Machine Learning Methods in the Environmental Sciences
Neural Network and Kernels

Exercise 3.4

Analyze the data file (Ex3_4_spec) in Matlab format or text format using Fourier spectral analysis. (a) Compute the autospectrum for the time series x1 (with the time series t giving the time of the observation in days). (b) Compute the autospectrum for time series x2, and compare with that in (a).

Exercise 3.5

Using the same time series x1 and x2 from Exercise 3.4, perform singular spectrum analysis (SSA) on (a) x1 and (b) x2, with the time series lagged by an extra 50 days in SSA (so that there is a total of 51 time series). Briefly discuss the difference between the SSA result and the Fourier spectral result in Exercise 3.4 -- in particular, which method is more efficient in capturing the variance?

William W. Hsieh