**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 *x*_{1}
(with the time series *t* giving the time of the observation in
days). (b) Compute the autospectrum for time series
*x*_{2}, and compare with that in (a).

## Exercise 3.5

Using the same time series *x*_{1} and *x*_{2}
from Exercise 3.4, perform singular spectrum analysis (SSA) on (a)
*x*_{1} and (b) *x*_{2}, 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