# Univariate time series in geosciences : theory and examples by Hans Gilgen

By Hans Gilgen

This is a close advent to the statistical research of geophysical time sequence, utilizing quite a few examples and routines to construct skillability. The routines lead the reader to discover the which means of strategies corresponding to the estimation of the linear time sequence (AMRA) types or spectra. The publication additionally serves as a advisor to utilizing the open-source "R" software for statistical research of time series.

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15,4). However, the calculation of the distribution of Y is less straightforward. In the ﬁrst step, the distribution of Y = X1 + X2 is calculated. 18) as the product of the densities f1 (x1 ) and f2 (x2 ). 19). 21). If this integral can be transformed into f (y) = 1/(σY 2π) ea , a = (−1/2)((y − µY )/σY )2 , µY = µ1 + µ2 , σY2 = σ12 + σ22 , it implies that Y = X1 + X2 is normally distributed with expectation µY = µ1 + µ2 and variance σY2 = σ12 + σ22 . 22) with the substitutions µY = µ1 +µ2 and σY2 = σ12 +σ22 .

For instance, from the smi and eth time series plotted in Fig. 4, the time series diﬀerence difts is obtained with difts <- smi - eth plot(difts,type="l",xlab=" ",ylab="W/m2") and then plotted in Fig. 8 (above). 33),c(-15,75), lty=2) lty=2) lty=2) lty=2) two time slices are marked oﬀ with dashed vertical lines. The ﬁrst starts in the middle of April and lasts until the end of May 1989, the second is in April 1992. In the ﬁrst time slice, unusually small negative diﬀerences are obtained from the measurements; in the second, unusually large diﬀerences were observed, as shown in detail in Fig.

7. ETH pyranometer daily values at Zurich-Reckenholz station from January 1991 to November 1992 smoothed with a running mean covering 11 days. Two R time series with identical time domains can be added, subtracted, multiplied or divided. The result is a time series with the original time domain and values calculated from the original series by addition, etc. For instance, from the smi and eth time series plotted in Fig. 4, the time series diﬀerence difts is obtained with difts <- smi - eth plot(difts,type="l",xlab=" ",ylab="W/m2") and then plotted in Fig.