**Problem 1.**
Given a zero mean stationary time series, X(1),...,X(N),
show that the sample periodogram I(w) and the sample autocovariance
c(h) constitute a Fourier pair.

**Problem 2.**
Apply the CM algorithm to estimate the frequencies in the following data
set made of several sinusoids plus additive WN. To download the data click on
the link: SineData.

**Problem 3.**
Let X(t), t=1,2,..., be a stationary time series with mean 0 and
autocovariance R(k). Define: Xu(t)=X(t)X(t+u)-R(u), and consider
the sum of two linear filters L1 and L2 plus WN:

**Problem 4.**
Using the monthly unemployment data Unemp.Women,
make a comparison between Box-Jenkins, Kriging, and BTG prediction,
and summarize your findings. The actual data are in the 4th column,
where every "13th" observation is the average of the previous 12
observations.

**Problem 5.**
Consider the time series x and y,
one of which is WN and the other is WN plus a weak sinusoid. Can
you tell which one is the WN series ?

**Problem 6.**
a.
Explain the effect on the spectrum of the filter
L(B) = (1+aB+B^2)/(1+a*eta*B + eta^2*B^2)
where B is the backward shift,
a = -2cos(theta), and eta in (0,1).

b. Suggest an application for this filter, and demonstrate it
using simulated data.

If you are looking for real time series data, some good sources are:

- http://lib.stat.cmu.edu/
- http://www.economagic.com/
- http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/
- http://www.epic.noaa.gov/tao/select/timeselect.html
- http://www.stls.frb.org/fred/
- http://www.skio.peachnet.edu/tseries.html
- http://ublib.buffalo.edu/libraries/units/lml/ Government_Doc/gov_publications/econhist.html