Machine Learning Methods in the Environmental Sciences

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
2009