This exercise is intended to help students to understand how to calculate basic statistical characteristics of a time series.
The file odp659data.txt contains marine oxygen isotope data from foraminifera sampled from a deep-see sediment core. Such isotope data reflect changes in global ice volume, in the case of planktonic foraminifere, also local sea surface temperature and salinity of the sea water on time scales of thousands of years. All three parameters show significant trends in the measures of central tendency and dispersion. The first column of the data represent age (in kyrs), the second column represent the oxygen isotope value, i.e., the ratio of the oxygen isotopes O18 and O16 converted to a percentage difference from the ratio found in a carbonate standard.
(1) Univariate statistics – Define two change points of the time series corresponding to the Intensification of the Northern Hemisphere Glaciation and the Mid Pleistocene Transtion. Compute the means and variance of the three sections separated by these change points. Show that the means and variances of the three sections are significantly different.
(2) Bivariate statistics – Compute the trends of the means and variances of the three time series. How significant are these trends?
Please use the publishing feature of MATLAB to publish the results of your experiment as a PDF file with all graphs included.
Solution
Here is a possible solution of the exercise. You need to rename to file exercise_2_solution.m before using it with MATLAB. Please send me your comments, improvements, corrections!