_f: Vec<f64>,
}

A struct representing Detrended Fluctuation Analysis (DFA) results.

DFA is a method used to find long-term statistical dependencies in time series data.

Fields

• alpha - The scaling exponent, which indicates the presence of long-range correlations.
• intercept - The intercept of the linear fit in the log-log plot.
• r_squared - The coefficient of determination, which indicates the goodness of fit.
• log_n - A vector containing the logarithm of the box sizes used in the analysis.
• log_f - A vector containing the logarithm of the fluctuation function values corresponding to the box sizes.

Fields

alpha: f64

intercept: f64

r_squared: f64

log_n: Vec<f64>

log_f: Vec<f64>

Implementations

impl DFAnalysis

pub fn dfa( data: &[f64], windows: &[usize], detrender: DetrendStrategy, ) -> Result<Self>

Performs Detrended Fluctuation Analysis (DFA) on the provided data.

This method computes the scaling exponent (Hurst exponent) and other statistical properties of a time series using the DFA algorithm. DFA is used to detect long-range correlations in time series data.

Arguments

• data: A slice of f64 representing the input time series data.
• windows: A slice of usize specifying the window sizes to use for the fluctuation analysis.
• detrender: A DetrendStrategy implementation used to remove trends from each segment.

Returns

If successful, this method returns a DFAnalysis instance containing:

• alpha: The estimated scaling exponent.
• intercept: The intercept of the log-log regression.
• r_squared: The coefficient of determination for the log-log fit.
• log_n: A vector of log-transformed window sizes.
• log_f: A vector of log-transformed fluctuation amplitudes.

Errors

This method returns an error if:

• windows is empty.
• The length of the input data is less than four times the largest window size.
• The smallest window size is less than 4.
• The detrender fails to detrend a segment.

Algorithm Overview

1. Integration:

   • The input data is transformed into a cumulative deviation profile (mean-centered).

2. Segment Detrending:

   • The profile is divided into overlapping segments, and each segment is detrended using the provided DetrendStrategy.

3. Variance Calculation:

   • Variances of the detrended segments are computed.

4. Log-Log Regression:

   • The log-transformed window sizes (log_n) and fluctuations (log_f) are used to perform a linear regression, yielding the scaling exponent alpha.

pub fn udfa( data: &[f64], windows: &[usize], detrender: DetrendStrategy, ) -> Result<Self>

Performs an unbiased Detrended Fluctuation Analysis (DFA) on the provided data. this algorithm uses overlapping windows.

This method computes the scaling exponent (Hurst exponent) and other statistical properties of a time series using the DFA algorithm. DFA is used to detect long-range correlations in time series data.

Arguments

• data: A slice of f64 representing the input time series data.
• windows: A slice of usize specifying the window sizes to use for the fluctuation analysis.
• detrender: A DetrendStrategy implementation used to remove trends from each segment.

Returns

If successful, this method returns a DFAnalysis instance containing:

• alpha: The estimated scaling exponent.
• intercept: The intercept of the log-log regression.
• r_squared: The coefficient of determination for the log-log fit.
• log_n: A vector of log-transformed window sizes.
• log_f: A vector of log-transformed fluctuation amplitudes.

Errors

This method returns an error if:

• windows is empty.
• The length of the input data is less than four times the largest window size.
• The smallest window size is less than 4.
• The detrender fails to detrend a segment.

Algorithm Overview

1. Integration:

   • The input data is transformed into a cumulative deviation profile (mean-centered).

2. Segment Detrending:

   • The profile is divided into overlapping segments, and each segment is detrended using the provided DetrendStrategy.

3. Variance Calculation:

   • Variances of the detrended segments are computed.

4. Log-Log Regression:

   • The log-transformed window sizes (log_n) and fluctuations (log_f) are used to perform a linear regression, yielding the scaling exponent alpha.

Trait Implementations

impl Clone for DFAnalysis

fn clone(&self) -> DFAnalysis

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for DFAnalysis

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.