.TH DFA 1  "31 July 2002" "DFA 4.2" "WFDB Applications Guide".SH NAMEdfa \- detrended fluctuation analysis.SH SYNOPSIS\fBdfa\fR  [ \fIoption\fR ... ].SH DESCRIPTION.PPThe method of detrended fluctuation analysis (DFA) has proven useful inrevealing the extent of long-range correlations in seemingly irregulartime series. .PPBriefly, the time series to be analyzed is first integrated.  Next,the integrated time series is divided into boxes of equal length,\fIn\fR. In each box of length \fIn\fR, a least squares line (orpolynomial curve of order \fIk\fR) is fit to the data (representingthe trend in that box).  Next, we detrend the integrated time seriesby subtracting the local trend in each box. The root-mean-squarefluctuation of this integrated and detrended time series is calculatedand denoted as \fIF(n)\fR..PPThis computation is repeated over all time scales (box sizes), from\fIn = minbox\fR to \fIn = maxbox\fR, to characterize the relationshipbetween \fIF(n)\fR, the average fluctuation, and \fIn\fR, the box size.Typically, \fIF(n)\fR will increase with box size \fIn\fR.  A linearrelationship on a log-log plot indicates the presence of power law(fractal) scaling.  Under such conditions, the fluctuations can becharacterized by a scaling exponent, i.e., the slope of the linerelating \fIlog[F(n)]\fR to \fIlog[n]\fR..PPThis program performs detrended fluctuation analysis on a sequence of dataread from the standard input (which should contain a single column of numbersin text format).  The standard output contains two columns of numbers, whichare the base 10 logarithms of \fIn\fR and \fIF(n)\fR.  Note that \fBdfa\fRdoes \fInot\fR compute a scaling exponent;  to do so, fit the output toa line and measure its slope..PP\fIOptions\fR may include:.TP\fB-d\fR \fIk\fRDetrend the data using a polynomial of degree \fIk\fR (1: linear, 2: quadratic,etc.).  Default: \fIk\fR = 1 (linear detrending)..TP\fB-h\fRPrint a usage summary and exit..TP\fB-i\fRDo not integrate the input series.  Use this option if the input series isalready integrated (for example, if it represents times of occurrence ratherthan intervals)..TP\fB-l\fR \fIminbox\fRSet the smallest box width.  The default, and the minimum allowed value for\fIminbox\fR, is \fI2k + 2\fR (where \fIk\fR is determined by the \fB-d\fRoption, see above)..TP\fB-s\fRPerform a sliding window DFA (measure the fluctuations using all possibleboxes at each box size).  By default, fluctuations are measured usingnon-overlapping boxes only.  Using the \fB-s\fR option will make thecalculation much slower..TP\fB-u\fR \fImaxbox\fRSet the largest box width.  The default, and the maximum allowed value for\fImaxbox\fR, is one-fourth the length of the input series..SH SEE ALSO.PPThe DFA method was first proposed in Peng C-K, Buldyrev SV,Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization ofDNA nucleotides. \fIPhys Rev E\fR 1994;\fB49\fR:1685-1689..PPA detailed description of the algorithm and its application tophysiologic signals can be found in Peng C-K, Havlin S, Stanley HE,Goldberger AL. Quantification of scaling exponents and crossoverphenomena in nonstationary heartbeat time series.\fIChaos\fR 1995;\fB5\fR:82-87..SH AVAILABILITY\fBdfa\fR is available as part of PhysioToolkit under the GPL (see\fBSOURCE\fR below)..SH AUTHORSJE Mietus (joe at physionet dot org), C-K Peng, and GB Moody, based on C-K Peng'soriginal Fortran implementation..SH SOURCEhttp://www.physionet.org/physiotools/dfa/dfa.c