?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=A+maximum+likelihood+based+technique+for+validating+detrended+fluctuation+analysis+(ML-DFA)&rft.creator=Botcharova%2C+M&rft.creator=Farmer%2C+SF&rft.creator=Berthouze%2C+L&rft.description=Detrended+Fluctuation+Analysis+(DFA)+is+widely+used+to+assess+the+presence+of+long-range+temporal+correlations+in+time+series.+Signals+with+long-range+temporal+correlations+are+typically+defined+as+having+a+power+law+decay+in+their+autocorrelation+function.+The+output+of+DFA+is+an+exponent%2C+which+is+the+slope+obtained+by+linear+regression+of+a+log-log+fluctuation+plot+against+window+size.+However%2C+if+this+fluctuation+plot+is+not+linear%2C+then+the+underlying+signal+is+not+self-similar%2C+and+the+exponent+has+no+meaning.+There+is+currently+no+method+for+assessing+the+linearity+of+a+DFA+fluctuation+plot.+Here+we+present+such+a+technique%2C+called+ML-DFA.+We+scale+the+DFA+fluctuation+plot+to+construct+a+likelihood+function+for+a+set+of+alternative+models+including+polynomial%2C+root%2C+exponential%2C+logarithmic+and+spline+functions.+We+use+this+likelihood+function+to+determine+the+maximum+likelihood+and+thus+to+calculate+values+of+the+Akaike+and+Bayesian+information+criteria%2C+which+identify+the+best+fit+model+when+the+number+of+parameters+involved+is+taken+into+account+and+over-fitting+is+penalised.+This+ensures+that%2C+of+the+models+that+fit+well%2C+the+least+complicated+is+selected+as+the+best+fit.+We+apply+ML-DFA+to+synthetic+data+from+FARIMA+processes+and+sine+curves+with+DFA+fluctuation+plots+whose+form+has+been+analytically+determined%2C+and+to+experimentally+collected+neurophysiological+data.+ML-DFA+assesses+whether+the+hypothesis+of+a+linear+fluctuation+plot+should+be+rejected%2C+and+thus+whether+the+exponent+can+be+considered+meaningful.+We+argue+that+ML-DFA+is+essential+to+obtaining+trustworthy+results+from+DFA.&rft.publisher=arXiv.org&rft.date=2013-06-21&rft.type=Working+%2F+discussion+paper&rft.language=eng&rft.source=++++arXiv.org%3A+Ithaca+(NY)%2C+USA.+(2013)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10081921%2F1%2F1306.5075v1.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10081921%2F&rft.rights=open