The purpose in this section is to examine evidence of nonlinear
dynamics in themood time series. As a first test, the
data are examined for correlation structure: if a time series
has no serial correlation, then genuine forecasts cannot be
made from it. An empirical approach to this analysis is the
method of surrogate data (Lu 2004; Kantz and Schreiber
2004). To test for correlation structure, we permute the
original series several times to obtain a surrogate set withseries having the same amplitude but from a random process.
A test statistic is then applied to the original and the
surrogates and the results displayed graphically to see if
there is a difference. For the null hypothesis of white noise,
we use the autocorrelation at varying lags as a test statistic.
Next, we consider the null hypothesis of a linear
stochastic model with Gaussian inputs. If this cannot be
not rejected, then there is a question over the use of more
complex, nonlinear models for forecasting. For this analysis,
the surrogate data must be correlated random numbers
with the same power spectrum as the original data.
This is a property of data which has the same amplitude
as the original data but in different phases. Amplitudeadjusted
Fourier transform (AAFT) surrogates (Kantz and
Schreiber 2004) have a slightly different power spectrum
from the original series because the original untransformed
linear process has to be estimated. To make the
surrogates match the original spectrum more closely, we
use corrected AAFT (CAAFT) surrogates (Kugiumtzis
2000).
The purpose in this section is to examine evidence of nonlineardynamics in themood time series. As a first test, thedata are examined for correlation structure: if a time serieshas no serial correlation, then genuine forecasts cannot bemade from it. An empirical approach to this analysis is themethod of surrogate data (Lu 2004; Kantz and Schreiber2004). To test for correlation structure, we permute theoriginal series several times to obtain a surrogate set withseries having the same amplitude but from a random process.A test statistic is then applied to the original and thesurrogates and the results displayed graphically to see ifthere is a difference. For the null hypothesis of white noise,we use the autocorrelation at varying lags as a test statistic.Next, we consider the null hypothesis of a linearstochastic model with Gaussian inputs. If this cannot benot rejected, then there is a question over the use of morecomplex, nonlinear models for forecasting. For this analysis,the surrogate data must be correlated random numberswith the same power spectrum as the original data.This is a property of data which has the same amplitudeas the original data but in different phases. AmplitudeadjustedFourier transform (AAFT) surrogates (Kantz andSchreiber 2004) have a slightly different power spectrumfrom the original series because the original untransformedlinear process has to be estimated. To make thesurrogates match the original spectrum more closely, weuse corrected AAFT (CAAFT) surrogates (Kugiumtzis2000).
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