This was also evident in the shape of the auto-correlation
function (not shown here).
The distribution of soil [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (0-5 cm) was spatially dependent and showed a high degree of auto-correlation
(61-82%), suggesting distinct patterns or `patches' of higher [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] concentrations (Fig.
The results of numerical simulation show that the auto-correlation
curve has the same full width at half maximum (FWHM)  and lower peak-side lobe, compared to the auto-correlation
curve of one chaotic signal.
Further, the value of the DW statistics indicate that there is no problem of first-order auto-correlation
However, if we recognize that cash-flow growth rate changes are permanent (an extreme form of auto-correlation
, with no fade back to the average), then the Gordon prices should be calculated for each scenario separately and the two prices averaged to get a price that accounts for this auto-correlation
With T = 18 only, as in our data and systems allowing first order auto-correlation
of errors, allowing the income and price coefficients to change with time precludes precise estimation of these coefficients.
5 continuous lunar cycles were included (the minimum necessary for auto-correlation
analysis for an examination of lunar periodicity).
A model was developed after the effect of auto-correlation
had been removed by the ARIMA procedures, and we performed the GLS regression analysis to assess the independent effects of each weather variable (Box & Jenkins, 1976).
We tested for auto-correlation
in the error term, and where appropriate, we adjusted the estimates using a Cochrane-Orcutt transformation.
Equation 1 contains the cross-correlation between Tm and Tmdn in the nominator and the auto-correlation
of Tmdn in the denominator.
The cepstrum and the auto-correlation
are closely related.
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