series 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).