Statistics 519, Autumn Quarter 2008
Problem Set 2
Problem 5 (10 points). You will shortly receive an e-mail message with time series data
from a Pacific Northwest wind energy site. This time series consists of 10-minute averages
of wind speed observed in miles per hour at a height of 101 feet during the 36-day period
from August 3 to September 7, 2002. Hence, there are 36 ×24 ×6 = 5,184 observations in
this data set. The first observation corresponds to the time interval from 0:00 am to 0:10am
on August 3; the last observation to the interval from 11:50 pm to 12:00 pm on September
7. The wind speed series for the first seven days is plotted below.
Wind Speed Data: 3−9 August 2002
Julian Day
Wind Speed
215 216 217 218 219 220 221 222
0 10 20 30 40
(a) Plot the time series for the full 36-day period, using a suitable format.
(b) Apply a suitable variant of the classical decomposition algorithm for seasonal models
with trend. Estimate and plot the trend component, the diurnal component, and the
random component. Present the results graphically, and discuss.
(c) Compute and plot the sample autocovariance function of the estimated random com-
ponent.
(d) Repeat parts (a) through (c) for the time series of hourly average wind speed, and
compare to the results for 10-minute averages. There are 36 ×24 = 864 observations
of hourly average wind speed in this data set, starting with the time interval between
0:00am and 1:00am on August 3.
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