Page 109 - MATLAB Recipes for Earth Sciences

102 5 Time-Series Analysis

amplitudes in the interpolated time series, which typically occur as neigh-
boring extreme minima and maxima. Since all these and other interpolation
techniques might introduce some artifacts to the data, it is always advisable
to (1) preserve the number of data points before and after interpolation, (2)
report the method employed for estimating the equally-spaced data sequence
and (3) explore the impact of interpolation on the variance of the data.
After this brief introduction to interpolation techniques, we apply the
most popular linear and cubic-spline interpolation techniques to unevenly-
spaced data. Having interpolated the data, we use the spectral tools that have
already been applied to evenly-spaced data (Chapters 5.3 and 5.4). Firstly,
we load the two time series:
series1 = load('series1.txt');
series2 = load('series2.txt');
Both synthetic data sets contain a two-column matrix with 339 rows. The
first column contains ages in kiloyears that are not evenly spaced. The second

column contains oxygen-isotope values measured on foraminifera. The data
sets contain 100, 40 and 20 kyr cyclicities and they are overlain by gaussian
noise. In the 100 kyr frequency band, the second data series is shifted by
5 kyrs with respect to the first data series. To plot the data we type

plot(series1(:,1),series1(:,2))
figure
plot(series2(:,1),series2(:,2))

The statistics of the spacing of the first data series can be computed by
intv1 = diff(series1(:,1));
plot(intv1)

The plot shows that the spacing varies around a mean interval of 3 kyrs with
a standard deviation of ca. 1 kyrs. The minimum and maximum value of the
time axis

min(series1(:,1))
max(series1(:,1))

of t =0 and t =997 kyrs gives some information of the temporal range of the
1 2
data. The second data series
intv2 = diff(series2(:,1));

plot(intv2)